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اساسيات الهندسه الكهربائيه باللغة العربية by MostafaOkasha

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									                      ‫א‬‫א‬‫א‬
                   ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                       ‫א‬‫א‬‫א‬‫א‬





 ١ J

        ١٤٠
     ‫א‬                                 ١٤٠                                      ‫א‬
                                        ١-                          



                W،،‫א‬‫א‬،‫א‬
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‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  ‫א‬ ‫א‬  ،‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                 
                                                              K‫א‬‫א‬‫א‬
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‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  ‫א‬        ،‫א‬ ‫א‬‫א‬  
‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬    ،  
‫א‬،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
     ‫א‬  ‫א‬   ،‫א‬   
                                     K‫א‬‫א‬،‫א‬‫א‬
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  ?  ? ١J   ? ‫א‬ ‫א‬  
   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬?
                                                                                                     
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬،‫א‬‫א‬‫א‬‫א‬
                           K‫א‬‫א‬‫א‬‫א‬‫א‬
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،‫א‬‫א‬‫א‬‫א‬
                                                                                               K‫א‬
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‫א‬‫א‬‫א‬‫א‬                                            
                                              ١٤٠                                             ‫א‬
                                              ١-                                



              ،KKK،‫א‬‫א‬‫א‬‫א‬
 
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                      K‫א‬‫א‬‫א‬
            
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                               
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
                               
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
   
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                               
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ‫א‬‫א‬
                                                                           K‫א‬
                    
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
                               K‫א‬‫א‬،‫א‬،‫א‬‫א‬
                                                                  
،‫א‬‫א‬‫א‬‫א‬،
                                                                                             
‫א‬،‫א‬‫א‬‫א‬‫א‬
                                                                                          K‫א‬‫א‬
                                           KKKKKK،‫א‬
                                                                                                         
                                                          ‫א‬‫א‬‫א‬
                                                     ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                                           ‫א‬‫א‬‫א‬‫א‬




                                        
                                   ١ J 
                               ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬




١
‫א‬‫א‬           ‫٠٤١ א‬                                       ‫א‬
  ‫א‬‫א‬           ١-                         ‫א‬‫א‬



               ‫א‬‫א‬‫א‬‫א‬
                                                                                 
                   W‫א‬‫א‬،‫א‬‫א‬‫א‬
                                              K‫א‬‫א‬‫א‬ •
                                       K‫א‬‫א‬‫א‬ •




                              -١-
       ‫א‬‫א‬                                    ‫٠٤١ א‬                                ‫א‬
   ‫א‬‫א‬‫א‬                   ١-                        



                                                                           ١J ١
             
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                               K‫א‬‫א‬‫א‬
                                   The International System of Units‫א‬‫א‬‫א‬ ٢J ١
                                           
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                         KK‫א‬
                                              The Measurement Units‫א‬‫א‬                   ١J ٢J ١
                                                               
،‫א‬‫א‬  ‫א‬‫א‬‫א‬          
                                                                                W‫א‬‫א‬
                                                  
              Symbol‫א‬          Unit‫א‬                       Quantity‫א‬
                   m                    Meter                          Length‫א‬
                   kg             Kilogram‫א‬                         Mass‫א‬
                   A                 Ampere                           Current‫א‬
                    s                 Second                           Time‫א‬
                   K                 Kelvin                       Temperature‫א‬‫א‬
                   cd                 Candle                   Luminous Intensity‫א‬

                           The Measurement Units‫א‬‫א‬E١-١F
                                                                                                        
K‫א‬‫א‬‫א‬ Luminous Intensity‫א‬Temperature‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬NForce‫א‬‫א‬،‫א‬‫א‬
                                                                            kg
Watt‫א‬Electric Power‫א‬‫א‬K             ‫א‬
                                                                            s2


                                                        -٢-
       ‫א‬‫א‬                                       ‫٠٤١ א‬                                 ‫א‬
   ‫א‬‫א‬‫א‬                        ١-                       


                                                          Nm
Electric Energy‫א‬‫א‬K           W
                                                           s
                                                K Nm  JJoule‫א‬
                                                   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬             ٢J ٢J ١
                  which attached to the measurement units، prefixes،Power of ten units
power ‫א‬The International System of Units‫א‬‫א‬‫א‬‫א‬
                      
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬of ten
                                                                                          W‫א‬‫א‬
                                 ‫א‬           ‫א‬         ‫א‬
                                Power of ten      Symbol         Prefixes to the Units
                                 1 * 10−18         a                Atto
                                 1 * 10−15         f                   Femto
                                 1 * 10−12        p                    Pico
                                 1 * 10−9         n                     Nano
                                 1 * 10−6         µ                Micro
                                 1 * 10−3         m                     Milli
                                 1 * 10−2         c                    Centi
                                 1 * 10 −1        d                    Deci
                                  1 *101          da                   Deka
                                  1 *102          h                Hecto
                                  1 *103          k                    Kilo
                                  1 *106          M                    Mega
                                  1 *109          G                    Giga
                                 1 *1012          T                     Tera‫א‬

                          ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢J ١F

                                      The Basic Electrical Quantities‫א‬‫א‬‫א‬ ٣J ١
‫א‬،Voltage‫א‬،Current‫א‬،Charge‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬KElectrical Resistance‫א‬‫א‬

                                                           -٣-
        ‫א‬‫א‬                                  ‫٠٤١ א‬                                      ‫א‬
    ‫א‬‫א‬‫א‬                     ١-                         



‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
،EJ ‫א‬FElectrons‫א‬‫א‬‫א‬KAtoms
                        KE‫א‬FNeutrons‫א‬،EH‫א‬FProtons‫א‬
                                                                                Charge‫א‬         ١J ٣J ١
‫א‬Electron‫א‬‫א‬،Q
،‫א‬K‫א‬‫א‬‫א‬‫א‬،Proton
                                                                 
K‫א‬
‫א‬‫א‬‫א‬،
                                                     
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                                 KC‫א‬Coulomb‫א‬
                                                                                 Current‫א‬       ٢J ٣J ١
،I‫א‬‫א‬‫א‬‫א‬‫א‬
                                                              
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 WKCurrent‫א‬‫א‬E‫א‬F‫א‬
                     dQ
               I=                                                                                        E١J ١F
                     dt
                                  W‫א‬،Ampere‫א‬
                      C
               A≡                                                                                        E٢J ١F
                      s
                                                                        KA‫א‬IW
                                                               KCCharge‫א‬WQ
                                                                           Kstime‫א‬Wt
          
‫א‬،‫א‬
                   K‫א‬‫א‬،‫א‬Electrons




                                                       -٤-
        ‫א‬‫א‬                                                   ‫٠٤١ א‬                             ‫א‬
    ‫א‬‫א‬‫א‬                                   ١-                    



                                                                                                                
                                                                         I



                                                            E                        Load
                                                                                                                     
                                                                  
                                                                  
                                                     ‫א‬E١J ١F
                            
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                         
 ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬،voltage source‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
 W‫א‬‫א‬‫א‬‫א‬K
                                                                                  Pure D.C. Current  K١
   KE٢J ١F،‫א‬‫א‬‫א‬‫א‬
                                              Current (I)




                                                                                  time (t)

                                         E٢J ١F

                                                                                      Pulsating Current  K٢
        KE١J ٣F،‫א‬
                                     current ( I )




                                                                 time ( t )
                                 
                                                                        -٥-
       ‫א‬‫א‬                                                      ‫٠٤١ א‬                                   ‫א‬
   ‫א‬‫א‬‫א‬                                         ١-                       




                                     current ( I )
                                                                        time ( t )
                                

                                                     current ( I )



                                                                         time ( t )
                                
                                Pulsating CurrentE٣J ١F
                                                                                            Alternating Current K٣
            
sin wave‫א‬‫א‬K‫א‬‫א‬
                                                                                       KAlternating Current‫א‬‫א‬
                                                 current ( I )




                                                                           time ( t )

                            
                                    Alternating CurrentE٤J ١F

                                                                                                   Voltage‫א‬         ٣J ٣J ١
Volt،‫א‬‫א‬(Work)‫א‬‫א‬
                                                                                       W‫א‬
                      J
               V≡                                                                                                         E٣J ١F
                      C
                                                                                                                      W
                     dW
              V=                                                                                                          E٤J ١F
                     dQ
                                                                                                                   W

                                                                           -٦-
        ‫א‬‫א‬                                           ‫٠٤١ א‬                                   ‫א‬
    ‫א‬‫א‬‫א‬                              ١-                      



                                                                                          KV‫א‬WV
                                                                                          KJ‫א‬WW
                                                                             KCCharge‫א‬WQ

                                                                                     Resistance‫א‬      ٤J ٣J ١
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬Electric Power‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬KOhm‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬K‫א‬
          
، Ω Ohm،‫א‬‫א‬‫א‬‫א‬
                                                                                       
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                       
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                 W‫א‬‫א‬
                                        Current (I)




                                                                        Resistance (R)
                                 
                                      ‫א‬‫א‬‫א‬E٥J ١F



                                                        Resistance of a wire‫א‬‫א‬             ٥J ٣J ١
                                                                       W‫א‬Wires‫א‬
                                                                   KL،Length‫א‬ K١
                                                      KA،Cross-section Area‫א‬ K٢


                                                                -٧-
       ‫א‬‫א‬                                ‫٠٤١ א‬                                    ‫א‬
   ‫א‬‫א‬‫א‬                   ١-                       



                                                                      
‫א‬K، ρ ،MaterialE‫א‬‫א‬F‫א‬ K٣
                                                                                                K
                                                 KT،Temperature‫א‬‫א‬ K٤
                                       W‫א‬‫א‬‫א‬
                     ρ.L
              R=                                                                                    E٧J ١F
                      A
                                                                                                    W
                                                K Ω Resistance‫א‬             WR
                                             K Ω.m ‫א‬‫א‬            Wρ
                                                      m،Length‫א‬               WL
                          K m 2 ‫א‬،Cross-section Area‫א‬              WA
                                                                                        E١J ١F
‫א‬K٥m‫א‬،٥mm‫א‬‫א‬
                                      1.72 * 10 −8 Ω m ‫א‬‫א‬، 20o C ‫א‬

                                                                                                      ‫א‬
                                      W،E٧J ١F‫א‬R‫א‬
                                                                                       ρ.L
                                                                                R =
                                                                                        A

                                                             ⎛        5      ⎞
                                   ∴ R = 1.72 ∗ 10   −8
                                                           ∗ ⎜               ⎟ = 4.38 Ω
                                                             ⎜
                                                               (        −3
                                                             ⎝ π 5 ∗ 10 2 ⎠)
                                                                           2 ⎟




                                                     -٨-
        ‫א‬‫א‬                                          ‫٠٤١ א‬                                     ‫א‬
    ‫א‬‫א‬‫א‬                             ١-                         




                                                                                    Types of Resistors‫א‬‫א‬
                                                                                     W‫א‬
                                                                          
‫א‬‫א‬‫א‬Opto-photo-ResistorsW‫א‬‫א‬                              K١
                
،‫א‬،‫א‬
                                                                               K‫א‬‫א‬
                                                                          
،‫א‬‫א‬‫א‬ Thermal-ResistorsW‫א‬‫א‬‫א‬                                   K٢
         
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                                   ‫א‬‫א‬‫א‬
                                           10000

                                               1000

                                               100
                                         ‫أوم‬




                                                10

                                                 1
                                                      0    40    80   120   160    180 200
                                                                                  ‫درﺟﺔ ﻣﺌﻮﻳﺔ‬

                             
                       ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٦J ١F
                                                                                                                         
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                       K‫א‬‫א‬‫א‬
‫א‬WVoltage Dependent Resistors‫א‬‫א‬‫א‬                                K٣
                                     K‫א‬‫א‬‫א‬،VDR
                            W‫א‬‫א‬‫א‬‫א‬WLinear Resistors‫א‬‫א‬                         K٤
                                                                                                  
                                            KW‫א‬‫א‬ K




                                                                -٩-
        ‫א‬‫א‬                                       ‫٠٤١ א‬                                           ‫א‬
    ‫א‬‫א‬‫א‬                         ١-                            



                                                                                     
 ‫א‬‫א‬‫א‬W‫א‬‫ א‬K
                                                
 ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                                                        W
 ‫א‬WPotentiometer‫א‬E١
      
  J ١F٣،٢،١‫א‬ ،Voltage Divider
 KMega Ohm‫א‬‫א‬‫א‬،EEF٧
                                           
 ‫א‬‫א‬‫א‬WRheostatE٢
                            
  Kilo ‫א‬
 ‫א‬‫א‬،‫א‬‫א‬،Ohm
 ‫א‬‫א‬‫א‬‫א‬،
                
 ‫א‬K‫א‬‫א‬‫א‬‫א‬
                                                                                           EEF٧J ١F
                                                                     
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬K
                      
 K‫א‬‫א‬،‫א‬‫א‬
                    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

                                                                                           ١
                                                                      +
                                                                                            ٢
                                          ٢                            V١٣                          +     
                  ١                           ٣
                                                                                           V٢٣
                                                                           -                        -
                                                                                                ٣
                                  EF                                       EF                  
                                    ‫א‬‫א‬E٧J ١F




                                                           -١٠-
       ‫א‬‫א‬                              ‫٠٤١ א‬                                 ‫א‬
   ‫א‬‫א‬‫א‬                 ١-                    




                                                                   Conductance‫א‬      ٦J ٣J ١
G‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬،Ampere per Volt‫א‬Siemens
                                                                                               W
                     1
              G=                                                                               E٥J ١F
                     R
                                                                          KSiemens
                                                                                              W
                     1
              R=                                                                              E٦J ١F
                     G
                                                                                 .Ohm
                      K‫א‬‫א‬G‫א‬
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
                                                                                                     
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                                                                                                     
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                                                  -١١-
    ‫א‬‫א‬                        ‫٠٤١ א‬                                     ‫א‬
‫א‬‫א‬‫א‬           ١-                         



                              ‫א‬‫א‬
                                         

                                 :‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K١
                                                                          ٢٩٠٠٠ kWE
                                                                               Ω ٧٠٠٠E

                                                                          ٠{٠٠٠٣ msE
                                                                                 ٠{٠٥ AE
                                                                           ٠{٠٠٠٠٩ VE
                                                                           ٧٠٠٠٠٠٠ VE
                                                                         ٠{٠٠٠٠٠٠٠٠٨ sE
                                                                               ٩٠٠٠ kWE

                                                                               W K٢
                                                                        A١٥mAE
                                                                         s٠{١ nsE
                                                                      mA µA ٨٠٠E
                                                                        A١٣ nAE

                                                                               W‫ א‬K٣
                                                                      µA ٨٠٠H١٥mAE
                                                                      ١٣ msH٠{١ nsE
                                                                         ١A+  µA ٨٠٠E
                                                                ٧٠٠٠ µA+١٣ nAE

                                                                               WA - B‫ א‬K٤
                                                             µA B=٨٠٠،A=١٥mAE
                                                               B=١٣ ns A=٠{١ msE
                                                         B= ١٠٠٠ nA ، µA A=٨٠٠E
                                                          B=٧٠٠٠ µV،A=١٣mVE
                                         -١٢-
    ‫א‬‫א‬                 ‫٠٤١ א‬                                 ‫א‬
‫א‬‫א‬‫א‬    ١-                    



                                                                                    
                                                                      A
                                                                      W ‫ א‬K٥
                                                                      B
                                                      µA B=٨٠٠،A=١٥mAE
                                                        B=١٣ ns A=٠{١ msE
                                                  B= ١٠٠٠ nA ، µA A=٨٠٠E
                                                   B=٧٠٠٠ µV،A=١٣mVE




                                  -١٣-
                                   ‫א‬‫א‬‫א‬
                              ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                    ‫א‬‫א‬‫א‬‫א‬




              ١ J
                  
 




٢
‫א‬‫א‬              ‫٠٤١ א‬                                    ‫א‬
                ١-                        



                  ‫א‬‫א‬‫א‬‫א‬
                                                                                    
                       W‫א‬‫א‬،‫א‬‫א‬‫א‬
                                 K‫א‬‫א‬‫א‬ •
                                       K‫א‬‫א‬‫א‬ •
                                       K‫א‬‫א‬‫א‬ •
                                         ‫א‬‫א‬‫א‬ •




                                - ١٤ -
    ‫א‬‫א‬                            ‫٠٤١ א‬                                     ‫א‬
                                  ١-                         



                                                                                              ١J ٢
‫א‬‫א‬‫א‬Fundamental Law‫א‬‫א‬‫א‬
                                                                     
K‫א‬‫א‬‫א‬،
‫א‬‫א‬‫א‬‫א‬
                                                                  
K‫א‬‫א‬‫א‬،‫א‬
                                  
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                           K‫א‬‫א‬‫א‬‫א‬
George Simon Ohm‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬K١٨٢٦Ohm’s Law
،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
      W‫א‬،‫א‬‫א‬‫א‬‫א‬

                       I
                                                               I       R
                                     
                                   Slope = R                   +                −
                                                                        V
                                                                                                       
                                              t                                                        
                              ‫א‬‫א‬E١J ٢F

                                                                Ohm’s Law ٢J ٢
                                                                           
،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                             K‫א‬
                                                  Current Formula‫א‬EF          ١J ٢J ٢
                             ‫א‬‫א‬‫א‬‫א‬
                                                                                 E       V
 E١J ٢F                                                                     I=      , I=
                                                                                 RT      R

                                                                KA‫א‬IW
                               KVVoltage Source‫א‬E
                      KV،Voltage Drop‫א‬‫א‬V
                                                   - ١٥ -
    ‫א‬‫א‬                              ‫٠٤١ א‬                                       ‫א‬
                                    ١-                           



                                                                                           E١J ٢F
                                    
،٥٠V‫א‬، 100Ω ‫א‬
                                                                                ‫؟‬‫א‬‫א‬‫א‬

                                                                 I
                                                                                                           
                                                        A                                                  
                                                                                                           
                                                             100Ω          V                               
                                                                                                           
                                                    
                      E١J ٢F‫א‬‫א‬‫א‬E٢J ٢F
                                                                                                       ‫א‬
                                                                       W‫א‬‫א‬
                                                                               V 50
                                                                          I=    =    = 0.5A
                                                                               R 100

                                                        Resistance Formula‫א‬          ٢J ٢J ٢
                                  
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
                                                                                          W‫א‬
                                                                                    V        E
 E٢J ٢F                                                                        R=     , RT =
                                                                                    I        IT
                                                                                                     W
                                         Ω ،‫א‬‫א‬‫א‬ W R T

                                                                      KA‫א‬I
                                                  K‫א‬‫א‬‫א‬‫א‬ I T
                                                         KV‫א‬E
                                          KV‫א‬‫א‬V




                                                    - ١٦ -
     ‫א‬‫א‬                              ‫٠٤١ א‬                                        ‫א‬
                                    ١-                             



                                                                                         E٢J ٢F
                                     
، 75µA  ‫א‬،١٥٠mV  ‫א‬
                                                                                       
                                                                                                     ‫؟‬‫א‬
                                                                                                             
                                                                                                             
                                                              I = 75µA                                       
                                                    A
                                                                                                             
                                                                 +
                                                                                                             
                                                                         V      150mV                        
                                                                                                             
                                                                 -
                                                                                                             
                       E٢J ٢F‫א‬‫א‬‫א‬E٣J ٢F
                                                                                                         ‫א‬
                                                                              W‫א‬
                                                         V 150 * 10 −3
                                                    R=     =         −6
                                                                        = 2 * 10 3 Ω = 2KΩ
                                                         I   75 * 10
                                                                                                             
                                                                                             WNote
،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                     K‫א‬‫א‬
                                                                                              E٣J ٢F
K٣٠V‫א‬‫א‬٠{٥ mA‫א‬ ‫א‬‫א‬
                                                                              K‫א‬‫א‬‫א‬‫א‬
                                                                                                         ‫א‬
                                                                              W‫א‬
                                                       E      30
                                              RT =       =         −3
                                                                      = 60 * 10 3 Ω = 60 kΩ
                                                      I T 0.5 * 10

                                                     - ١٧ -
     ‫א‬‫א‬                               ‫٠٤١ א‬                                      ‫א‬
                                    ١-                            



                                                                                        E٤J ٢F

‫א‬،١٠mAR١‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                        
                                                           ‫؟‬‫א‬‫א‬،٢٥ V‫א‬



                                          V = 25 V

                                              V
                                                                                 I = 10 mA
                                                                        A                                   
                                                                                                            
                                            R1
                                                   
                       E٤J ٢F‫א‬‫א‬‫א‬E٤J ٢F
                                                                                                       ‫א‬

                                                        V     25
                                               R1 =       =       −3
                                                                     = 2.5 * 10 3 Ω = 2.5 kΩ
                                                        I 10 * 10

                                                         Voltage Formula             ٣J ٢J ٢
       
K‫א‬‫א‬‫א‬‫א‬‫א‬
                           K‫א‬‫א‬‫א‬
                                                          Voltage Drop‫א‬              ١J ٣J ٢J ٢
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                   
E‫א‬‫א‬F‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
                                                   
‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬
                                                                         K‫א‬

 E٣J ٢F                                                                                  V = I.R


                                                       - ١٨ -
     ‫א‬‫א‬                              ‫٠٤١ א‬                                         ‫א‬
                                     ١-                             



                                                     Voltage Source‫א‬                  ٢J ٣J ٢J ٢
‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                        ، R T ‫א‬‫א‬

 E٤J ٢F                                                                                 E = IT .R T

                                                                                          E٥J ٢F
‫א‬‫א‬ 500 Ω ‫א‬ ‫א‬،‫א‬‫א‬
                                                                                                 ٠{١A‫א‬
                                                                                                         ‫א‬

                                                                  E = I T .R T = 0.1 * 500 = 50 V

                                                                                           E٦J ٢F
             ٣mA‫א‬‫א‬ 27 KΩ ‫א‬،‫א‬‫א‬
                                                                                                          ‫א‬

                                                   E = I T .R T = 3 * 10 −3 * 27 * 10 3 = 81 V

                                                                                          E٧J ٢F
                 ٠{٨mA‫א‬‫א‬‫א‬، 28 kΩ ‫א‬

                                                                                                          ‫א‬
                                                  V = I * .R = 0.8 *10−3 * 28 *103 = 22.4 V
                                                                                                              
                                                                                              WNote
‫א‬‫א‬ 
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬
                                                            W‫א‬‫א‬‫א‬



                                                     - ١٩ -
     ‫א‬‫א‬                                  ‫٠٤١ א‬                                       ‫א‬
                                         ١-                          



                                                                                                               
                                                             V                                                 

                                                         I           R

                                       E٥J ٢F
                                                                                                               
                           W‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

E٥J ٢F                                                                         V = I*R

                                                                                                    V
 E٦J ٢F                                                                                      I =
                                                                                                    R
                                                                                                    V
E٧J ٢F                                                                          R=
                                                                                                    I


                                                                                          K‫א‬
                                                                                          Summary‫א‬
                                     K‫א‬‫א‬‫א‬‫א‬ K١
،‫א‬،‫א‬،‫א‬ Current‫א‬ K٢
                                                                                         V
                                                                                  KI =     W
                                                                                         R
                                   W،‫א‬‫א‬‫א‬ K٣
                                                                                          V = I*R
‫א‬‫א‬‫א‬ I T ‫א‬‫א‬‫א‬‫א‬ K٤
    K‫א‬‫א‬، R T ‫א‬‫א‬‫א‬
                                                 
‫א‬‫א‬‫א‬ K٥
                                                                                 K‫א‬‫א‬‫א‬



                                                             - ٢٠ -
    ‫א‬‫א‬                         ‫٠٤١ א‬                                      ‫א‬
                               ١-                          



                                   ‫א‬‫א‬
                                                                                   
‫א‬‫א‬‫א‬‫א‬ K١
                                                      
                                                                                       W
                                                                                        
                                                     K‫א‬ EF
                                                        K٧٥٪‫א‬ EF
                                                                                              
                                                                                                
                                                               K‫א‬ EF
                                                         K٣٥٪‫א‬ EF
                                                                                                 
                                                                                             
                                                            K‫א‬‫א‬‫א‬‫א‬EF
                                                                                         
                                                       K‫א‬‫א‬‫א‬‫א‬ EF
                                                                                               
                                          W‫א‬،‫א‬‫א‬ K٢
                                                                       V = 5V , R = 1Ω EF 
                                                                                          
                                                                       V = 15V , R = 10Ω EF
                                                                  V = 50V , R = 100Ω EF 
                                                                 V = 30V , R = 15KΩ EF  
                                                              V = 250V , R = 5.6MΩ EF    

 ‫؟‬‫א‬‫א‬‫א‬،١٢V10KΩ  K٣

                                                            
،J J J W‫א‬‫א‬‫א‬ K٤
       K١٢V‫א‬‫א‬‫א‬‫א‬،

‫א‬‫א‬‫א‬‫א‬،٢٥V K٥
                      KJ J J W‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٦
    
 8Ω ‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                                       W‫א‬

                                               - ٢١ -
     ‫א‬‫א‬                              ‫٠٤١ א‬                                         ‫א‬
                                     ١-                             




                                           Fuse                                                         

                                                        R
                                   120V                                      V       100V
                                                                                                        
                                                                                                        
                                                                                                        
،‫א‬‫א‬‫א‬Fuse‫א‬
                                                        
                        ‫؟‬١٠٠ V‫א‬‫א‬‫א‬
                                                                                                        
                          W‫א‬‫א‬R‫א‬I‫א‬‫א‬ K٧
                                                                           I = 2A ,        R = 18Ω EF
                                                                     I = 2.5A ,        R = 680Ω EF
                                                                             I = 5A ,      R = 56Ω EF
                                                                                                        
‫א‬،٣A 27Ω ‫א‬‫א‬ K٨
                                                                  ‫؟‬‫א‬K

                      W‫א‬‫א‬I‫א‬،V‫א‬‫א‬ K٩
                                                                           I = 2A ,       V = 10V EF
                                                                        I = 45A ,        V = 90V EF
                                                                           I = 5A ,       V = 50V EF
                                                                                                        
 R = 100Ω ‫א‬،‫א‬‫א‬‫א‬‫א‬ K١٠
‫א‬‫א‬‫א‬،‫א‬Variable Voltage Source
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K١٠٠ V‫א‬‫א‬


                                                     - ٢٢ -
     ‫א‬‫א‬                              ‫٠٤١ א‬                                        ‫א‬
                                     ١-                            



                                                                           
‫א‬‫א‬KI‫א‬V‫א‬‫א‬K
                                                 ‫؟‬‫א‬‫א‬‫א‬‫؟‬

                        
K V = 1V  ‫א‬ I = 5mA ‫א‬‫א‬ K١١
                                   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                             V = 1.5V EF     
                                                                                             
                                                                                  V = 2 V E F
                                                                               V = 3V EF   
                                                                               V = 4 V E F 
                                                                             V = 10V EF     
                                K‫א‬‫א‬،I‫א‬V‫א‬،‫א‬

                    
، ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ K١٢
                                                                             K

                                                                                                       
                             R = 3.3kΩ                                 R = 3 .9 k Ω
                                                                                                       
                                                                                                       
               50V                                      75V
                                                                                                       




                                               R = 4 .7 k Ω


                             100V




                                                     - ٢٣ -
                                         ‫א‬‫א‬‫א‬
                                      ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                          ‫א‬‫א‬‫א‬‫א‬




                   ١ J
                     ‫א‬‫א‬
 ‫א‬‫א‬




٣
 ‫א‬‫א‬                         ‫٠٤١ א‬                                    ‫א‬
  ‫א‬‫א‬                      ١-                        



                                ‫א‬‫א‬‫א‬‫א‬
                                                                                                  
                                      W‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                     K‫א‬‫א‬‫א‬ •
                                     K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •




                                                - ٢٤ -
   ‫א‬‫א‬                           ‫٠٤١ א‬                                    ‫א‬
    ‫א‬‫א‬                        ١-                        



                                                                         Introduction ١J ٣
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬ ‫א‬       K‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬  
KPower‫א‬‫א‬‫א‬‫א‬
                           K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                        
                                                                                Power ‫٢ א‬J ٣
                                           
KP،Watt‫א‬‫א‬K‫א‬‫א‬‫א‬
    W‫א‬‫א‬t‫א‬‫א‬

                          Energy
               Power =                                                                          E١J ٣F
                           time

                     E
               P=                                                                               E٢J ٣F
                     t

                                                                                               W
                                                                 ‫א‬L‫א‬Z‫א‬
                                                                                                W
                                                  KWatt‫א‬Power‫א‬            WP
                      K Watt ⋅ second ⋅‫א‬‫א‬JEnergy‫א‬          WE
                                          Ksecondtime‫א‬            Wt
                                                                                                        
                                                                                       Note
   WattW،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
               W‫א‬‫א‬‫א‬‫א‬،‫א‬Joule‫א‬
                                                                                                        
                          Joule
                Watt =                                                                          E٣J ٣F
                         sec ond



                                                    -٢٥-
 ‫א‬‫א‬                         ‫٠٤١ א‬                                  ‫א‬
  ‫א‬‫א‬                      ١-                      



                                                                             E١J ٣F
             ‫؟‬‫א‬‫א‬،٥ sec‫א‬١٠٠ J‫א‬‫א‬
                                                                                                
                                                                                             ‫א‬
                                                                    W‫א‬
                       Energy E 100 J
             Power =         = =      = 20 Watt
                        time  t 5 sec

                                                                             E٢J ٣F

 ‫؟‬‫א‬Kt = ٣٠ sec‫א‬‫א‬‫א‬،P = ١٠٠ W‫א‬‫א‬
                                                                                             ‫א‬
                       Energy
             Power =            ⇒ Energy = Power * time
                         time
             E = P * t = 100 * 30 = 3000J = 3 kJ
                                                                                WNote
                                   KWEEnergy‫א‬‫א‬
                                                                             E٣J ٣F
                        W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                    ٠{٠٤٥ W EF  
                                                                  ٠{٠٠٠٠١٢ W EF
                                                                      ٣٥٠٠ W EF
                                                             ٠٠٠ W، ٠٠٠،١٠ EF 
                                                                                             ‫א‬
  ‫א‬‫א‬‫א‬KMWkWWmW‫א‬‫א‬
‫א‬‫א‬،mW‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،
‫א‬‫א‬‫א‬‫א‬KKW‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                        KMW‫א‬‫א‬‫א‬

             mW‫א‬‫א‬‫א‬،‫א‬،P=٠{٠٤٥ W EF
                                                                                  

                                                -٢٦-
 ‫א‬‫א‬                           ‫٠٤١ א‬                                    ‫א‬
  ‫א‬‫א‬                        ١-                        



                                                                                W

              P = 0.045 W = 0.045 * 10 3 * 10 −3 W = 45 * 10 −3 = 45 mW

  ‫א‬،‫א‬‫א‬،P=٠{٠٠٠٠١٢ W               
                                                                                           EF
   ‫א‬، µW ‫א‬‫א‬‫א‬‫א‬،‫א‬
                                                                                       W

             P = 0.000012 W = 0.000012 * 10 6 * 10 −6 W = 12 µW

                                                                                            
                             W‫א‬kW،P=٣٥٠٠ W EF

             P = 3500 W = 3500 * 10 −3 * 10 3 W = 3.5 kW

                                                                                        
                        WMW‫א‬P=١٠{٠٠٠{٠٠٠ W EF

             P = 10,000,000 W = 10,000,000 * 10 −6 * 10 6 W = 10 MW

                                                                                    WNote
                                                         W‫א‬‫א‬‫א‬
                       K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J
                    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J 
       K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫ א‬‫א‬‫א‬‫א‬J
        K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J

                                                                                 E٤J ٣F
                                                       W‫א‬‫א‬‫א‬
                                                 K‫א‬١٤٠٠ WEF
                                                      K٢٥٠٠ WEF
                                          K١٠٠٠{٠٠٠ WEF
                                                                                                 ‫א‬

                                                      W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                  -٢٧-
 ‫א‬‫א‬                            ‫٠٤١ א‬                                       ‫א‬
  ‫א‬‫א‬                         ١-                           


                        1400
             1400 W =           = 1.4 kW                                                          EF
                        10 3
             W = P * t = 1.4 kW * 1h = 1.4 kWh

                        2500
             2500 W =           = 2.5 kW                                                          EF
                        10 3
             W = P * t = 2.5 kW * 2h = 5 kWh

                           1000000
             1000000 W =               = 1000 kW                                                  EF
                                10 3
             W = P * t = 1000 kW * 5h = 5000 kWh

                               Power in Electric Circuit‫א‬‫א‬‫א‬‫א‬           ٣J ٣
        
    ‫א‬،‫א‬‫א‬Power‫א‬
   ‫א‬،‫א‬،‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
  KOhm’s Law‫א‬‫א‬‫א‬‫א‬‫א‬
                                                      W‫א‬‫א‬‫א‬
              P = V.I                                                                             E٤J ٣F
                                                                                                  W
                                             KWatt‫א‬،Power‫א‬             WP
                                                              KA‫א‬      WI
                                              KV،‫א‬             WV




                                                   -٢٨-
     ‫א‬‫א‬                            ‫٠٤١ א‬                                  ‫א‬
      ‫א‬‫א‬                         ١-                      



                                                                                               
                                                              I
                                                                  +
                                                                                                    
                                                              R   V
                                                                                                    
                                                                                                    
                               ‫א‬E١J ٣F
                                                                                                    
        ‫א‬ V = I.R ‫א‬‫א‬‫א‬
                                                                        W‫א‬
                 P = V.I = I.R.I = I 2 .R                                                          E٥J ٣F

                                                                                                    
                       V
    ‫א‬ I =       ‫א‬،
                       R
                                                                        W‫א‬

                              V V2
                  P = V.I = V. =                                                                   E٦J ٣F
                              R  R

                       V        E
                  R=     , RT =                                                                    E٧J ٣F
                       I        IT

                                                                                    E٥J ٣F
                         W‫א‬‫א‬،10Ω ‫א‬‫א‬
                                                                             I=٠{٧AEF
                                                                          I=١{٤AEF
                                                                           I=٢{١AEF



                                                       -٢٩-
  ‫א‬‫א‬                          ‫٠٤١ א‬                                             ‫א‬
   ‫א‬‫א‬                       ١-                                 



                                                                                                          ‫א‬
                                                                 W‫א‬‫א‬

               P = I 2 .R = (0.7)2 *10 = 4.9W                                      EF

              P = I 2 .R = (1.4) 2 *10 = 19.6W                                      EF

              P = I 2 .R = (2.1) 2 *10 = 44.1W                                      EF

  IP‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                                                       WK
               P α I2                                                                                  E٨J ٣F
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                             W‫א‬‫א‬‫א‬
                                                                P = 4.9 Watt ← I = 0.7 A EF
                                                        P = 19.6 Watt ← I = 1.4A EF
                                                                                                             
                                  KEF‫א‬EF‫א‬EF
                                                                                       E٦J ٣F
     ،١٥ V10 kΩ ‫א‬‫א‬،E٢J ٣F‫א‬
                                                                             ‫؟‬12 kΩ ‫א‬‫א‬
                                                                                                             
                                                      12 kΩ            I                                     
                                                 
                                                 +                 -
                                                            V                 +
                                                                                                             
                                                                   10kΩ           ١٥V                        
                                                                              −                              

                     E٦J ٣F‫א‬‫א‬‫א‬E٢J ٣F


                                                  -٣٠-
 ‫א‬‫א‬                               ‫٠٤١ א‬                                        ‫א‬
  ‫א‬‫א‬                            ١-                            



                                                                                                       ‫א‬
                                                               W‫א‬‫א‬‫א‬‫א‬

                    V    15      15
              I=      =        = 4 = 1.5 mA
                    R 10 * 10 3 10

                                               W12 kΩ ‫א‬‫א‬‫א‬

              V = I*R

                   = 1.5 * 10 −3 * 12 * 10 3 = 12 V

                                                  KV=١٢ V 12 kΩ ‫א‬‫א‬

                                                                                                            

                                                                                     Summary‫א‬
                                 Joule
                     K Watt =           W،‫א‬‫א‬‫א‬‫• א‬
                                sec ond
                                           K‫א‬ •
  ‫א‬‫א‬‫א‬‫• א‬
                                                                                  K‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                               K‫א‬‫א‬‫א‬ •
                              Kopen circuit‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
     ‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                                                          K
                                          KAmpere. Hourx‫א‬ •
                                                  K١١x‫א‬ •
                                                   
                                                   
                                                   
                                                       -٣١-
 ‫א‬‫א‬                           ‫٠٤١ א‬                                              ‫א‬
  ‫א‬‫א‬                        ١-                                 



                                    ‫א‬‫א‬
                     ‫؟‬ 350 j s ‫א‬‫א‬‫א‬–١
                                   ‫؟‬ 5 h  7500 j ‫א‬‫א‬–٢
                                  500 ms 1000 j ‫א‬‫א‬‫א‬–٣
                                                             kw ‫א‬‫א‬‫א‬–٤
                            3750w EF           1000w EF
                                     500 w EF  50000w EF
                                                                                                          
  Kx‫א‬Ex‫א‬ 5 *106 F‫א‬–٥
‫א‬ 2A  75V ‫א‬‫א‬‫א‬–٦
                                                                                           ‫؟‬ R L ‫א‬
      ‫א‬‫א‬ 3A ‫א‬120V –٧
                                                                                   ‫؟‬‫א‬
                    ‫؟‬100µA 10kΩ ‫א‬‫א‬‫א‬–٨
                                                                                                              




                                                  -٣٢-
                                                                           ‫א‬‫א‬‫א‬
                                                                        ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                                                            ‫א‬‫א‬‫א‬‫א‬




                                           ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                   ١ J
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬




٤
             ‫א‬‫א‬‫א‬                                       ‫٠٤١ א‬                           ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                   ١-                   



                                            ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                                
                                                 W‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                                   K‫א‬‫א‬‫א‬‫א‬ •
                                                                    K‫א‬‫א‬‫א‬ •
                                                                            K‫א‬‫א‬‫א‬ •
                                             K‫א‬‫א‬‫א‬‫א‬ •
                                                         K‫א‬‫א‬‫א‬ •
                                                     K‫א‬‫א‬‫א‬‫א‬ •
                                                  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •




                                                         - ٣٣ -
                ‫א‬‫א‬‫א‬                                       ‫٠٤١ א‬                     ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                    ١-            



                                                                                    Introduction ١J ٤
                         
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
                                                              
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                         
‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                       
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                                                 K‫א‬

                                                           Series Connection‫א‬‫א‬‫א‬ ٢J ٤
                                              
                                              
‫א‬،‫א‬‫א‬‫א‬‫ א‬ ‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                                            
،‫א‬‫א‬K‫א‬
                                                                 K‫א‬‫א‬‫א‬‫א‬
                                                                                                          
                    R١                                                R١                                  
      a                                                a                                         R١
                                                                                                          
                                                                                      a
                                                                      R٢
                                                                                                          
                                              R٢                                                  R٢
           I                                                                                              
                                                                      R٣
                    R٣
                                                                                                  R٣
                                                                                                          
     b                                                                                                            b
                                                                      R٤
                                                   b                                                          I
                                                           I

                                    ‫א‬‫א‬‫א‬E١J ٤F




                                                            - ٣٤ -
                  ‫א‬‫א‬‫א‬                                     ‫٠٤١ א‬                            ‫א‬
     ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                ١-                    



                                                          Total Resistance (RT)‫א‬             ١J ٢J ٤
         W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
   E١J ٤F                                                       R T = R1 + R 2 + R 3 + K + R n
                                                                                                E١J ٤F
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                     W‫א‬
                                                R 1 = 56 Ω           R 2 = 100 Ω                                     
                                                                                                           
                                                             I                                             
                                   VS                                                   R٣ = ٢٧ Ω          
                                                R 5 = 5.6 Ω R 4 = 10 Ω                                     
                                                                                                           
                        E١J ٤F‫א‬‫א‬‫א‬E٢J ٤F
                                                                                                                ‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

                                                         R T = 56Ω + 100Ω + 27Ω + 10Ω + 5.6Ω
                                                                                              = 198.6Ω
                                                                                      ∴ R T = 198.6Ω

                                                                                               E٢J ٤F
                                       
  ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
                                                                                                            K 22 Ω
                                                                                                                ‫א‬
                                ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  E٢J ٤F                                                                                   Q R T = nR
                                                                                ∴ R T = 8 * 22 = 176 Ω

                                                                                    K‫א‬ n W
                                                           - ٣٥ -
                ‫א‬‫א‬‫א‬                                        ‫٠٤١ א‬                       ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                    ١-               



                            Ohm's Law in Series Circuits ‫א‬‫א‬‫א‬ ٣J ٤
                                       
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                        K‫א‬
                                                                                             E٣J ٤F
،12.6 kΩ ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                 
                                               W‫א‬‫א‬‫א‬ 3.9 kΩ ‫א‬Voltage Drop‫א‬
                                                        R1                 R2                                   
                                                                                                                
                                                                                        +                       
                      Vs = ٢٠ V                                        R٣ =٣٫٩ kΩ       V=?                     
                                                                                        _                       
                                                                                                                
                      E٣J ٤F‫א‬‫א‬‫א‬E٣J ٤F
                                                                                                          ‫א‬
                         
I‫א‬،‫א‬ R٢،R١‫א‬‫א‬‫א‬‫א‬
                                                                                
                                                    W‫א‬‫א‬‫א‬
                                                                             VS     20
                                                                        I=      =           = 1.59mA
                                                                             R T 12.6 * 103

                                                     V = I * R 3 = 1.59 *10−3 * 3.9 *103 = 6.19V
                                                              ٦{١٩ VR٣‫א‬‫א‬∴
                                                                                             E٤J ٤F
KVs،‫א‬‫א‬‫א‬‫א‬
                                                                   
                 K 5mA Fuse‫א‬ Vs‫א‬




                                                             - ٣٦ -
                ‫א‬‫א‬‫א‬                                     ‫٠٤١ א‬                              ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                 ١-                      



                                                                                                                    
                                      5 mA Fuse     R 1 = 1 kΩ          R 2 = 3 .3 k Ω


                         +
                                                   I = 1mA
                         VS                                                              R 3 = 4.7 kΩ
                         −
                                                                                                                    
                                                                                                                        

                      E٤J ٤F‫א‬‫א‬‫א‬E٤J ٤F
                                                                                                               ‫א‬
                                                            W‫א‬‫א‬
                                               V1 = IR 1 = (1mA ) ⋅ (1KΩ ) = 1 * 10 −3 * 10 3 = 1V
                                                                                           ∴ V1 = 1V
                                                                                    (         )
                                                          V2 = IR 2 = (1mA ) ⋅ 3.3 * 10 3 = 3.3V
                                                                                         ∴ V 2 = 3.3V
                                                      (                 )
                                 V3 = IR 3 = (1mA ) ⋅ 4.7 * 10 3 Ω = 1 * 10 3 * 4.7 * 10 3 = 4.7 V
                                                                                         ∴ V3 = 4.7 V

                                                           KRTVS‫א‬
                                                                       ∴ R T = 1 + 3.3 + 4.7 = 9KΩ
                                                                     VS = 1 * 10 −3 * 9 * 10 3 = 9V
                                                  WVSV١،V٢ ،V٣ 
                                                                             VS = V1 + V2 + V3 = 9V

      
EKirchhoff’s Voltage LawF‫א‬
‫א‬VS‫א‬EF‫א‬
                                                                                   K‫א‬‫א‬‫א‬
                                                                                                      WNote
                                  K‫א‬‫א‬‫א‬EKVLF
                                                          - ٣٧ -
               ‫א‬‫א‬‫א‬                                       ‫٠٤١ א‬                             ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                      ١-                  



٥mA‫א‬‫א‬
                                                                                       W‫א‬
                                                                                      VS = 5mA * 9KΩ
                                                                       VS = 5 * 10 −3 * 9 * 10 3 = 45V

                                                                                                E٥J ٤F
                   ‫؟‬VS‫א‬،1mA ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                     
                                        − VS +                                                    
                                                                                                                    
                                                                                                                    
                                                                                                                    
                            1 .5 k Ω                                                 1.2 kΩ                         
                                                            I
                                                                                                                    
                                                                                                                    
                                                  1.2 kΩ            5 .6 k Ω

                          E٥J ٤F‫א‬‫א‬‫א‬E٥J ٤F

                                                                                                              ‫א‬
                                                                  
                                      RT‫א‬‫א‬ ،VS‫א‬
                                                                 R T = 1.2 + 5.6 + 1.2 + 1.5 = 9.5kΩ
                                                                                          ∴ R T = 9.5kΩ

                                                                               VS‫א‬

                                              VS = IR T = (1mA ) ⋅ (9.5kΩ ) = 1 * 10 −3 * 9.5 * 10 3
                                                                                            ∴ VS = 9.5V




                                                           - ٣٨ -
                ‫א‬‫א‬‫א‬                                ‫٠٤١ א‬                        ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬            ١-                



                                              Voltage Sources in Series‫א‬‫א‬‫א‬ ٤J ٤
                                                                             
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
         
K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                        
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                         K‫א‬‫א‬‫א‬K‫א‬
                                                                                     E٦J ٤F
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ E٢،E١‫א‬W‫א‬‫א‬‫א‬
                                                                                                     KRT
                                                                                                         
                                      +                                                                  
                                   30 V                                                                  
                                                E1
                                    +
                                     −                        R T = 200 Ω                                
                                   20 V        E2                                                        
                                      −                                                                  
                                               
                      E٦J ٤F‫א‬‫א‬‫א‬E٦J ٤F
                                                                                                   ‫א‬
‫א‬‫א‬،‫א‬‫א‬ E١،E٢‫א‬
                                                                                              W‫א‬

                                                                              E T = E1 + E 2
                                                                          E T = 30 + 20 = 50V
                                                                                W
                                                                            ET   50
                                                                    ∴I =      =    = 0.25A
                                                                            R T 200
                                                                                  ∴ I = 0.25A

                                                     - ٣٩ -
                 ‫א‬‫א‬‫א‬                              ‫٠٤١ א‬                      ‫א‬
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬          ١-              



                                                                              
 ‫א‬‫א‬،ESeries–OpposingF‫א‬‫א‬
                                
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                   E٧J ٤F
                                                 ‫؟‬‫א‬‫א‬‫א‬‫א‬
                                                                                                      
                                   +
                                  25V                                                                 
                                   −
                                               E1                                                     
                                   +                           RT
                                  15V                                                                 
                                               E2
                                                                                                          
                                     −                                                                    
                                                                                                          

                       E٧J ٤F‫א‬‫א‬‫א‬E٧J ٤F
                                                                                                ‫א‬
                                                                
 ‫א‬‫א‬‫א‬ E١،E٢‫א‬
                                                                   
 ‫א‬–H‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                                         
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
                                                        W‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                                               E = E1 − E 2
                                                                         E = 25 − 15 = 10 V




                                                    - ٤٠ -
                 ‫א‬‫א‬‫א‬                                       ‫٠٤١ א‬                         ‫א‬
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                   ١-                 



                                                                                              E٨J ٤F
                                  
 ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                     ‫؟‬‫א‬‫א‬
                                           − E1 +        − E 2 + − E3 + − E 4 +



                                                 1.5V      1.5V           1.5V     1 .5 V

                                                                  ET
                       E٨J ٤F‫א‬‫א‬‫א‬E٨J ٤F
                                                                                                            ‫א‬
                                                                                  E T = 4 * 1 .5 = 6 V 

                                                     Kircchoff's voltage law (KVL) ٥J ٤
                                                 
?‫א‬‫א‬ ‫א‬‫א‬‫א‬
                                                    
                                                K?‫א‬EF‫א‬‫א‬‫א‬
                                                                                                 W
 Voltage Drops‫א‬‫א‬‫א‬
                                                                                        ?‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬Voltage Drops‫א‬‫א‬
                                                                                                      
 ،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                             
 ‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                           K‫א‬‫א‬‫א‬‫א‬




                                                             - ٤١ -
                ‫א‬‫א‬‫א‬                                 ‫٠٤١ א‬                                  ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬              ١-                         



                                                                                         R٤
                                                                                                                    
                                     R1          R2                      R3
                                                                                                                    
                                 − V1 +        − V2 +             − V3 +              − V4 +                        
                                                                                                                    
                                                                                                                    
                                                                                                                    
                                                      VS                                                            
                           ‫א‬‫א‬‫א‬‫א‬‫א‬E٩J ٤F

                                                                              v s = v1 + v 2 + v 3 + v 4

‫א‬Voltage Drops‫א‬
                                                       
                                                                                                K‫א‬

                                                                   v s = v1 + v 2 + v 3 + ..........
                                                                                                E٩J ٤F
                                  W‫א‬‫א‬‫א‬‫א‬ VS ‫א‬
                                                                                                                    
                      +                           + 5V -
                                                                                    +                               
                      VS
                                                                                    10V
                      −                                                                                             
                                                                                     −
                                                                                                                    
                                                                                                                    
                     E٩J ٤F‫א‬‫א‬‫א‬E١٠J ٤F
                                                                                                              ‫א‬
                                                                      K
                                                                                          v s = v1 + v 2
                                                                                    v s = 5 + 10 = 15v
                                                                                              ∴ v s = 15v


                                                      - ٤٢ -
                ‫א‬‫א‬‫א‬                                   ‫٠٤١ א‬                            ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬               ١-                    



                                                                                          E١٠J ٤F
‫א‬، I = 200mA ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                 ‫؟‬ R 4  R 3 ، R 2 ، R1 ‫א‬
                                                                                                                
                                              R 3 = 100 Ω R 2 = 47 Ω                                            
                                                                                                                
                                                                                                                
                                 R4                                              R 1 = 10 Ω
                                                                                                                
                                                                                                                
                                                                                                                
                                                                  I = 200 mA                                    
                                                 E=١٠٠ V
                                                                                                                
                    E١٠J ٤F‫א‬‫א‬‫א‬E١١J ٤F
                                                                                                          ‫א‬
 Ohm’s Law‫א‬‫א‬
                                                                                  KKirchhoff's Voltage Law
                                    Voltage Drops‫א‬

                                                           V1 = IR 1 = 200 * 10 −3 * 10 = 2V
                                                        V2 = IR 2 = 200 * 10 −3 * 47 = 9.4V
                                                        V3 = IR 3 = 200 * 10 −3 * 100 = 20V
                            WE R 4 ‫א‬‫א‬F v 4 

                                                                  v s − (v 1 + v 2 + v 3 + v 4 ) = 0
                                                                     100 − 2 − 9.4 − 20 − v 4 = 0
                                                                                      68.6 − v 4 = 0
                                                                                     ∴ v 4 = 68.6V

                                                        - ٤٣ -
                ‫א‬‫א‬‫א‬                                     ‫٠٤١ א‬                              ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                   ١-                   



                                                 Kirchhoff's Current Law (KCL)  ٦J ٤
                                                                 W‫א‬
‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ENodeF?
             
                                                              ?‫א‬‫א‬‫א‬‫א‬
                  K‫א‬‫א‬ Node‫א‬

                                                        R٢
                                                                                                                    
                                              Node                    R4                                            
                                         R١
                                                                                                                    
                                                                      I2
                                 I3                                                                                 
                                                        R٣
                                                                                                                    
                     ‫א‬‫א‬‫א‬E١٢J ٤F

                                                                            W
                                                                                          I1 = I2 + I3
                                                  W‫א‬KCL‫א‬
                 
              ?‫א‬‫א‬‫א‬‫א‬Node‫א‬‫א‬‫א‬‫א‬?
                                                        W‫א‬‫א‬‫א‬‫א‬
                                                                                         I1 − I 2 − I3 = 0

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KCL
                                  
‫א‬‫א‬‫א‬Nods‫א‬‫א‬‫א‬،‫א‬‫א‬
                                
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ KCL
                                                                                                              K‫א‬

                                                                                 Voltage Divider ‫א‬ ٧J ٤
                                                                           
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                            
Voltage Dividers‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                         K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

                                                          - ٤٤ -
                ‫א‬‫א‬‫א‬                                ‫٠٤١ א‬                                ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬               ١-                     



                                                                                                                
                                               − V1 +                                                           
                                                                                                                
                                                     R1         I                                               
                            +                                                    +
                            VS                                      R٢           V2                             
                            −                                                    _                              
                                                 
           ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٣J ٤F
                                                                                                                    
                        
‫א‬‫א‬ R 2 ، R1 ‫א‬‫א‬
                                                                                        ‫א‬‫א‬
                                                                                           V1 = IR 1
                                                                                          V2 = IR 2

K R1, R 2  V2 ، V1 ‫א‬‫א‬
                W R 2 = 100Ω ، R1 = 50Ω ، VS = 10V ‫א‬،

                                                                             R T = 50 + 100 = 150Ω

                                                                                        10 V  1
                                                                                  I=         = A
                                                                                       150 Ω 15

                                                                                  1       1
                                                                 V1 = IR 1 =        * 50 = * 10 V
                                                                                 15       3

                                                                                              1
                                                                                     ∴ V1 =     (10) V
                                                                                              3

                                                                                 1        1
                                                               V2 = IR 2 =         * 100 = (20 ) V
                                                                                15        3

                                                                                              2
                                                                                     ∴ V2 =     (10) V
                                                                                              3

                                                     - ٤٥ -
                ‫א‬‫א‬‫א‬                                   ‫٠٤١ א‬                            ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                ١-                   



                              K‫א‬ V2 ‫א‬ V1 ‫א‬
                                        K‫א‬‫א‬‫א‬‫א‬‫א‬
                                         Voltage Divider Formula‫א‬‫א‬‫א‬              ١J ٧J ٤
                                                       
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                                                           
                                    R١            R٢                  R٣               R٤
                                                                                                           
                                 V١ + −          V٢ + −             V٣ + −           V٤ + −                
                I
                                                                                                           
                                                                                                           
                                                                                                           
                                                       VS + −
                                                                                                           
                          ‫א‬‫א‬E١٤J ٤F

            ،‫א‬ X  VX ‫א‬‫א‬

                                                                                            VX = IR X
                                                                         ٤ ، ٣، ٢،١‫א‬ x W
                                                                                                            
                                                          W‫א‬‫א‬‫א‬
                                                                                                   VS
                                                                                             I=
                                                                                                   RT
                                                              VX ‫א‬ I ‫א‬
                                                                                          ⎛V ⎞
                                                                                     VX = ⎜ S ⎟R X
                                                                                          ⎜R ⎟
                                                                                          ⎝ T⎠
                                                                               W VX ‫א‬
                                                                                            ⎛ RX ⎞
                                                                                  VX = ⎜
                                                                                        ⎜        ⎟VS
                                                                                                 ⎟
                                                                                            ⎝ RT ⎠
                                                                                                                

                                                        - ٤٦ -
             ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                             ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                ١-                     



                                                                                           E١١J ٤F
                                            ‫؟‬‫א‬‫א‬‫א‬ V2 ‫א‬ V1 ‫א‬
                                                                                                               
                                                                                     +                         
                                                                R 1 = 100Ω
                                                                                     V1                        
                     +
                                                                                     −
                     VS = 10 V                                                                                 
                     −                                                               +                         
                                                                 R 2 = 56 Ω
                                                                                     V2
                                                                                                               
                                                                                     −
                                                                                                               
                                                                                                               
                 E١١J ٤F‫א‬‫א‬‫א‬E١٥J ٤F
                                                                                                         ‫א‬
                                                          ‫א‬‫א‬ V2 ، V1 
                                                                                       ⎛R ⎞
                                                                                  VX = ⎜ X ⎟VS
                                                                                       ⎜R ⎟
                                                                                       ⎝ T⎠
                                                                           R T ‫א‬‫א‬
                                                                           R T = 100 + 56 = 156Ω
                                                               ⎛R ⎞      100
                                                          V1 = ⎜ 1 ⎟VS =
                                                               ⎜R ⎟          * 10 = 6.41V
                                                               ⎝ T⎠      156
                                                                                     ∴ V1 = 6.41V

                                                                                       V2 
                                                                   ⎛R ⎞         56
                                                       V2 = ⎜ 2 ⎟VS =
                                                             ⎜R ⎟          * 10 = 3.59V
                                                             ⎝ T⎠      156

                                                                      ‫א‬

                                                        V2 = VS − V1 = 10 − 6.41 = 3.59V



                                                      - ٤٧ -
             ‫א‬‫א‬‫א‬                                ‫٠٤١ א‬                           ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬            ١-                   



                                                                                    E١٢J ٤F
                                    W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                           C to D (e) B to D (d) B to C (c) A to C (b)  A to B (a)
                                                            W‫א‬
                             VCD (e) VBD (d)       VBC (c) VAC (b)        VAB (a)
                                               
                                           R١ = ١kΩ
                                  A
                                                                        B
                                              
                                                                         R٢ = ٨٫٢kΩ
                                              
              VS = ٢٥V                                                   C
                                              
                                                                          R٣ = ٣٫٣kΩ
                                              
                                                                        D

                 E١٢J ٤F‫א‬‫א‬‫א‬E١٦J ٤F
                                                                                                   ‫א‬
                                                                          R T ‫א‬‫א‬

                                                                       R T = R1 + R 2 + R 3
                                                                         R T = 1 + 8.2 + 3.3
                                                                                R T = 12.5KΩ

                                                       W‫א‬‫א‬‫א‬
                                                                                    ⎛R ⎞
                                                                          VAB = ⎜ 1 ⎟VS
                                                                                 ⎜R ⎟
                                                                                 ⎝ T⎠
                                                                                1
                                                                      VAB =        * 25 = 2V
                                                                               12.5
                                                                                ∴ VAB = 2V


                                                  - ٤٨ -
                ‫א‬‫א‬‫א‬                                 ‫٠٤١ א‬                               ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬             ١-                       



                                                                                    ⎛ R1 + R 2    ⎞
                                                                          VAC = ⎜
                                                                                 ⎜                ⎟VS
                                                                                                  ⎟
                                                                                    ⎝ R3          ⎠

                                                                  VAC = ⎛
                                                                           9 .2 ⎞
                                                                         ⎜      ⎟ * 25 = 18.4V
                                                                              ⎝ 12.5 ⎠
                                                                             ∴ VAC = 18.4V
                                                                       C،B‫א‬‫א‬
                                                                                        ⎛R ⎞
                                                                                  VBC = ⎜ 2 ⎟VS
                                                                                        ⎜R ⎟
                                                                                        ⎝ T⎠
                                                                           ⎛ 8.2 ⎞
                                                                     VBC = ⎜      ⎟ * 25 = 16.4V
                                                                           ⎝ 12.5 ⎠
                                                                                   ∴ VBC = 16.4V
                                                                                 ⎛ 8.2 + 3.3 ⎞
                                                                           VBD = ⎜           ⎟ * 25
                                                                                 ⎝ 12.5 ⎠
                                                                               ⎛ 11.5 ⎞
                                                                         VBD = ⎜      ⎟ * 25 = 23V
                                                                               ⎝ 12.5 ⎠
                                                                                     ∴ VBD = 23V

                                                                                              VCD ‫א‬

                                                                     VCD = ⎛
                                                                                   3 .3 ⎞
                                                                            ⎜           ⎟ * 25 = 6.6
                                                                                ⎝ 12.5 ⎠

                                                                                 ∴ VCD = 6.6V

                                                  Power in a Series Circuit ‫א‬‫א‬‫א‬‫٨ א‬J ٤
                            
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
                                                                                          W

                                                                   PT = P1 + P2 + ........... + Pn
                                                                   K‫א‬‫א‬‫א‬ PT 
                                   W‫א‬‫א‬‫א‬‫א‬
                                                                                     1)      PT = VS I
                                                      - ٤٩ -
             ‫א‬‫א‬‫א‬                               ‫٠٤١ א‬                             ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬           ١-                     



                                                                               2) PT = I 2 R T

                                                                                          2
                                                                                         VS
                                                                                 3) PT =
                                                                                         RT

                                                                                                         
                                                                                     E١٣J ٤F
                                                                     W‫א‬‫א‬‫א‬‫א‬‫א‬

                                                              R٢ = ١٨ Ω


                                                                           R٣ = ٥٦ Ω
                              VS = ١٥ V

                                                                           R٤ = ٢٢ Ω



                 E١٣J ٤F‫א‬‫א‬‫א‬E١٧J ٤F
                                                                                                    ‫א‬
                                                                           K‫א‬‫א‬
                                                           R T = 10 + 18 + 56 + 22 = 106 Ω

                         W‫א‬E٣F‫א‬‫א‬‫א‬‫א‬
                                                                   VS (15)2
                                                                    2
                                                           ∴ PT =    =     = 2.12 W
                                                                   RT   106
                                                                               ∴ PT = 2.12 W




                                                 - ٥٠ -
                ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                          ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                 ١-                 



                                                                                          E١٤J ٤F
          
،٠{٥ W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                       ‫؟‬‫א‬‫א‬‫א‬
                                                      R١ = ١kΩ         R٢ = ٢٫٧kΩ                             
                                                                                                              
                                                                                      R٣ = ٩١٠Ω               
                   VS = ١٢٠ V                                                                                 
                                                                                     R٤ = ٣٫٣kΩ
                                                                                                              
                                                                                                              
                    E١٤J ٤F‫א‬‫א‬‫א‬E١٨J ٤F
                                                                                                       ‫א‬
                                                                                    ‫א‬‫א‬

                                                                      R T = R1 + R 2 + R 3 + R 4
                                                         R T = 1 + 2.7 + 0.91 + 3.3 = 7.91 kΩ
                                                                                     R T = 7.91 kΩ

                                                                                                              
                                                          ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                               VS 120
                                                                       I=        =     = 15.2 mA
                                                                               R T 7.91
                                                                      W‫א‬
                                                      P1 = I 2 R 1 = (15.2 mA )2 (1 kΩ ) = 231 mW

                                        P2 = I 2 R 2 = (15.2 mA )2 (2.7 kΩ ) = 624 mW = 0.62 W

                                          P3 = I 2 R 3 = (15.2 mA )2 (910 Ω ) = 210 mW = 0.21 W
                                                                                    762
                      P4 = I 2 R 4 = (15.2 mA )2 (3.3 kΩ ) = 762 mW =                  = 0.762 W
                                                                                   1000



                                                         - ٥١ -
                ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                                ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                     



                                                                                       
‫א‬‫א‬  R 4 ، R 2 ‫א‬‫א‬
                                    W‫א‬‫א‬،15.2mW
                                                                                 P2 = 0.62 W > 1 W
                                                                                                2
                                                                                P4 = 0.762 W > 1 W
                                                                                                2
 K‫א‬١w‫א‬‫א‬‫א‬

                                       Voltage With Respect to Ground ‫א‬ ٩J ٤
                                                                     
E‫א‬F‫א‬‫א‬‫א‬ 
    
 K‫א‬‫א‬‫א‬‫א‬‫א‬،Reference Point.
‫א‬،١٠٠V‫א‬‫א‬‫א‬
                                                                 
 KCircuit Ground‫א‬‫א‬‫א‬١٠٠V‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬Ground‫א‬‫א‬‫א‬‫א‬
                                         
                                                                       KE١٩J ٤F




                                                         - ٥٢ -
                 ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                                 ‫א‬
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                ١-                     



                                                                                                                    
                                                                                                                        
                                                                               +                                        
                                                                      R1       V1
                          +
                                                                                                                        
                                                                               −
                          V2                                           a                                                
                          −                                                                                             
                                                                                   +
                                                                     R2            V2   V                               
                                                                                   −                                    
                                                                                                                        
                                                                                                                        
                                           ‫א‬‫א‬E١٩J ٤F
                                                                                              Note
                                                a‫א‬‫א‬
                                                                                             E١٥J ٤F
          
،‫א‬‫א‬‫א‬‫א‬‫א‬
                                       K٢٥ VVoltage Dropped ‫א‬‫א‬
                                                                                                                        
                     +            −       +     −                              +        −        +          −
          a                                           c                 a                                      c
                                      b                                                     b                      
+                                                     +       +                                                     +
100V                                                          100V                                                      
−                                     −         +     −        −                             −              +       
                                                                                                                    −
          e                                           d                 e                                           d
                                                                                                                        
                                     (a)                                               (b)
                                                                                                                    
                E١٥J ٤F‫א‬‫א‬‫א‬ b)،(aE٢٠J ٤F



                                                          - ٥٣ -
                ‫א‬‫א‬‫א‬                                         ‫٠٤١ א‬                          ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                      ١-                 



                                                     

                                               +         −         C
                                                                                    c
                                         a
                                                             b
                                 +                                                      +
                                 100V
                                 −                            −             +           −
                                         e                                              d

                                                             (c)
                  E١٥J ٤F‫א‬‫א‬‫(א‬c)E٢٠J ٤F
                                                                                                              ‫א‬
                                                                                              W‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬EaF‫א‬‫א‬
 Va ‫א‬،a‫א‬‫א‬، Va ‫א‬
                                      K‫א‬a‫א‬‫א‬a‫א‬
                W‫א‬‫א‬‫א‬‫א‬‫א‬ EaF‫א‬‫א‬
                                                                                                  Ve = 0
                                                                                              Vd = +25V
                                                                                              Vc = +50V
                                                                                              Vb = +75V
                                                                                             Va = +100V

                           W‫א‬‫א‬d‫א‬Eb F‫א‬‫א‬

                                                                                             Ve = −25V
                                                                                              Vd = 0V
                                                                                             Vc = +25V
                                                                                              Vb = +50

                                                         - ٥٤ -
                ‫א‬‫א‬‫א‬                                ‫٠٤١ א‬                            ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬             ١-                   



                                                                                   Va = +75V
            W‫א‬‫א‬،c‫א‬،EcF‫א‬‫א‬

                                                                                   Ve = −50V
                                                                                   Vd = −25V
                                                                                     Vc = 0V
                                                                                   Vb = +25V
                                                                                     Va = +50V

 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬،a‫א‬‫א‬‫א‬
                                                                                    K‫א‬
                                                                                         W‫א‬‫א‬
                                                
Ke ← ،d،c،b‫א‬‫א‬a‫א‬‫א‬‫א‬
                                         
KJ ،H‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                       W VA EaF‫א‬‫א‬
                                                                                Va = VS = 100V
                                                                           Vb = 100 − 25 = +75V
                                                                   Vc = 100 − 25 − 25 = +50V
                                                              Vd = 100 − 25 − 25 − 25 = +25V

                                                                 ‫א‬e‫א‬
                                                                Ve = Vs + Vb + Vc + Vd + Ve
                                                              Ve = 100 − 25 − 25 − 25 − 25 = 0
                                                                                        ∴ Ve = 0

                                                                                              Note 
          W‫א‬‫א‬‫א‬‫א‬


                                                     - ٥٥ -
                ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                               ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                 ١-                     



                                                                             
‫א‬‫א‬‫א‬‫ א‬‫א‬W‫א‬‫ א‬E١
                                                                      
‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬
                                                                     KE‫א‬‫א‬F‫א‬‫א‬
                                                                      
‫א‬‫א‬‫א‬W‫א‬‫ א‬E٢
 
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                   W R1 ‫א‬
                                                                                        Vb = Vs − IR 1

                                               Kc،b،a‫א‬‫א‬‫א‬‫א‬

                                                                      Troubleshooting ‫א‬‫א‬ ١٠J ٤
              W‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                  KOpen Circuit           ‫א‬‫א‬‫א‬‫א‬‫א‬ E١F
                                                   KShort Circuit‫א‬‫א‬‫א‬‫א‬‫א‬ E٢F
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                               
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،Open Circuit‫א‬‫א‬
               W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
                                                   
‫א‬‫א‬‫א‬‫א‬ K١
                                                                   
                                                                                            V = IR = 0
‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                          K‫א‬
                                               Cheek For Burned Resistor‫א‬‫א‬ K٢
                                                 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                         K‫א‬‫א‬‫א‬‫א‬‫א‬



                                                         - ٥٦ -
                ‫א‬‫א‬‫א‬                                     ‫٠٤١ א‬                               ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                   ١-                    



                                                                                                                      
                                                   0V                            0V                 
                                                               + 10V −
                                                                                                                          
                                                                                                                              
                                       R1           R2                           R2
                                                                                                                          
                                                     VS = 10V
                                                                                                                          
                                    Short Circuit‫א‬‫א‬E٢١J ٤F
‫א‬‫א‬KShort‫א‬‫א‬‫א‬
                                                                                                             
‫א‬‫א‬‫א‬‫א‬
                                                               
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
                                                                                                   
                                                   K‫א‬‫א‬‫א‬‫א‬ 
                                                                                               E١٦J ٤F
        
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                         W‫א‬، VS = 100V 
                                                                      K‫א‬‫א‬‫א‬‫א‬‫א‬E
                  ‫؟‬‫א‬‫؟‬‫א‬،‫א‬‫א‬ A, B ‫א‬Short‫א‬E
                                                                                                                  
                                              10Ω                  18Ω                                            
                                                          c
                                                                                  b
                                                                                                                  
                  −
                                                                                                                  
                  VS = 100V                                                       33Ω
                                                                                                                  
                  +
                                                                39Ω                                               
                                                                                                                  
                                        a
                                                    
                    E١٦J ٤F‫א‬‫א‬‫א‬E٢٢J ٤F




                                                          - ٥٧ -
                ‫א‬‫א‬‫א‬                                       ‫٠٤١ א‬                             ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                     ١-                  



                                                                                                              ‫א‬
                                                                      K R T ‫א‬W
                                                                                                              

                                                                 R T = 10 + 18 + 33 + 39 = 100 Ω
                                                                                                100
                                                                                          I=       =1A
                                                                                                100
                                                                                                        
‫א‬‫א‬‫א‬K A, B ‫א‬ShortW 
                                                             K‫א‬‫א‬‫א‬ A, B ‫א‬
                                                                 ‫א‬‫א‬‫א‬
                                                                                 R T = 18 + 10 = 28 Ω
                                                                                                                    
                                              10Ω                 18Ω                                               
                                                                                   b                                
                                                            C
                 −                                                                                           
                 VS = 100V                          I                                  33Ω                          
                 +                                                     
                                     a                                                                              
                                                                 39Ω
                                                        
                      E١٦J ٤F‫א‬‫א‬‫א‬E٢٣J ٤F

                                                                                       VS 100
                                                                                I=       =    = 3.57 A
                                                                                       RT   28

                                                                                                          W‫א‬
K 3.57 A 1 A ‫א‬‫א‬، A, B ‫א‬
                                                       
‫א‬‫א‬‫א‬‫א‬‫א‬
    
 A, C ،‫א‬‫א‬‫א‬
             
‫א‬‫א‬18 Ω ، 33 Ω ، 39 Ω ‫א‬‫א‬‫א‬
                                                                              
                                                                                          K‫א‬‫א‬‫א‬‫א‬

                                                            - ٥٨ -
                ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                           ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                ١-                   



                                                                                        R T = 10 Ω
                                                                                   VS 100
                                                                             I=      =   = 10 A
                                                                                   R T 10

                                                                             10 A ‫א‬‫א‬
                                                                                          Summary ‫א‬
                                                              K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                 K‫א‬‫א‬‫א‬‫א‬
                     KKVL‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                    K‫א‬‫א‬‫א‬‫א‬
                                                                              
Series-Opposition‫א‬‫א‬ ‫א‬
                                                             K‫א‬‫א‬‫א‬‫א‬
      K‫א‬‫א‬‫א‬Voltage Drops‫א‬
                                                  
‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬
                                                 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                      K‫א‬‫א‬
                  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                              K‫א‬‫א‬‫א‬‫א‬
          K‫א‬‫א‬‫א‬‫א‬Ground‫א‬
    K‫א‬Negative Ground‫א‬‫א‬
                            
‫א‬‫א‬‫א‬‫א‬‫א‬Positive Ground‫א‬‫א‬
                                                                                             K
‫א‬‫א‬‫א‬‫א‬‫א‬Open circuit‫א‬‫א‬‫א‬‫א‬
                                                                                                   K‫א‬



                                                         - ٥٩ -
                ‫א‬‫א‬‫א‬                                       ‫٠٤١ א‬                            ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                     ١-                  



                                               ‫א‬‫א‬‫א‬
                                                                                                                    
    K A, B ‫א‬‫א‬‫א‬‫א‬‫א‬ K١
           A
                             R١
                                                            A                      B                                
                              R٢                                                                                    
                                                                R١         R٢          R٣                           
                              R٣
                                              B                                                                     
                                                                                                                    
                                                                                                                  
                          A
                                                  R٢
                                                                                                                    
                                                                                            B
                                                                                                                    
                        R١                                            R٤
                                                  R٣
                                                                                       R٥
                                                                                                                    
                                                                                                                    
                                                                                                                    

12V ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ K٢
                                                                                120Ω ‫א‬‫א‬
               
‫א‬‫א‬، 5mA ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٣
                                                                                   ‫؟‬‫א‬‫א‬‫א‬
                                                        A                                                           
                                                                      R٣                                            
                                   +               5 mA
                                                                                   A                                
                                   VS
                                                                                                                    
                                   −
                                                                                                                    
                                                                           R1
                                                                                                                    
                                                                                                                    
                                                       A
                                                                      R2
                                                                                                                    

                                                            - ٦٠ -
             ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                            ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                  



                                                                                                              
                  W‫א‬‫א‬‫א‬ R T ‫א‬‫א‬ K٤
                                                                                 1000 Ω ، 500 Ω EF
                                                                                56 Ω ، 47 Ω EF
                                                                      10 kΩ ، 2.2 kΩ ،1.5 kΩ EF
                                                           2.2 MΩ ،1 kΩ ، 470 kΩ ،1 MΩ EF
                                                                                                              
                                                     ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٥
                R 2 = 10 Ω                                                                                    
                                                                                                              
                                                     R 2 = 10 Ω R1 = 4.7 Ω
                                                                                                              
                                                                                        R 3 = 12 Ω
             R 1 = 25.6 kΩ                                                                                    

                                                         R4 =1Ω
                                                                                                              
                                                                                                              
                R 3 = 2.2 kΩ
                                                                                                              
                     (a )                                          ( b)
                                                                                                              
                                                                                                              
                                           R 1 = 1 MΩ R 5 = 10 M Ω                                            
                                                                                                              
                                                                             R1 = 1 MΩ
                                                                                                              
                                                                                                              
                                                                                                              
                                                                             R 2 = 560 kΩ
                                                                                                              
                                           R 3 = 5.6 MΩ                                                       
                                                                                                              
                                                   (c)                                                        
                                                                                                              

                                                      - ٦١ -
                 ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                                ‫א‬
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                 ١-                      



‫א‬، 100 mA ‫א‬‫א‬‫א‬‫א‬‫א‬ K٦
                                                                                                       ‫؟‬‫א‬‫א‬

                                                         R 1 = 45 Ω
                                  −
                                  VS                                            R 2 = 15 Ω
                                  +
                                                       R 3 = 90 Ω
                                               A



       
، 25V  R 2 ‫א‬، 25mA  R1 ‫א‬‫ א‬‫א‬‫א‬‫א‬ K٧
                                                                                          ‫؟‬ R 2 


                                                A
                                                              R1
                              −
                              VS                                     R2           V
                              +
                                                             R3



، R1 = 10Ω ‫א‬، VS = 48V ‫א‬‫א‬‫א‬ K٨
                                                    ‫؟‬‫א‬‫א‬‫ ؛‬R 3 = R 4 = 47Ω ، R 2 = 96Ω

، VS = 24V ‫א‬ R 2 = 5.6 kΩ ، R 1 = 4.7 kΩ ‫א‬‫א‬ K٩
                                                                   ‫؟‬‫א‬
                                                                                                                         
                                           
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٠
                                                                                            W‫؟‬ VS
                                                        ، R 3 = 330Ω ، R 2 = 56Ω ، R 1 = 100Ω

                                                          - ٦٢ -
                ‫א‬‫א‬‫א‬                                      ‫٠٤١ א‬                           ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                    ١-                 



                                                      V5 = 1.124V & R 5 = 47Ω ، R 4 = 220Ω
                                                                                                                    
                                                       R1                     R2                                    
                                                                                                                    
                                                       I                                                            
                                                                                                                    
                                                                                   R3                               
                                       VS
                                                       R5                  R4                                       
                                                                                                                    
                                                           V                                                        
                                                                                                                    
                                                                               
، V1 = 4.69 V  R1 ‫א‬‫א‬ VS = 15 V ‫א‬‫א‬‫א‬ K١١
                                                                          ‫؟‬ R 1 = 1.5 kΩ  R 2 

                                                                        R 1 = 1.5 kΩ, V1 = 4.69 V
                                                                                                                    
                                                               V                                                    
                                                                                                                    
                                 +                             R1                 R2
                                                                                                                    
                                 VS = 15V                                                                           
                                 −
                                                                                                                    
                                                                                                                    
                                                  
 I = 1.43mA ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٢
، V1 = 2V2 ‫א‬‫א‬، VS = 15V 
                                                               ‫؟‬ R 3 ، R 2 ، R1 ، V2 = 2V3

                                         ‫؟‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٣


                                                           - ٦٣ -
                ‫א‬‫א‬‫א‬                                    ‫٠٤١ א‬                           ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-              



                                                                       ، R 2 = 10KΩ ، R 1 = 15KΩ
                                                                       R 4 = 2.2KΩ ، R 3 = 6.8KΩ

                                                                                                

                                                        R1                  R2                                   
                                              a

                                                                                                                 
                            VS1 = 24V
                                                                                 R3
                                                                                                                 
                           VS2 = 12V                                                                             
                                                                            R4
                                                                                                                 
                                                                                                                 
                                                                 
 VS1 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٤
                                          ‫؟‬‫א‬‫א‬،a‫א‬‫א‬
                                                                                 
                                                                                                             
                          W 2.16V  R1 ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ K١٥
                                        WK،E R 3 ‫א‬‫א‬F V3 ‫א‬،E V1 = 2.16V F
                                      R 4 = 220KΩ & R 3 = 560Ω ، R 2 = 1KΩ ، R 1 = 390Ω

                                                                                                                 
                                                              VS2                                                
                                              R 1 = 390 Ω            R 2 = 1 kΩ                                  
                                       A
                                                                                                                 
                                                  I                                                              
                                                                                      R 3 = 560 Ω
                             VS1                                                                                 
                                                                                                                 
                                                             R 4 = 220 Ω
                                                                                                                 
                                                                                                                 


                                                         - ٦٤ -
                ‫א‬‫א‬‫א‬                                         ‫٠٤١ א‬                          ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                     ١-                  



‫א‬ VS2 ، VS1 = 15V ‫א‬E١٥F‫א‬‫א‬‫א‬ K١٦
                                              KE V1 = 3.77V FW 3.77V  R1 ‫א‬‫א‬
                                                                                                                 
‫א‬‫א‬ R1 ‫א‬‫א‬ VS 2 ‫א‬ K١٧
‫א‬‫א‬‫א‬ VS2 ‫א‬EE١٥F‫א‬‫א‬F R 2
                    ‫؟‬‫א‬‫א‬‫א‬ V4 ، V3 ، V2 ، V1 ‫א‬‫א‬،E١٦F
         
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٨
 A, B, C, D ‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F
                                                                                                 W‫؟‬
                                    R 1 = 12 kΩ, R 2 = 22 kΩ, R 3 = 47 kΩ & R 4 = 15 kΩ 
                                     d                                                                 
                                                                                   c
                                                                                                                     
                                                         R4
                                                                                                                     
                                                                          R3
                                                                                                                     
                                                                            b                                        
                                                                                                                     
                +
                                                                          R2                                         
                VS = 48V
                −                                                           a                                        
                                                                                       +
                                                                          R1                                         
                                                                                       V1
                                                                                       −                             
                                                                                                                     
                                                                                                                     
‫א‬‫א‬‫א‬ 560 Ω ‫א‬‫א‬‫א‬‫ א‬K١٩
                                                                                   ‫؟‬ R = 27 Ω ‫א‬‫א‬

                           W‫א‬‫א‬‫א‬ A, B ‫א‬‫א‬ K٢٠
                                                                                                                     

                                                              - ٦٥ -
             ‫א‬‫א‬‫א‬                               ‫٠٤١ א‬                 ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬           ١-         



                                                                    A                         
                                                 100 Ω
                                                                                              
                                           +                                                  
                                           12V            56 Ω
                                                                                              
                                           −
                                                                                              
                                                                    B                         
                                                                                              
                                                                                              
                                                                                              
                                                     1kΩ                                      
                                                                                              
                                                                        A
                                                                                              
                                            +      2.2kΩ
                                            8V
                                            −
                                                   3.3kΩ


                                                                        B



                                                      b




                                                 - ٦٦ -
                                                                         ‫א‬‫א‬‫א‬
                                                                      ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                                                          ‫א‬‫א‬‫א‬‫א‬




                                                    ١ J
                                           ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬




٥
           ‫א‬‫א‬                                   ‫٠٤١ א‬                             ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                 



                                          ‫א‬‫א‬‫א‬‫א‬
                                                                                                           
                                               W‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                                           K‫א‬‫א‬‫א‬ •
                                                               K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                       K‫א‬‫א‬‫א‬ •
                                 K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                                       K‫א‬‫א‬‫א‬ •
                                                                             K‫א‬ •
                                                K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •




                                                      - ٦٧ -
              ‫א‬‫א‬                                       ‫٠٤١ א‬                                      ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                      ١-                          



                                                                                                Introduction ١J ٥
                                     
،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬KVoltage Drop‫א‬‫א‬
                                                                                   KVoltage Divider
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                        
،‫א‬،‫א‬‫א‬
                                                         
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬،KCL
 K‫א‬‫א‬Current Divider‫א‬
                                                                                Parallel Circuit‫א‬‫א‬‫א‬
‫א‬EF‫א‬‫א‬‫א‬
E‫א‬F‫א‬‫א‬E‫א‬F‫א‬‫א‬
،‫א‬‫א‬‫א‬K‫א‬‫א‬
                                                  
E١J ٥F‫א‬‫א‬‫א‬K‫א‬
                                                                                                      K‫א‬‫א‬‫א‬
                    A                                                                                                      
                                            I1                             A          I         I1        I2
                                I                      I2                                                                  
                               R1                                                     R1                 R2                
                                                  R2
                                                                                                                           
                   B                                                       B                                               
                                                                                                                           
                                             R1                        A
               A                                                                  I                                        
                         I           I1
                                                                                           I1             I2
                                             R2
                         I2                                                         R1                          R2
                                                                                                                           
               B                                                       B                                            
                                       K‫א‬‫א‬‫א‬EJ ١J ٥F
                                                              - ٦٨ -
               ‫א‬‫א‬                                ‫٠٤١ א‬                               ‫א‬
    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬               ١-                   



                                        I1                                                                    

                               R1                           A
                                                                                       I2
                                                                     I       I1
                 A                                                          R1              R2
                           I
                                        R2
                                                           B
                                        I2                                        R3        I٢
                  B

                                  K‫א‬‫א‬‫א‬EJ ١J ٥F

                                 Voltage Drop in Parallel Circuit‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥
                                        
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
     K‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
                                                                                         E١J ٥F
                                        E٢J ٥F‫א‬‫א‬
                                                                                                              
                               VS =                                                                           
                               25V
                                                                                                              
         R1 =                                    R2 =            R3 =              R4 =             R5 =
        1.8kΩ
                                 F
                                                 1kΩ             2.2kΩ             2.2kΩ            3.3kΩ 
                                                
                                                                                                              
                                KE١J ٥F‫א‬‫א‬‫א‬E٢J ٥F
                                                                                                          ‫א‬
                                                                    
 ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                 W‫א‬‫א‬‫א‬

 V1 = V2 = V3 = V4 = V5 = VS = 25V

                                                        - ٦٩ -
             ‫א‬‫א‬                                   ‫٠٤١ א‬                            ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                



                                            Kirchhoff’s Current Law٣J ٥
                                                                      
‫א‬‫א‬‫א‬‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Node
                                                                       
                                                       K‫א‬‫א‬‫א‬‫א‬

                                                                                          E٢J ٥F
،E٣J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                    K A ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                            
                                                      A
                                                                               I 2 = 12mA
                                               IT          I1 = 5mA
                             +                                                                              
                             VS                           R1                    R2
                                                                                                            
                             −                  IT                                                          
                                                                                                            
                                                      B
                        KE٢J ٥F‫א‬‫א‬‫א‬E٣J ٥F

                                                                                                        ‫א‬
‫א‬ R1 ‫א‬‫א‬ 5mA ‫א‬‫א‬ A ‫א‬‫א‬‫א‬
                                   W A ‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬12mA

              I T = I1 + I 2

                   = 5mA + 12mA = 17 mA
              ∴ I T = 17mA

                                                                                                            




                                                       - ٧٠ -
             ‫א‬‫א‬                                              ‫٠٤١ א‬                               ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                          ١-                      



                                                                                                        E٣J ٥F
                                            KE٤J ٥F‫א‬ R 2 ‫א‬‫א‬‫א‬
                                                                                                                              
                                                                                                                              


                      IT = 100mA                                                                                          
                                                   A
                                                                                                       I 3 = 20mA         
                                     I1 = 30mA
           +                                                                     I2
           VS                                           R1                    R2                       R3
                                                              
           −
                                IT                            
                                                   B          
                                                                  


                        KE٣J ٥F‫א‬‫א‬‫א‬E٤J ٥F
                                                                                                                      ‫א‬
                                                                   I T  A ‫א‬‫א‬‫א‬‫א‬‫א‬

               I T = I1 + I 2 + I 3

               ∴ 100mA = 30mA + I 2 + 20mA

               ∴ I 2 = 100mA − 50mA = 50mA

                                                                                                        E٤J ٥F
‫א‬ A1 , A 2 ‫א‬‫א‬‫א‬‫א‬
                                                                                                                    W‫א‬
                                            5A          x                        y           I3                           
                                                                                                                          
                           +                                           
                           VS                      R1                       R2                    R3                      
                           −
                                                             I1 = 1.5A                 I 2 = 1A                           
                                              IT
                                                                                                                          
                        KE٤J ٥F‫א‬‫א‬‫א‬E٥J ٥F

                                                               - ٧١ -
             ‫א‬‫א‬                                   ‫٠٤١ א‬                            ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                



                                                                                                          ‫א‬
              W 5A  x ‫א‬‫א‬‫א‬‫א‬‫א‬
               5A = 1.5A + I A1

                                                       K A1 ‫א‬‫א‬‫א‬ I A1 W
              ∴ I A1 = 5 − 1.5 = 3.5A

                                            K 3.5A ‫א‬‫א‬‫א‬ y ‫א‬‫א‬
               ∴3.5A = 1A + I A 2
               ∴ I A 2 = 3.5 − 1 = 2.5A

                                                                                W‫א‬‫א‬‫א‬∴
               I A1 = 3.5A
               I A 2 = 2 .5 A

                        Total Parallel Resistors‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٥
                                             ‫א‬‫א‬ R T ‫א‬‫א‬W
                                                                                         
‫א‬‫א‬‫א‬‫א‬‫א‬
  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                 I1          R1                                             
                                                                                                            
                                                 I2          R2                                             
                                            
                                                 IT                                                         
                                                                                                            

                                                              + VS −
                                                                                                  
                                                                                                            
                                    R1 , R 2 ‫א‬‫א‬E٦J ٥F




                                                         - ٧٢ -
             ‫א‬‫א‬                                   ‫٠٤١ א‬                                ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                    



                                                                           
‫א‬‫א‬،‫א‬‫א‬ R1, R 2 ‫א‬‫א‬‫א‬‫א‬
                                                                              W‫א‬ R T E‫א‬‫א‬F
                                                           W‫א‬،

               I T = I1 + I 2                                                                             E١J ٥F

                                      W‫א‬‫א‬‫א‬‫א‬
               VS VS VS
                  =  +                                                                                    E٢J ٥F
               R T R1 R 2

                                            K VS ‫א‬‫א‬‫א‬
                1   1   1
                  =   +                                                                                   E٣J ٥F
               R T R1 R 2

                              
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣J ٥F‫א‬
                                                        
‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                                                             W‫א‬‫א‬
                1  R + R2
                  = 1                                                                                     E٤J ٥F
               R T R1 ∗ R 2
                                                                                                          W
                        R1 ∗ R 2
               RT =                                                                                       E٥J ٥F
                        R1 + R 2

    K‫א‬‫א‬‫א‬ R T 
                                                           ‫א‬‫א‬ R T W




                                                         - ٧٣ -
             ‫א‬‫א‬                                ‫٠٤١ א‬                             ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬               ١-                 



                                                                                                          
                                             I1            R1                                             
                                                                                                          
                                                                                                          
                                             I2            R2
                                                                                                          
                                                                                                          
                                             I3            R3
                                                                                                          
                                                                                                          
                                              IT
                                                                                                          
                                                                                                          
                                                           + VS −                                         
                                                   
                         R1, R 2 , R 3 ‫א‬‫א‬E٧J ٥F
                                                                     W
               IT = I1 + I 2 + I3                                                                   E٦J ٥F
                                                                   W‫א‬
               VS VS VS VS
                  =  +   +                                                                          E٧J ٥F
               R T R1 R 2 R 3
                                                                             W‫א‬ VS 
                1   1   1   1
                  =   +   +                                                                         E٨J ٥F
               R T R1 R 2 R 3
                                                                                         W
                            R1 ∗ R 2 ∗ R 3
               RT =                                                                                 E٩J ٥F
                        R1R 2 + R1R 3 + R 2 R 3

‫א‬‫א‬‫א‬‫א‬ R T ‫א‬‫א‬
      
                                                            K‫א‬




                                                   - ٧٤ -
             ‫א‬‫א‬                                  ‫٠٤١ א‬                            ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                ١-                 



                                                                                
‫א‬‫א‬ R T ‫א‬‫א‬‫א‬
                                                                                         W‫א‬‫א‬
                                           1
               RT =                                                                  E١٠J ٥F
                         1     1     1       1
                        ( ) + ( ) + ( ) +K+ ( )
                         R1    R2    R3      Rn

                                                                                        E٥J ٥F
                                    W‫א‬‫א‬ A, B ‫א‬ R T ‫א‬‫א‬‫א‬
                                                                                                           
                   A

                                                                                                           
                                               R 1 = 100Ω         R 2 = 47Ω             R 3 = 22Ω          
                                                                                                           
                   B                                                                                       
                        KE٥J ٥F‫א‬‫א‬‫א‬E٨J ٥F
                                                                                                       ‫א‬
                                                      WE٩J ٥F‫א‬‫א‬‫א‬

                            R1 ∗ R 2 ∗ R 3
               RT =
                        R1R 2 + R1R 3 + R 2 R 3

                                                                        

                                100 ∗ 47 ∗ 22
               RT =                                   = 13Ω
                        100 ∗ 47 + 100 ∗ 22 + 47 ∗ 22

                                                        ‫א‬‫א‬‫א‬‫א‬١J ٤J ٥
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                 W

              QR1 = R 2 = R 3 = K = R n = R                                          E١١J ٥F



                                                       - ٧٥ -
              ‫א‬‫א‬                                    ‫٠٤١ א‬                                    ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                        


                            1
               ∴R T =         R                                                               E١٢J ٥F
                            n
                              R
               or R T =                                                                       E١٣J ٥F
                              n

                                   K‫א‬‫א‬‫א‬‫א‬‫א‬ R W
                                                                           
،‫א‬‫א‬‫א‬
         K‫א‬‫א‬‫א‬
                                                                                                  E٦J ٥F
  K R T ‫א‬‫א‬‫א‬‫א‬ 8Ω 

                                                                                                                 ‫א‬
                            W‫א‬‫א‬
                         R 8
               RT =       = = 2Ω
                         n 4

             Determining an unknown Parallel Resistor‫א‬‫א‬‫א‬٥J ٥
،‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                        
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
‫א‬‫א‬‫א‬ R T ‫א‬‫א‬‫א‬‫א‬
                  WEE٥J ٥FF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                          R1R 2
                RT =
                         R1 + R 2

                                                                                 
‫א‬ R X ‫א‬ R A ‫א‬‫א‬
                                                                                                                   W‫א‬




                                                          - ٧٦ -
             ‫א‬‫א‬                               ‫٠٤١ א‬                             ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬              ١-                 


                                                                                                               




                                                         RA                                               
                                                                                                          
                                                         RX                                               
                                                                                                          
                                                                                                          
                                                          RT
                                                  
                       K‫א‬E٩J ٥F

 R X ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                        W

                         R AR X
               RT =                                                         E١٤J ٥F
                        RA + RX

               R T (R A + R X ) = R A R X                                   E١٥J ٥F

               RTR A + RTR X = R AR X                                       E١٦J ٥F

               R T R A = (R A − R T )                                       E١٧J ٥F

                             RTRA
              ∴R X =                                                        E١٨J ٥F
                            RA − RT

                                                                                           E٧J ٥F
‫א‬‫א‬‫א‬ 150Ω ‫א‬‫א‬
                                            ‫؟‬‫א‬‫א‬‫א‬K 330Ω ‫א‬
                                                  
                                                  R A = 330Ω
                                                                                                          
                                                  
                                                   RX

                       KE٧J ٥F‫א‬‫א‬‫א‬E١٠J ٥F
                                                   - ٧٧ -
             ‫א‬‫א‬                                  ‫٠٤١ א‬                            ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                 ١-                



                                                                                                       ‫א‬
‫א‬ 330Ω ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                   W‫א‬‫א‬‫א‬‫א‬‫א‬

                         R AR X
                RT =
                        RA + RX

                         330R X
                150 =
                        330 + R X

                150(330 + R X ) = 330R X

                150 * 330 = 330R X − 150R X

                           150 * 330
              ∴R X =                 = 275Ω
                             180

                                                                                             E٨J ٥F
                            KE١١J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬
                           10mA                                                                            
                                                                                                           
            +                                                                                              
            VS                             R 1 = 220Ω      R 2 = 560Ω        R 3 = 1kΩ
                                                                                                           
            −
                                                                                                           
                                                                                                           
                       KE٨J ٥F‫א‬‫א‬‫א‬E١١J ٥F
                                                                                                       ‫א‬
 R T ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
                                                                                     W

                             R1 ∗ R 2 ∗ R 3
                RT =
                        R 1R 2 + R 1R 3 + R 2 R 3


                                                        - ٧٨ -
              ‫א‬‫א‬                                  ‫٠٤١ א‬                                  ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                 ١-                     


                                  220 ∗ 560 ∗ 1000
               RT =                                          = 136Ω
                         220 ∗ 560 + 220 ∗ 1000 + 560 ∗ 1000
               ∴ V = IT * R T = 10mA * 136Ω = 1.36V

                                                                                                 E٩J ٥F
          
 ‫א‬،1kΩ ‫א‬ R 3 = 680Ω ‫א‬‫א‬‫א‬
                                                                                                  K IT = 10mA
                                                                                                             ‫א‬
                                                  W R T ‫א‬‫א‬‫א‬‫א‬

                              R1 ∗ R 2 ∗ R 3
                RT =
                         R 1R 2 + R 1R 3 + R 2 R 3

                                  220 ∗ 560 ∗ 680
                RT =                                       = 128Ω
                         220 ∗ 560 + 220 ∗ 680 + 560 ∗ 680

               ∴ V = I T * R T = 10mA * 128Ω = 1.28V

              Current Division in Parallel Circuits‫א‬‫א‬‫א‬‫א‬EF٦J ٥
،‫א‬‫א‬‫א‬‫א‬ R T ‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬KBranches‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                      
                                 
‫א‬‫א‬‫א‬‫א‬‫א‬Current Divider Law‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
                                            W‫א‬،E١٢J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬




                                                        - ٧٩ -
              ‫א‬‫א‬                                    ‫٠٤١ א‬                                 ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                   ١-                    



                                            I1           R1                                                        


                                            I2           R2


                                                 I


                                                            + VS −
                                                        
                               K‫א‬‫א‬‫א‬‫א‬E١٢J ٥F

                          W I ‫א‬ I1 , I 2 ‫א‬‫א‬‫א‬

               V = I*RT                                                                     E١٩J ٥F

               V = I1 * R 1                                                                 (٢٠J ٥F

               V = I2 * R 2                                                                 E٢١J ٥F

                 W،‫א‬‫א‬،E٢٠J ٥F‫א‬E١٩J ٥F‫א‬

               I * R T = I1 * R 1                                                           E٢٢J ٥F

                         RT
               I1 = I                                                                       E٢٣J ٥F
                         R1

                        W،‫א‬‫א‬،E٢١J ٥FE١٩J ٥F‫א‬
                         RT
               I2 = I                                                                       E٢٤J ٥F
                         R2

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬Node‫א‬‫א‬‫א‬
                                                                                
                                                             W‫א‬‫א‬‫א‬


                                                        - ٨٠ -
             ‫א‬‫א‬                                      ‫٠٤١ א‬                            ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                     ١-                


                         RT
               IX = I                                                                    E٢٥J ٥F
                         RX
                                                                                   K X = 1,2,3,K, n W
                                            K‫א‬‫א‬‫א‬‫א‬‫א‬ W      RT
                                                      K‫א‬‫א‬‫א‬‫א‬ W    RX
‫א‬‫א‬‫א‬ X ‫א‬ X ‫א‬‫א‬ W                     IX
                                                                                         K‫א‬




                                                           - ٨١ -
             ‫א‬‫א‬                                      ‫٠٤١ א‬                           ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                     ١-               



                                                                                           E١٠J ٥F
                                       KE١٣J ٥F‫א‬Branch‫א‬
                                                 I1       R1 = 680Ω                                           

                                                                                                              
                                                 I2       R 2 = 330Ω


                                                 I3        R 3 = 220Ω


                                                  10A
                                                                                                                  

                      KE١٠J ٥F‫א‬‫א‬‫א‬E١٣J ٥F

                                                                                                          ‫א‬
‫א‬‫א‬‫א‬، 10A ‫א‬‫א‬‫א‬‫א‬
                                           K‫א‬ R T ‫א‬‫א‬
                              R1 ∗ R 2 ∗ R 3
               RT =
                         R 1R 2 + R 1R 3 + R 2 R 3

                                  680 ∗ 330 ∗ 220
               RT =                                        = 111Ω
                         680 ∗ 330 + 680 ∗ 220 + 330 ∗ 220

                          RT        111
              I1 = I T       = 10 ∗     = 1.63A
                          R1        680

                           RT        111
              I2 = IT         = 10 ∗     = 3.36A
                           R2        330

                           RT        111
              I3 = IT         = 10 ∗     = 5.05A
                           R3        220




                                                            - ٨٢ -
              ‫א‬‫א‬                                ‫٠٤١ א‬                                  ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬               ١-                     



           W I 3 ‫א‬ I1 , I 2 

                I T = I1 + I 2 + I 3

                10 = 1.63 + 3.36 + I 3

                I 3 = 10 − (1.63 + 3.36)

               ∴ I 3 = 5.05A

                                                 
‫א‬‫א‬‫א‬‫א‬
K I1 = 1.63A  R1 = 680Ω ‫א‬‫א‬‫א‬K
           
‫א‬K I3 = 5.05A  R 3 = 220Ω ‫א‬
                                                                                                       K‫א‬




                                                      - ٨٣ -
             ‫א‬‫א‬                                     ‫٠٤١ א‬                            ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                  



                         
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                             IT                                                     W
                                                                                                      
                                                          I1                   I2
                                                                                                      
                                                          R1                  R2                      
                                                                                                      
                                                                                                      
                          K‫א‬‫א‬‫א‬‫א‬E١٤J ٥F
                                                    
                                     WE٥J ٥F‫א‬E٢٣J ٥F‫א‬‫א‬
                          RT
              I1 = I T                                                       E٢٣J ٥F
                          R1
                                                                                                     
                         R 1R 2
               RT =                                                          E٥J ٥F
                        R1 + R 2

                                                             WE٢٣J ٥F‫א‬ R T 
                            R1
              I1 = I T                                                                  E٢٦J ٥F
                          R1 + R 2
                                                                W‫א‬‫א‬ I 2 
                             R2
              I2 = IT                                                                   E٢٧J ٥F
                           R1 + R 2

 I1 , I 2 ‫א‬‫א‬‫א‬‫א‬E٢٧J ٥F،E٢٦J ٥F‫א‬‫א‬‫א‬
                                                    
‫א‬ I1 , I 2 , I 3 ‫א‬‫א‬،‫א‬‫א‬ R1, R 2 , R 3 
                                                                                               W‫א‬‫א‬‫א‬




                                                        - ٨٤ -
           ‫א‬‫א‬                                        ‫٠٤١ א‬                              ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                     ١-                    



                                                                                                                 
                                                                                                                 
                                           I1              R1
                                                                                                                 
                                                                                                                 
                                            I2             R2
                                                                                                                 
                                                                                                                 
                                            I3             R3                                                    
                                                                                                                 
                                                                                                                     
                                             IT                                                                      

                                                                                                                 

                                                           + VS −
                                                                                                                 
                                                       
                            K‫א‬‫א‬‫א‬‫א‬E١٥J ٥F
                                                                                                                 
                                     W‫א‬ R1 ‫א‬‫א‬ I1 ‫א‬
                       RT
            I1 = IT                                                           E٢٣J ٥F
                       R1
                                          ‫א‬‫א‬ R T ‫א‬‫א‬
                          R1 ∗ R 2 ∗ R 3
             RT =                                                                          E٢٨J ٥F
                      R1R 2 + R1R 3 + R 2 R 3
                                                            W‫א‬‫א‬ R T 
                               R2 ∗ R3
            I1 = IT .                                                                      E٢٩J ٥F
                        R1R 2 + R1R 3 + R 2 R 3
                                                                               W I 2 , I 3 

                                  R1 ∗ R 3
             I2 = IT .                                                                     E٣٠J ٥F
                          R 1R 2 + R 1R 3 + R 2 R 3

                                  R1 ∗ R 2
             I3 = IT .                                                                     E٣١J ٥F
                          R 1R 2 + R 1R 3 + R 2 R 3

                                                       - ٨٥ -
             ‫א‬‫א‬                                     ‫٠٤١ א‬                               ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                 ١-                    



                                                   Power in Parallel Circuits‫א‬‫א‬‫א‬‫א‬٧J ٥
 WE‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬ PT ‫א‬‫א‬‫א‬‫א‬‫א‬
               PT = P1 + P2 + P3 + K + Pn                                                  E٣٢J ٥F
                                                                                                               
                                  IT                                                                           

                                                           I2
                                                                                                               
                                             I1                               I3             In
                                                                                                               
                   PT                  R1          R2                    R3           Rn
                                             P1           P2                  P3             Pn                
                                                                                                               
                                                                                                               
                                  K‫א‬‫א‬‫א‬‫א‬E١٦J ٥F

                                              V2
               PT = V.I =          2
                                 I T .R T   =                                              E٣٣J ٥F
                                              RT
                                                                                    W‫א‬
                     2
               P1 = I1 .R 1                                                                E٣٤J ٥F

               P2 = I 2 .R 2
                      2                                                                    E٣٥J ٥F
                      2
               P3 = I 3 .R 3                                                               E٣٧J ٥F

               PT = P1 + P2 + P3                                                           E٣٨J ٥F

                                                                                    KWatt‫א‬




                                                        - ٨٦ -
             ‫א‬‫א‬                                 ‫٠٤١ א‬                           ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                ١-               



                                                                                      E١١J ٥F
                                                       ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                         
                                                                                                         
                                                                                                         
                                 R 1 = 68 Ω          R 2 = 33 Ω            R 3 = 22Ω
                                                                                                         
                                                                                                         
                                                                                                         
                      KE١١J ٥F‫א‬‫א‬‫א‬E١٧J ٥F
                                                                                                     ‫א‬
                                                         ‫א‬‫א‬

                              R1 ∗ R 2 ∗ R 3
               RT =
                         R 1R 2 + R 1R 3 + R 2 R 3

                               68 ∗ 33 ∗ 22
                    =                               = 11.1Ω
                        68 * 33 + 68 * 22 + 33 * 22
                       2
              Q PT = I T .R T

                        = (2) 2 * 11.1 = 44.4W

              ∴ PT = 44.4W

                  
‫א‬K‫א‬‫א‬‫א‬
                                                                  K‫א‬

              VS = I.R T = 2 * 11.1 = 22.2V
                    2
                   VS (22.2) 2
              P1 =    =        = 7.25W
                   R1   68




                                                       - ٨٧ -
           ‫א‬‫א‬                            ‫٠٤١ א‬                       ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬           ١-           


                  2
                 VS (22.2) 2
            P2 =    =        = 14.9 W
                 R2   33

                  2
                 VS (22.2) 2
            P3 =    =        = 22.4W
                 R3   22

           Q PT = P1 + P2 + P3

                    = 7.25 + 14.9 + 22.4

           ∴ PT = 44.6W

            KE‫א‬F‫א‬‫א‬‫א‬‫א‬‫ א‬‫א‬‫א‬
                                             
                                             
                                             
                                             
                                             
                                             
                                             
                                             
                                             
                                             
                                             
                                             
                                             
                                             




                                             - ٨٨ -
              ‫א‬‫א‬                                    ‫٠٤١ א‬                                     ‫א‬
   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                   ١-                        



                                             ‫א‬‫א‬
                                                                                                                       
                                                                 W‫א‬‫א‬‫א‬E١F
                                                           ‫א‬EF‫א‬EF
                                                          EF‫א‬EF
                                                                                                                       
‫א‬،‫א‬‫א‬ 100Ω ‫א‬1.2kΩ ‫א‬E٢F
                                                                                                         R T ‫א‬
                          1.2kΩ 100Ω EF1.2kΩ EF
                                               90Ω EEF 90Ω 100Ω EF
                                                                                                                       
 ‫א‬‫א‬،‫א‬‫א‬ 68Ω ، 270Ω  330Ω E٣F
                                                           47Ω EF 668Ω EF
                                                             22Ω EF 68Ω EF
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،1kΩ ‫א‬‫א‬‫א‬E٤F
                    
                                                                                               ‫א‬‫א‬
                                                  1kΩ EF 8kΩ EF
                                                     500Ω EF1kΩ EF
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                      ‫א‬‫א‬‫א‬‫א‬E٥F
                                                          EFEF
                                  ‫א‬‫א‬EFEF
                                                                                                          
                    ‫א‬‫א‬‫א‬‫א‬‫א‬E٦F
                                                EF‫א‬‫א‬EF
                                                      EFEF

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             ‫א‬‫א‬                                    ‫٠٤١ א‬                                 ‫א‬
  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬                  ١-                      



                                             
K 3A ‫א‬، 5A ‫א‬‫א‬‫א‬E٧F
                                                                                            W‫א‬‫א‬‫א‬
                                                               EF 2A EF
                                            K‫א‬EF 8A EF
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               
‫א‬‫א‬،‫א‬‫א‬ 390 Ω, 560 Ω, 820 Ω ‫א‬‫א‬E٨F
                                                                                                  
                                                                    560Ω EF 390Ω EF
                                  K‫א‬EF 820Ω EF
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                                             ‫א‬‫א‬‫א‬‫א‬‫א‬E٩F
                                                ‫א‬EFEF
                                               EFEF‫א‬EF‫א‬‫א‬EF
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 W‫א‬‫א‬‫א‬‫א‬‫א‬E١٠F
                                                                   ‫א‬‫א‬‫א‬‫א‬‫א‬EF
                                                         ‫א‬‫א‬‫א‬‫א‬EF
                                                    E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬EF
                                                                                   K‫א‬EF
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            W‫א‬‫א‬‫א‬،1W ‫א‬‫א‬‫א‬‫א‬E١١F
                                                                         4W EF1W EF
                                                                        16W EF 0.25W EF
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                                        ‫א‬‫א‬‫א‬
                                     ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                         ‫א‬‫א‬‫א‬‫א‬




                   ١ J
                    ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬




٦
‫א‬‫א‬              ‫٠٤١ א‬                                  ‫א‬
‫א‬‫א‬‫א‬           ١-                      



                  ‫א‬‫א‬‫א‬‫א‬
                                                                                  
                       W‫א‬‫א‬،‫א‬‫א‬‫א‬
                                                      K‫א‬‫א‬‫א‬ •
                  K‫א‬‫א‬‫א‬ •
                                K‫א‬‫א‬‫א‬‫א‬ •
                                   K‫א‬‫א‬‫א‬‫• א‬




                                - ٩١ -
     ‫א‬‫א‬                                  ‫٠٤١ א‬                                          ‫א‬
     ‫א‬‫א‬‫א‬                              ١-                              



                                                                                       ١J ٦
                       
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                      
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬
                                                                K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬W‫א‬‫א‬–‫א‬‫א‬‫א‬
                       K‫א‬‫א‬–‫א‬‫א‬‫א‬E١J ٦F‫א‬‫א‬

                                                                                  ‫א‬‫א‬–‫א‬‫א‬ ٢J ٦
                                                                                             E١J ٦F
                            KE١J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                     R٢                                                            
                                         R١                                                                        
                                                     R٣                                                            
                                                                                                                   
                                                                     R٦        R٥        R٤                        
                                               R٨
                                                                                                                   
                                                               R٧
                                                                                                                   
                                                R٩
                                                                                                                   
                         KE١J ٦F‫א‬‫א‬‫א‬E١J ٦F
                                                                                                                ‫א‬
                                                  
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R 1 , R 7 ‫א‬‫א‬‫א‬
                                                                                            
        
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
                                                                                                W‫א‬

                                    R T = R1 + R 2 // R 3 + R 4 // R 5 // R 6 + R 7 + R 8 // R 9
                                                                                                 W


                                                          - ٩٢ -
     ‫א‬‫א‬                                  ‫٠٤١ א‬                                          ‫א‬
     ‫א‬‫א‬‫א‬                               ١-                             


                                   R 2R 3          R 4R 5R 6                 R 8R 9
                 R T = R1 +               +                         + R7 +
                                  R 2 + R 3 R 4R 5 + R 4R 6 + R 5R 6        R8 + R9
                                                                                                E٢J ٦F
                                  K‫א‬‫א‬‫א‬‫א‬،E٢J ٦F‫א‬‫א‬‫א‬
                                                                                                                   
                                             R1
                                                                                                                   
                                                        IT                     A
                       +
                                                                     I3             I2                             
                       VS                                            R3            R2                              
                       −                      R4                                                                   
                                                             IT                B
                                                                                                                   
                        KE٢J ٦F‫א‬‫א‬‫א‬E٢J ٦F
                                                                                                                ‫א‬
 R1 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                    
                                                                                
K R 3 ‫א‬‫א‬، R 2 ، A ‫א‬
 R1, R 4 ‫א‬‫א‬K R 4 ‫א‬‫א‬ B ‫א‬
                                                                                                    
                                              
‫א‬، R 2 // R 3 ،‫א‬‫א‬ R 2 , R 3 ‫א‬K‫א‬‫א‬
                                                                                          W R T ‫א‬

                                                                           R T = R1 + R 2 // R 3 + R 4
                                                                                                E٣J ٦F
                                               KE٣J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬




                                                         - ٩٣ -
    ‫א‬‫א‬                                  ‫٠٤١ א‬                                          ‫א‬
     ‫א‬‫א‬‫א‬                              ١-                             



                                                                                                                 
                                                 R1                                                              
                                                                                                                 
                                                                                                                 
                             +                                           R2        R3
                                                                                                                 
                             VS
                             −
                                                                                                                 
                                                                         R4        R5                            
                                                                                                                 
                                                        
                          KE٣J ٦F‫א‬‫א‬‫א‬E٣J ٦F
                                                                                                               ‫א‬
                                   KE٤J ٦F‫א‬‫א‬‫א‬‫א‬
                                            R1                                                                   
                                                                                                                 
                                                                                                                 
                        +                                           R2          R3
                                                                                                                 
                        VS
                                                                                                                 
                        −
                                                                                R5
                                                                                                                 
                                                                    R4                                                
                                                                                                                      
                                                                                                                      

                                                                                                                 
                       KE٣J ٦F‫א‬‫א‬‫א‬E٤J ٦F
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                W‫א‬ R T ‫א‬
                                                             R T = R1 + R 2 // R 3 + R 4 // R 5R T1




                                                        - ٩٤ -
‫א‬‫א‬                               ‫٠٤١ א‬                                ‫א‬
‫א‬‫א‬‫א‬                            ١-                    



                                                                              E٤J ٦F
                      KE٥J ٦F‫א‬ A, D ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                  R2         R3                                  
                                R1
                                                                                                 
                 A
                                                                                                 
                                                   R4
                                        R6                                                       
                 D                                                                               
                                                   R5
                                                                                                 
                       KE٤J ٦F‫א‬‫א‬‫א‬E٥J ٦F




                                                 - ٩٥ -
       ‫א‬‫א‬                                  ‫٠٤١ א‬                                       ‫א‬
        ‫א‬‫א‬‫א‬                             ١-                            



                                                                                                               ‫א‬
   ‫א‬ R 2 , R 3 ‫א‬‫א‬‫א‬‫א‬ R T1 ‫א‬‫א‬
                                                                         W R 4 ‫א‬‫א‬‫א‬
                                                                                      (R 2 + R 3 ) ⋅ R 4
                                                                           R T1 =
                                                                                     (R 2 + R 3 ) + R 4
                                                                                                                  
        KE٦J ٦F R 5 ‫א‬‫א‬ R T1 ‫א‬‫א‬
                                                                                                                  
                         A                                                                                        
                                         R1                      R T1
                                                                                                                  
                                                  R6
                                                                                                                  
                                                                 R5                                               
                         D                                                                                        
                          KE٤J ٦F‫א‬‫א‬‫א‬E٦J ٦F

                                 W‫א‬‫א‬ D, A ‫א‬‫א‬‫א‬‫א‬

                                                                       R T = R1 + R 6 //(R T1 + R 5 )
                                                                                               E٥J ٦F
 K A, B, C ‫א‬‫א‬‫א‬‫א‬،E٧J ٦F‫א‬‫א‬‫א‬
                                                                 B                                                
                                                                                                                  
                                                  R2                       R1                                     
                                                                                                                  
                                                                                                                  
                                              A                                  C                                
                                                              R3
                                                          
                              KE٥J ٦F‫א‬‫א‬‫א‬E٧J ٦F

                                                          - ٩٦ -
      ‫א‬‫א‬                              ‫٠٤١ א‬                                         ‫א‬
      ‫א‬‫א‬‫א‬                           ١-                             



                                                                                                            ‫א‬
                                                 
  ‫א‬‫א‬ R 1 , R 3  A, B ‫א‬‫א‬‫א‬
                          W R T ‫א‬‫א‬ R 2 ‫א‬‫א‬
                                                                                  R 2 * (R 1 + R 3 )
                                                                     R TAB =
                                                                                  R 2 + (R 1 + R 3 )
                                             W B, C  A, C ‫א‬‫א‬
                                                                                  (R 1 + R 2 ) * R 3
                                                                       R TAC =
                                                                                  (R 1 + R 2 ) + R 3
                                                                                  (R 2 + R 3 ) * R 1
                                                                     R TBC =
                                                                                  (R 2 + R 3 ) + R 1
                          Analysis of Series-Parallel Circuits‫א‬‫א‬–‫א‬‫א‬‫א‬ ٣J ٦
  ‫א‬‫א‬‫א‬‫א‬‫א‬
  W‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦
    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦
                        K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦
                                                                                            E٦J ٦F
 KE٨J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                               
                                            R 2 = 47Ω R 3 = 47Ω
                                        A                                     B
                                                R 4 = 68Ω                                                      
                             R 1 = 100Ω                           R 6 = 75Ω
            +
            VS
                                               R 5 = 39Ω
            −
                            KE٦J ٦F‫א‬‫א‬‫א‬E٨J ٦F
                                                                                                               
                                                                                                               

                                                      - ٩٧ -
    ‫א‬‫א‬                             ‫٠٤١ א‬                                         ‫א‬
    ‫א‬‫א‬‫א‬                          ١-                             



                                                                                                         ‫א‬
                                         ‫א‬‫א‬ R 2 , R 3 ‫א‬
                                                           R T2,3 = 47 + 47 = 94Ω
                                                                                       
 R 6 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R 4 , R 5 ‫א‬‫א‬
                                                                                                  W
                                                                         68 * 39
                                                          R T4,5, 6 =           + 75 = 99.8Ω
                                                                         68 + 39
                                                                                                            
                      ‫א‬‫א‬‫א‬‫א‬ 99.8Ω , 94Ω ‫א‬

                                                                              99.8 * 94
                                                                R TA , B =             = 48.41Ω
                                                                              99.8 + 94
                                                       94Ω                                                  
                                               A                   B
                                                                                                            
                                   100Ω
                     +                                99.8Ω                                                 
                     VS                                                                                     
                     −
                                                                                                            
                      KE٦J ٦F‫א‬‫א‬‫א‬E٩J ٦F

                                                                                ∴ R AB = 48.41Ω

                                                    ∴ R T = 100Ω + 48.41Ω = 148.41Ω
                                                                                         E٧J ٦F
    KE١٠J ٦F R 3 ‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬




                                                   - ٩٨ -
     ‫א‬‫א‬                                  ‫٠٤١ א‬                                            ‫א‬
     ‫א‬‫א‬‫א‬                               ١-                               



                                                                                                                     
                                                                                                                     
                                 IT       R1 = 1kΩ                                                                   
                                                                                                                     
                                                                       I2      I3
                +                              R 2 = 2 .2 k Ω                           R 3 = 3.3kΩ
                VS = 22V
                −


                        KE٧J ٦F‫א‬‫א‬‫א‬E١٠J ٦F
                                                                                                                  ‫א‬
‫א‬‫א‬‫א‬‫א‬  R 3 ‫א‬ R 2 ‫א‬‫א‬
                                                                        K A ‫א‬‫א‬
                K R T ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

                                                                                                R 2R 3
                                                                               R T = R1 +
                                                                                               R2 + R3

                                                                                      (2.2kΩ)(3.3kΩ)
                                                                     R T = 1kΩ +
                                                                                       2.2kΩ + 3.3kΩ
                                                                  ∴ R T = 1kΩ + 1.32kΩ = 2.32kΩ

                                                                                      ∴ R T = 2.32kΩ

                                                                            VS    22V
                                                                IT =          =       = 9.48mA
                                                                            R T 2.32kΩ

                                                             ‫א‬‫א‬

                                                                                    3.3kΩ
                                                                  I 2 = 9.48mA *          = 5.69mA
                                                                                    5.5kΩ

                                                                                    2 .2 k Ω
                                                                  I 3 = 9.48mA *             = 3.79mA
                                                                                    5 .5 k Ω


                                                         - ٩٩ -
       ‫א‬‫א‬                                    ‫٠٤١ א‬                                      ‫א‬
        ‫א‬‫א‬‫א‬                           ١-                               



                                                                                                E٨J ٦F
       VS = 50V ‫א‬‫א‬‫א‬‫א‬ R 4 ‫א‬‫א‬‫א‬
                                                                                                                   
                                                                                        I2                         
                                                    I1
                                                                            R2                                     
                         +                     R1
                                                                            330Ω A                                 
                         VS = 50V              560Ω
                                                                      I3                        I4                 
                         −
                                                                     R3                       R4
                                                                     330Ω                     560Ω



                              KE٨J ٦F‫א‬‫א‬‫א‬E١١J ٦F
                                                                                                                ‫א‬
   ‫א‬‫א‬، 50V ‫א‬‫א‬‫א‬‫א‬
   K R 3 , R 4 ‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬ R1 ‫א‬
                                            W‫א‬‫א‬ R 4 ‫א‬‫א‬ I 4 ‫א‬
                                    K R 2 , R 3 , R 4 ‫א‬‫א‬‫א‬W
 K R 2 , R 3 , R 4 ‫א‬‫א‬‫א‬ I 2 W
        K‫א‬ I 4 ‫א‬ A ‫א‬ I 2 W

                                                                             R T2,3, 4 = R 2 + R 3 // R 4

                                                                                               R 3R 4
                                                                                    = R2 +
                                                                                              R3 + R4

                                                                                    330 * 560
                                                                          = 330 +             = 538Ω
                                                                                    330 + 560

                                                                                    ∴ R T2,3, 4 = 538Ω

                                                                                           50
                                                                                    I2 =       = 93mA
                                                                                           538

                                                           - ١٠٠ -
    ‫א‬‫א‬                                 ‫٠٤١ א‬                                          ‫א‬
     ‫א‬‫א‬‫א‬                             ١-                             



                                                                      W‫א‬‫א‬

                                                                           ⎛ R3        ⎞
                                                                   I4 = I2 ⎜
                                                                           ⎜R + R      ⎟ = 34.5mA
                                                                                       ⎟
                                                                           ⎝ 3    4    ⎠

                                                                                 ∴ I 4 = 34.5mA
              Voltage Drops in Series-Parallel Circuits‫א‬‫א‬‫א‬‫א‬‫א‬ ٤J ٦
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                   
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                 K‫א‬‫א‬‫א‬‫א‬
                                                                                             E٩J ٦F
‫א‬،E١٢J ٦F‫א‬‫א‬‫א‬ A ‫א‬‫א‬‫א‬‫א‬
                                                                                     K R1 ‫א‬‫א‬
                                                                                                                
                                              R1 = 150Ω                                                         
                                                                                                                
                                                                                A
                                                                                                                
                      +                                    R 2 = 560 Ω               R 3 = 560 Ω                
                      VS = 80V
                                                                                                                
                      −                                                         B
                                                                                                                
                                                       
                        KE٩J ٦F‫א‬‫א‬‫א‬E١٢J ٦F
                                                                                                              ‫א‬
‫א‬،‫א‬‫א‬ R 2 , R 3 ‫א‬‫א‬
                                                                     K‫א‬‫א‬
                                                                                                          W
                                                                                560 * 560
                                                                    R T2,3 =             = 280Ω
                                                                                560 + 560

                                                      - ١٠١ -
      ‫א‬‫א‬                              ‫٠٤١ א‬                                        ‫א‬
      ‫א‬‫א‬‫א‬                           ١-                            



                                      ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                   1
                                                                       R TAG = (560) = 280Ω
                                                                                   2

 W‫א‬‫א‬‫א‬‫א‬، R1 ‫א‬‫א‬‫א‬ 280Ω ‫א‬
                                                                                                              
                                               R1 = 150Ω
                                                                                   A                          
                                                                                                              
                          +                                                 280Ω                              
                          VS = 80V                                                                            
                          −                                                                                   
                                                                                   B
                                                                                                              
                        KE٩J ٦F‫א‬‫א‬‫א‬E١٣J ٦F

                                                                   W R T ‫א‬‫א‬‫א‬
                                                                   R T = 150 + 280 = 430Ω
                                                             VAG ‫א‬‫א‬
                                                                                        ⎛ R AG ⎞
                                                                               VAG = ⎜
                                                                                      ⎜        ⎟VS
                                                                                               ⎟
                                                                                        ⎝ RT ⎠
                                                                                                              
                                                                         K‫א‬‫א‬ R AG 
                                                                    VAG = ⎛
                                                                                 280 ⎞
                                                                           ⎜         ⎟ * 80 = 52.1V
                                                                               ⎝ 430 ⎠
                                         R1 ‫א‬‫א‬

                                                                                 VS = V1 + VAG
                                                                                   V1 = VS − VAG

                                                                              = 80 - 52.1 = 27.9V


                                                     - ١٠٢ -
    ‫א‬‫א‬                                   ‫٠٤١ א‬                                    ‫א‬
    ‫א‬‫א‬‫א‬                                ١-                        



                                                                                 ∴ V1 = 27.9V
                                                                                         E١٠J ٦F
                          KE١٤J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬
                                         R1 = 1kΩ                                                            
                                                                                                             
                            IT = 1mA         I1
                                                                                                             
                                             I2
                     +                                                                                       
                     VS                R 2 = 2 .2 k Ω                                                        
                     −                                                  I3         R 4 = 1.5kΩ
                                                                                                             
                                                                                   I4
                                                          R 3 = 3.9kΩ              R 5 = 560Ω                
                                                                                                             
                                                                                                             
                           KE١٠J ٦F‫א‬‫א‬‫א‬E١٤J ٦F
                                                                                                          ‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                            
‫א‬ R1 ‫א‬‫א‬K‫א‬‫א‬ R1, R 2 ‫א‬‫א‬‫א‬
                                                                                          
                                           W‫א‬‫א‬ R 2 ‫א‬‫א‬

                                                                                        ⎛ R2       ⎞
                                                                               I1 = I T ⎜
                                                                                        ⎜R + R     ⎟
                                                                                                   ⎟
                                                                                        ⎝ 1    2   ⎠

                                                                       ⎛    2 .2 k Ω ⎞
                                                                  = 1mA⎜             ⎟ = 688µA
                                                                       ⎝ 1kΩ + 2.2kΩ ⎠

                                                                                  ∴ I1 = 688µA
                                                                  R1 ‫א‬‫א‬‫א‬

                                                                      V1 = I1 .R 1 = 688µA * 1kΩ

                                                                                 V1 = 688mV ∴
                                                        - ١٠٣ -
‫א‬‫א‬                  ‫٠٤١ א‬                                         ‫א‬
‫א‬‫א‬‫א‬               ١-                             



                  W‫א‬ R 3 ‫א‬ I 3 ‫א‬

                                                             ⎛     R4 + R5        ⎞
                                                   I3 = I T ⎜
                                                             ⎜                    ⎟
                                                             ⎝ R 3 + (R 4 + R 5 ) ⎟
                                                                                  ⎠
                                   W‫א‬ I T 
                                                                I3 = 346µA
                                  W R 3 , R 4 , R 5 ‫א‬‫א‬‫א‬

                                                V3 = I 3 .R 3 = (346µA)(3.9kΩ)

                                                                  ∴ V3 = 1.35V
                       W، R 4 ‫א‬‫א‬ V4 

                                                            I 4 = I5 = IT − I3

                                                                = 1mA - 346µA

                                                            = 1mA - 0.346mA

                                                             ∴ I 4 = 0.654mA

                                     V4 = (0.654mA)(1.5kΩ) = 0.981V

                                                              ∴ V4 = 981mV

                                                       V5 = I 5 * R 5 = 366mV




                                   - ١٠٤ -
    ‫א‬‫א‬                             ‫٠٤١ א‬                                      ‫א‬
     ‫א‬‫א‬‫א‬                         ١-                          



                                                                                     E١١J ٦F
     KE١٥J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                         
                                     R 1 = 3.3kΩ                                                         
                        A                            B                                                   
         +                                                        R 3 = 1kΩ                              
         VS = 8V                       R 2 = 6.2kΩ                             C                         
         −                                                                                               
                                                                                    R 5 = 680Ω
                                                                                                         
                                                               R 4 = 1kΩ                                 
                                                                                    R 6 = 390Ω
                                                                                                         
                                                                           D                             
                       KE١١J ٦F‫א‬‫א‬‫א‬E١٥J ٦F
                                                                                                      ‫א‬
                    
،‫א‬‫א‬‫א‬‫א‬
                                                          
‫א‬‫א‬،‫א‬‫א‬‫א‬E١٥J ٦F‫א‬
                                W A, B ‫א‬‫א‬RAB‫א‬‫א‬‫א‬
                                                                            R1R 2
                                                                 R AB =            = 2.15kΩ
                                                                           R1 + R 2

      W C, D ‫א‬‫א‬RCD‫א‬‫א‬‫א‬‫א‬
                                                                      R 4 (R 5 + R 6 )
                                                          R CD =                      = 517Ω
                                                                      R 4 + R5 + R6

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                    KE١٦J ٦F




                                                  - ١٠٥ -
‫א‬‫א‬                             ‫٠٤١ א‬                                ‫א‬
‫א‬‫א‬‫א‬                          ١-                    



                                                                                               
                                   R AB = 2.15kΩ

                                                                                               
            +                                                   R 3 = 1kΩ                      
            VS = 8V                                                                            
            −                                                   R CD = 517Ω                    
                                                                                               

                  KE١١J ٦F‫א‬‫א‬‫א‬E١٦J ٦F

                             W‫א‬‫א‬‫א‬‫א‬

                                                                 ⎛R ⎞
                                                           VAB = ⎜ AB ⎟VS = 4.69V
                                                                 ⎜ R ⎟
                                                                 ⎝ T ⎠

                                                                 ⎛R     ⎞
                                                           VCD = ⎜ CD
                                                                 ⎜ R    ⎟VS = 1.13V
                                                                        ⎟
                                                                 ⎝ T    ⎠

                                                                  ⎛R ⎞
                                                             V3 = ⎜ 3 ⎟VS = 2.18V
                                                                  ⎜R ⎟
                                                                  ⎝ T⎠
                                                              W‫א‬‫א‬

                                                                 ⎛ R AB ⎞
                                       VAB = V1 = V2 = 4.69V⎜
                                                             ⎜          ⎟VS = 4.69V
                                                                        ⎟
                                                                 ⎝ RT ⎠
                         K (R 5 + R 6 ) ‫א‬‫א‬ R 4 ‫א‬ VCD ‫א‬

                                                           ⎛ R5       ⎞
                                                      V5 = ⎜
                                                           ⎜R + R     ⎟VCD = 718mV
                                                                      ⎟
                                                           ⎝ 5    6   ⎠

                                                           ⎛ R6       ⎞
                                                      V6 = ⎜
                                                           ⎜R + R     ⎟VCD = 412mV
                                                                      ⎟
                                                           ⎝ 5    6   ⎠


                                              - ١٠٦ -
    ‫א‬‫א‬                                  ‫٠٤١ א‬                                       ‫א‬
     ‫א‬‫א‬‫א‬                              ١-                           



                                                                                           E١٢J ٦F
                                                     KE١٧J ٦F‫א‬‫א‬‫א‬‫א‬
                                                                                                               
                               IT                            Rc                                                
                                            A                        B
                                     Ra
                      VS                                                                    RL
                                                   Rb                    Rd
                                     

                                             C                       D
                                                        
                       KE١٢J ٦F‫א‬‫א‬‫א‬E١٧J ٦F
                                                                                                             ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                  
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                                                            W
                                                             K R d // R L ‫א‬‫א‬ R d , R L 
                                       R C + R d // R L  R C ‫א‬‫א‬‫א‬
‫א‬ R b ‫א‬‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬
                                                                                           
                                                                                                      
                                                                R b //[R C + (R d // R L )]
                                                                                       
‫א‬، R a ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                     W‫א‬‫א‬‫א‬
                                                             R T = R a + R b //[R C + (R d // R L )]
                                                                                                               




                                                        - ١٠٧ -
    ‫א‬‫א‬                             ‫٠٤١ א‬                                         ‫א‬
    ‫א‬‫א‬‫א‬                          ١-                             



                       W ‫א‬‫א‬‫א‬ R T ‫א‬‫א‬
                                                                                                            
                                                                                                            
                                    IT
                                                                               A                            
                                                               Ib                   Ic                      
                                              Ra
                                                                          Rc
                                                                                B                           
                        +
                                                                                                            
                        VS                               Rb         Rd                   RL
                        −                                           Id                   IL                 
                                                                               C                            
                                                   
                                                                    D
                                                   
                      KE١٢J ٦F‫א‬‫א‬‫א‬E١٨J ٦F

                                                W‫א‬‫א‬‫א‬‫א‬

                                                                                         Ia = IT

                                                                                IT = Ib + IC

                                                                              IC = Id + IL
                                                                                
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬D‫א‬
                                                                                      W I T ‫א‬

                                                                          IT = I b + Id + I L

                                                           ‫א‬‫א‬‫א‬‫א‬‫٥ א‬J ٦
                                                               
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬
                                                                           
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬



                                                   - ١٠٨ -
         ‫א‬‫א‬                                 ‫٠٤١ א‬                                    ‫א‬
         ‫א‬‫א‬‫א‬                             ١-                        



                             
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                               K‫א‬‫א‬‫א‬E١٣J ٦F
                                                                                           E١٣J ٦F
                                    W‫؟‬‫א‬،E١٨J ٦F‫א‬‫א‬‫א‬
                                                      V1 = 12V, V2 = 8V, V3 = 8V, V4 = 5V 
                                                                                                               
                                                   R1
                                                                                                               
                                                                                                               
                               +                                                                               
                                                                       R2           R3
                               VS
                                                                                                               
                               −                   R4                                                          
                                                                                                               
                           KE١٢J ٦F‫א‬‫א‬‫א‬E١٩J ٦F
                                                                                                             ‫א‬
     VS ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                             W

                                                                               VS = V1 + V2 + V4

                                                                                = 12 + 8 + 5 = 25V
                                                                                           E١٤J ٦F
                                                  KE٢٠J ٦F‫א‬‫א‬‫א‬‫א‬
                                            R 3 = 50Ω             R 5 = 50Ω                                    



                    R 2 = 100Ω                 R 4 = 100Ω              R 6 = 100Ω           R 7 = 100Ω

                          R1 = 50Ω
                                                                                                               

                                                          - ١٠٩ -
 ‫א‬‫א‬                               ‫٠٤١ א‬                                       ‫א‬
  ‫א‬‫א‬‫א‬                           ١-                           



                    KE١٤J ٦F‫א‬‫א‬‫א‬E٢٠J ٦F
                                                                                                    ‫א‬

                                                                                  Q R 6 // R 7

                                                                             100 * 100
                                                               ∴ R 6, 7 =             = 50Ω
                                                                             100 + 100
                                                   W‫א‬ R 6,7 ‫א‬‫א‬ R 5

                                                              R 5 + R 6,7 = 50 + 50 = 100Ω

                                            R 4 //( R 5 + R 6 // R 7 ) = 100 // 100 = 50Ω

                            K‫א‬‫א‬ R 3 ‫א‬‫א‬‫א‬‫א‬

                                       R 3 + R 4 //( R 5 + R 6 // R 7 ) = 50 + 50 = 100Ω
                      W، R 2 ‫א‬‫א‬‫א‬‫א‬‫א‬

                                                                             100 * 100
                              R 2 //[R 3 + R 4 //(R 5 + R 6 // R 7 )] =               = 50Ω
                                                                             100 + 100

                                R T ‫א‬ R1 ‫א‬‫א‬‫א‬‫א‬‫א‬

                                                                   R T = 50 + 50 = 100Ω
                                                                                     E١٥J ٦F
                      W، VS  V4 = 28.2V ‫א‬W‫א‬‫א‬‫א‬

 R 1 = 2.7kΩ, R 2 = 2.2kΩ, R 3 = 5.6kΩ, R 4 = 10kΩ, R 5 = 15kΩ, R 6 = 820Ω
                                      R1                                                                 
                      IT




                                                 - ١١٠ -
           ‫א‬‫א‬                                       ‫٠٤١ א‬                                                 ‫א‬
           ‫א‬‫א‬‫א‬                                   ١-                                   



                                                                                                                                     
                                                    I1
                                                         I2                                    IT                                    
                   +
                   VS                                 R2                       I3                                  I5
                                                                                             I4
                   −
                                                                               R3                    R4          R5

                                      R6            IT
                                                                                                                                     
                              KE١٥J ٦F‫א‬‫א‬‫א‬E٢١J ٦F
                                                                                                                                  ‫א‬
                                                                            W،‫א‬

                                                                                                I T = I3 + I 4 + I 5
     ، R 3 , R 4 , R 5 ‫א‬‫א‬ V4 = 28.2V 
                                                            
                                                                                           W I 3 , I 4 , I 5 ‫א‬‫א‬

                                                                                                     28.2
                                                                                             I4 =         = 2.82mA
                                                                                                     10k

                                                                                                     28.2
                                                                                              I5 =        = 1.88mA
                                                                                                     15k

                                                                                                     28.2
                                                                                             I3 =           = 5.04mA
                                                                                                     5 .6 k
                                                      ∴ I T = 5.04mA + 1.88mA + 2.82mA = 9.74mA


 R eq ‫א‬‫א‬ I T 
                                                                    W I T  R 3 , R 4 , R 5 
                                                                                                                      V4
                                                                                                         IT =
                                                                                                                    R eq

                                                                                                                            W
                                                                   - ١١١ -
    ‫א‬‫א‬                               ‫٠٤١ א‬                                           ‫א‬
     ‫א‬‫א‬‫א‬                           ١-                               


                                                                 R 3R 4 R 5
                                               R eq =                                = 2.896kΩ
                                                        R 3 R 4 ,+ R 3 R 5 + R 4 R 5

                                                                               28.2
                                                                ∴IT =                     = 9.74mA
                                                                           2.896 * 10 3
                                                                             K‫א‬‫א‬
                                       R1 // R 2 ‫א‬‫א‬‫א‬‫א‬

                                                                         V1 = V2 = I T (R 1 // R 2 )

                                                                                            R 1R 2
                                                                                 = IT (            )
                                                                                           R1 + R 2

                                                                     W‫א‬‫א‬
                                                                               V1 = V2 = 11.8V
                                                                   R 6 ‫א‬‫א‬

                                                     V6 = I T .R 6 = 9.74 * 10 −3 * 0.82 * 10 3

                                                                                 ∴ V6 = 7.99V
                                                                                        VS ‫א‬

                                                                             VS = V1 + V4 + V6

                                                                    = 11.8 + 28.2 + 7.99 = 48V

                                                                                   ∴ VS = 48V
‫א‬‫א‬ VS E١F
                                                                                   K‫א‬‫א‬
 VS ‫א‬‫א‬‫א‬ VS E٢FKW
                                                                                       W‫א‬

                                                                                  VS = IT * R T
                                                                                             Summary‫א‬
                                                    - ١١٢ -
     ‫א‬‫א‬                                 ‫٠٤١ א‬                                           ‫א‬
     ‫א‬‫א‬‫א‬                              ١-                              



‫א‬‫א‬‫א‬E‫א‬–‫א‬F‫א‬‫א‬‫א‬E١F
                                                                                 K‫א‬‫א‬
                                        
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢F
                                                           ‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣F
                              E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤F
                                                                                                 ⎛ RX ⎞
                                                                                   VX = VS ⎜
                                                                                            ⎜         ⎟
                                                                                                 ⎝ RT ⎟
                                                                                                      ⎠
                                                                                                                   
                                                                                                             W
                                                  ‫א‬‫א‬‫א‬W R X 
                                                                     ‫א‬‫א‬‫א‬W VX 
                                                                                      ‫א‬W VS 
                                                                            K‫א‬‫א‬‫א‬W R T 
                                                                                                                   
                                                           
‫א‬E‫א‬‫א‬F‫א‬E٥F
                                       
                K‫א‬Common Reference Point




                                                       - ١١٣ -
   ‫א‬‫א‬                              ‫٠٤١ א‬                                               ‫א‬
    ‫א‬‫א‬‫א‬                          ١-                                  



                                            ‫א‬
                                                                       
                                                W‫א‬‫א‬‫א‬‫א‬‫א‬J ١
                                                                                                                   
                              R1               R2

           A                                                                              B
                              R3              R4                R5                                                 
                                                                                                                   

                                                                R 3 , R 4 , R 5 ‫א‬‫א‬ R1 , R 2 EF
                                                                                  K‫א‬‫א‬ R1, R 2 EF
                                                                             ‫א‬‫א‬ R 3 , R 4 , R 5 EF
                       R 3 , R 4 , R 5 ‫א‬‫א‬‫א‬‫א‬ R1, R 2 ‫א‬‫א‬EF
                                                                                EF،EF‫א‬EF
                                                                                                                   
  W‫א‬‫א‬، R T ‫א‬‫א‬‫א‬‫א‬–٢
                                                                            R1 + R 2 + R 3 // R 4 // R 5 EF
                                                                           R1 // R 2 + R 3 // R 4 // R 5 EF
                                                                       (R1 + R 2 ) //(R 3 + R 4 + R 5 ) EF
                                                                               EF
                                                                                                                   
‫א‬ A, B ‫א‬‫א‬‫א‬‫א‬‫א‬–٣
                                          
                                                                                            W‫א‬‫א‬
                               R 3 , R 4 , R 5 EF R 5 EF
                                    ‫א‬EF R1, R 2 EF
                                                                                                                   


                                                   - ١١٤ -
           ‫א‬‫א‬                                      ‫٠٤١ א‬                                                ‫א‬
           ‫א‬‫א‬‫א‬                                  ١-                                   



1kΩ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬–٤
     ‫א‬‫א‬، 2.2kΩ ‫א‬‫א‬‫א‬،‫א‬‫א‬
                                                       
                                                                               ،٦V1kΩ ‫א‬‫א‬
                                                                                                                                    
                                                    V1 = 6V               1kΩ

                                                       1kΩ
                                                                         2.2kΩ
                                                                                                                                    
                                                                                                                                    
                                                                      : 2.2kΩ ‫א‬‫א‬‫א‬
                                                                           ٣VEF٦VEF
                                                                      ١٣{٢VEF                         ١٢VEF
                                                                                                                                    
                       ‫א‬‫א‬‫א‬، 330Ω,470Ω ‫א‬‫א‬‫א‬–٥
    100V ‫א‬‫א‬‫א‬K1kΩ 
                                                                      W‫א‬‫א‬‫א‬
                                                                                                                                    
                                                                                                                                    
                                                               1kΩ
                                                                                                                                    
                                      330Ω                     1kΩ
                                                                                                                                    
                                                                1kΩ                                                                 
                                       470Ω                    1kΩ                                                                  




                                                100V


                                                                  - ١١٥ -
    ‫א‬‫א‬                                ‫٠٤١ א‬                                           ‫א‬
     ‫א‬‫א‬‫א‬                           ١-                                



                                                               W‫א‬‫א‬
                                                470Ω EF 330Ω EF1kΩ EF
                                                                                                                 
     ‫א‬،E٥F‫א‬‫א‬‫א‬‫א‬J ٦
                                                   470Ω EF 330Ω EF1kΩ EF
                                                                                                                 
              
‫א‬‫א‬‫א‬‫א‬‫א‬،E٥F‫א‬‫א‬‫א‬‫א‬J ٧
                                                                                                     W1kΩ
                                     ٣١{٣٪ EF             ٥٠٪EF ٢٥٪EF١٠٠٪EF
                                                                                                                 
‫א‬F‫א‬٩V‫א‬‫א‬‫א‬J ٨
         W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، E‫א‬‫א‬
                           EF              
                                                    ‫א‬EF EFEF
                                                                                                                 
F10kΩ ‫א‬J ٩
                                                W‫א‬E‫א‬‫א‬
                                                                                                                 


                                                   10kΩ
              +
              V2
              −
                                                    10kΩ
                                                                       output




                                                    - ١١٦ -
        ‫א‬‫א‬                            ‫٠٤١ א‬                                     ‫א‬
        ‫א‬‫א‬‫א‬                         ١-                         



                                                                                          
1MΩ EFK‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                 10kΩ EF         100kΩ EF 20kΩ EF
                          W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J ١٠
                                    ‫א‬‫א‬EF EF EFEF
                                                                                                           




                                                     - ١١٧ -
‫א‬‫א‬                                  ‫٠٤١ א‬                                         ‫א‬
‫א‬‫א‬‫א‬                              ١-                             



                                   ‫א‬‫א‬
                                                
                              W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K١
                                                                                                            
                                        R1 = 56Ω
                                                                                                            
                                                                                                            
          +                                                                                                 
                                                          R 2 = 100Ω                  R 3 = 100Ω
          VS = 1.5V
                                                                                                            
          −
                                        R 4 = 27Ω                                                           
                                                                                                            
                                                  (a )                                                      
                                                                                                            
                                                                R1
                                                                                                            
                 +
                                                                680Ω                                        
                 VS = 3V
                 −                                                                                          
                                                 R2                        R3            R4
                                                 680Ω
                                                                                                            
                                                                           330Ω          180Ω
                                                                                                            
                                                                                                            
                                                               (b)
                                                                                                            
                                                                                                            
                                                                     R 2 = 6 .2 k Ω
                                                                                                            
                                                                                                            
                                           +                         R 3 = 3.3kΩ
                                                                                                            
                      R 1 = 1kΩ            5V
                                                                     R 4 = 10kΩ                             
                                           −
                                                                                                            
                                                                 R 5 = 5.6kΩ
                                                                                                            
                                                   
                                                               (c)
                                                  - ١١٨ -
    ‫א‬‫א‬                               ‫٠٤١ א‬                                          ‫א‬
    ‫א‬‫א‬‫א‬                            ١-                              



                           K‫א‬‫א‬‫א‬١‫א‬‫א‬‫א‬‫א‬K٢
                                                                                                               
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬K٣
                                                          ‫א‬‫א‬‫א‬‫א‬‫א‬
                                                      R 2 = 1kΩ                                                
                                                                                                               
               −                                                                                               
              1V                   R 1 = 1kΩ                    R 3 = 2.2kΩ                     R 4 = 3.3kΩ
               +




                                                           W‫א‬‫א‬‫א‬‫א‬K٤
                                                                         4.7 kΩ
                                         A                                                  B
                                                                                                               
                                                           10kΩ
                                                                                            5 .6 k Ω
                                   +
                                   100V                                                     C
                                                                  E
                                   −                                                        1kΩ
                                                           1.8kΩ
                                          F                                                 D
                                                                            1kΩ

                      W‫א‬‫א‬ (A, B) ‫א‬‫א‬J ٥
                                                                                                               
                            R1 = 1kΩ           R 2 = 330Ω
                                                                                                               

      +                                   R 3 = 470Ω                  R 5 = 1kΩ                 R 6 = 1.5kΩ
                                    A                                                   B
      100V
                           R 4 = 560Ω                                                       R 7 = 680Ω
       −                                        R 8 = 100Ω


                                                      - ١١٩ -
    ‫א‬‫א‬                               ‫٠٤١ א‬                                           ‫א‬
     ‫א‬‫א‬‫א‬                          ١-                              



                                                         W‫א‬‫א‬J ٦
                                                                                                              
                                                        P = 20 W                    R2                        
                               4A                               R1                P = 2W
                                                  20V
                       +                                                          5V
                                            R3                       R4      R5          R6       1V
                       40V
                       −                                         1A               R8

                                       R7                                                                     
                                                                             1A
                                                                                                              
                                                                                                              
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J ٧
‫א‬، R L = 10kΩ ‫א‬KE (A, B) ‫א‬FNo Load‫א‬‫א‬
                                                                             K‫א‬‫א‬‫א‬‫א‬
                                                                                                              
                                                                                                              
                           +                                R 1 = 10kΩ
                                                                                                              
                           22V                                                                A
                                                                                                              
                           −                             R 2 = 5 .6 k Ω

                                                                                                  RL
                                                           R 3 = 2 .7 k Ω

                                                                                              B
                                                                                                              
                                                                              W‫א‬‫א‬J ٨
                                                                            R T ‫א‬‫א‬‫א‬EF
                                                                      I T ‫א‬‫א‬‫א‬‫א‬EF
                                                                            910Ω ‫א‬‫א‬EF
                                                       K VA , VB  A, B ‫א‬EF
                                                   - ١٢٠ -
    ‫א‬‫א‬                                ‫٠٤١ א‬                                       ‫א‬
    ‫א‬‫א‬‫א‬                             ١-                           



                                                                                                             
                     +                             56Ω                      56Ω
                                                                                                             
                     60V
                                                             910Ω                                            
                     −
                                                                                                             
                                                                                       560kΩ                 
                                     1kΩ                                   1kΩ
                                                 560kΩ


                                          A      1kΩ              B           1kΩ

                                                         WLadder Network‫א‬‫א‬‫א‬J ٩
                                                                                    R T ‫א‬‫א‬EF
                                                                             VA ،A‫א‬‫א‬EF
                                                                                 VB ،B‫א‬‫א‬
                                                R 3 = 1kΩ                                                    
                         R 1 = 5 .6 k Ω                                           R 5 = 1kΩ
                                          A                       B
                                                                                                             
                                                                                                             
                                              R 2 = 2.2kΩ             R 4 = 2 .2 k Ω           R 6 = 1kΩ
       18V                                                                                                   


                                                                                                             

‫א‬‫א‬‫א‬‫א‬ A, B ‫א‬‫א‬‫א‬‫א‬J ١٠
                                                                                                       W‫א‬




                                                     - ١٢١ -
    ‫א‬‫א‬                                      ‫٠٤١ א‬                                     ‫א‬
     ‫א‬‫א‬‫א‬                                ١-                           



                                                                                                                 
                      R1 = 100Ω                    R 3 = 220Ω                                                    
                                                                                     R 5 = 100Ω
            A
                       IT                I2                       I3         I4                      I5
            +
                         R 2 = 820Ω                                                                              
                                                         R 4 = 820Ω                                 R 6 = 680Ω
            −                                                                                                    
                       R 9 = 100Ω
                                                                                                                 
            B
                            IT                     R 8 = 220Ω                      R 7 = 100Ω                    
‫א‬‫א‬١٠‫א‬‫א‬‫א‬‫א‬‫א‬J ١١
                                               ‫؟‬ VS = 10V ،١٠V A, B ‫א‬‫א‬
                                                                                                                 
                    
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬J ١٢
                                                                        W‫א‬‫א‬‫א‬
                             R 1 = 10kΩ, R 2 = 20kΩ, R 3 = 60kΩ, R 4 = 15kΩ, R 5 = 5kΩ
                                                                                                                 
                                                                                                                 
                                                   R3         A             R5

                                                                                         +
                                  R2
                                                                                         100V
                            VA                           R4            VC
                                   B                                                     −
                                   R١         VB
                                                                                                                 
                                                              C                                                  




                                                          - ١٢٢ -
                                                 ‫א‬‫א‬‫א‬
                                             ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
                                                   ‫א‬‫א‬‫א‬‫א‬




                            ١ J
                          ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬




٧
 ‫א‬‫א‬                           ‫٠٤١ א‬                              ‫א‬
‫א‬‫א‬‫א‬                   ١-                  



                             ‫א‬‫א‬‫א‬‫א‬
                                                                                            
                                   W‫א‬‫א‬،‫א‬‫א‬‫א‬
          K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                              K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                                  K‫א‬‫א‬‫א‬‫א‬‫א‬ •
                        K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •
                           K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •




                                           - ١٢٣ -
     ‫א‬‫א‬                                ‫٠٤١ א‬                                     ‫א‬
    ‫א‬‫א‬‫א‬                        ١-                         



                                                                               Introduction  ١J ٧
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                      
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
                                 K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
                                                                   
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
                                                           
KE٢J F‫א‬،‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                      K

                                                     ‫א‬‫א‬‫א‬‫א‬ ٢J ٧
Voltage Source‫א‬‫א‬‫א‬
          K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،Current Source
                                        Constant Voltage Source ‫א‬‫א‬                   ١J ٢J ٧
                       
‫א‬‫א‬ ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬ R S ‫א‬‫א‬
                                                                                                   KE١J ٧F
                                                                                                            
                        +                                 RS
                        VS                                                                                  
                                                                                        RL                  
                        −
                                                                                                            
                                                    
                                  E١J ٧F

                            
 R S ،Ideal Voltage Source‫א‬‫א‬
                                                       
                                                                          W‫א‬‫א‬

                   R L >> R S                                                                         E١J ٧F


                                                    - ١٢٤ -
     ‫א‬‫א‬                                   ‫٠٤١ א‬                                        ‫א‬
    ‫א‬‫א‬‫א‬                           ١-                            



                                            Constant Current Source                       ٢J ٢J ٧
 R S ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                  
‫א‬‫א‬‫א‬‫א‬‫א‬
                             KE٢J ٧F،
                                                                         A                                        
                                                                                                                  
                              iS      A                       RS                                                  
                                                                                                                  
                                                                           B                                      
                      EJ ٢J ٧F
                                                       
                                                                          A                                       
                                                                                                                  
                              iS       A                         RS           RL                                  
                                                                                                                  
                                                                        B

                        EJ ٢J ٧F

 R S ،Ideal Current Source ‫א‬‫א‬
                                                        
                                                                                W‫א‬‫א‬

                    R S 〉〉 R L                                                                             E٢J ٧F

                                                                                         
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                   K‫א‬‫א‬

                                               ?Source Conversions " ‫א‬                        ٣J ٢J ٧
                    
 ‫א‬،‫א‬‫א‬‫א‬
                             K‫א‬E٣J ٧F‫א‬

                                                       - ١٢٥ -
 ‫א‬‫א‬                              ‫٠٤١ א‬                               ‫א‬
‫א‬‫א‬‫א‬                    ١-                     



                                                                                                
                                                                                        A       
                                        A
                                             iL                                               iL
+                       RS
VS
−
                                             RL     ≡       iS    I          RS              RL
                                                                                                
                                                                                                
                                                                                                
                                         B                                              B       
                 KE٣J ٧F
                                                                                                
                                              W IL ‫א‬‫א‬‫א‬

                     VS
           IL =                                                                           E٣J ٧F
                   RS + R L

                                         
     KW IL ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

                ⎛ RS ⎞
           IL = ⎜
                ⎜ R + R ⎟iS
                        ⎟                                                                 E٤J ٧F
                ⎝ S    L⎠


                                        WE٤J ٧FE٣J ٧F‫א‬‫א‬

            VS = R S ⋅ i S                                                               E٥J ٧F




                                              - ١٢٦ -
      ‫א‬‫א‬                                      ‫٠٤١ א‬                                    ‫א‬
     ‫א‬‫א‬‫א‬                              ١-                        



                                                                                               E١J ٧F
                                                     W‫א‬‫א‬‫א‬‫א‬
                                          (a )R L = 100Ω  (b)R L = 560Ω  (c)R L = 1KΩ
                                                                               A
                                                                                                                  
                                                                                    iL
                                                                                                                  
                                    iS
                                               I                     RS             RL                            
                                    1A
                                                                   10kΩ                                           
                                                                                B                                 
                              KE١J ٧F‫א‬‫א‬‫א‬E٤J ٧F
                                                                                                             ‫א‬
                                                                            R L = 100Ω 
                                                                            IL ،E٣J ٧F

                     ⎛ RS ⎞
                     ⎜ R + R ⎟iS
                IL = ⎜       ⎟
                     ⎝ S    L⎠


                     ⎛ 10kΩ ⎞
                IL = ⎜        ⎟ * 1 = 990mA = 0.99A
                     ⎝ 10.1kΩ ⎠

                                                                               W، R L = 560Ω 

                     ⎛ 10kΩ ⎞
                IL = ⎜         ⎟ *1 = 0.947A
                     ⎝ 10.56kΩ ⎠

                                                             IL  R L = 1KΩ 

                     ⎛ 10kΩ ⎞
                IL = ⎜      ⎟ * 1 = 0.909A
                     ⎝ 11kΩ ⎠

                                                                                
 R L  iS ٪١٠ I L ‫א‬‫א‬‫א‬‫א‬‫א‬
                                          K‫א‬‫א‬‫א‬‫א‬ R S ‫א‬


                                                           - ١٢٧ -
 ‫א‬‫א‬                                 ‫٠٤١ א‬                                  ‫א‬
‫א‬‫א‬‫א‬                         ١-                      



                                                                                    E٢J ٧F
             K IL = 750mA ‫א‬ R L ،‫א‬‫א‬‫א‬
                                                                                                      
                                                                      A                               
                                                                              iL                      
                                                                                                      
                   i S = 1A       I                   R S = 10kΩ              RL
                                                                                                      
                                                                                                      
                                                                          B
                                                 
                         KE٢J ٧F‫א‬‫א‬‫א‬E٥J ٧F
                                                                                                 ‫א‬
                                                  W‫א‬،E٣J ٧F‫א‬‫א‬
                ⎛ RS ⎞
                ⎜ R + R ⎟iS
           IL = ⎜       ⎟
                ⎝ S    L⎠

                                           W‫א‬ iS ، R S ‫א‬

           0.75(10 + R L ) = 10

           7.5 + 0.75R L = 10

           0.75R L = 2.5
                     2.5
           RL =          = 3.33kΩ
                    0.75




                                                 - ١٢٨ -
 ‫א‬‫א‬                                   ‫٠٤١ א‬                              ‫א‬
‫א‬‫א‬‫א‬                           ١-                  



                                                                                  E٣J ٧F
                              K‫א‬E٦J ٧F‫א‬‫א‬‫א‬
                                                                                 A                  
                         +                                   R S = 50Ω                              
                         VS = 100V
                                                                                                    
                         −
                                                                                                    
                                                                                  B                 
                         KE٣J ٧F‫א‬‫א‬‫א‬E٦J ٧F
                                                                                              ‫א‬
                   VS 100
           iS =       =   = 2A
                   R S 50




                                                   - ١٢٩ -
     ‫א‬‫א‬                                      ‫٠٤١ א‬                                        ‫א‬
    ‫א‬‫א‬‫א‬                              ١-                           



 W،E٧J ٧F‫א‬‫א‬‫א‬
                                                                                      A                              
                                                                                                                     
                                  i S = 2A         I                     R S = 50Ω
                                                                                                                     
                                                                                      B                              
       KE٣J ٧F‫א‬‫א‬‫א‬E٧J ٧F
                                                                Superposition Theorem ‫א‬ ٣J ٧
?‫?א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                          
‫א‬‫א‬
                                                                                                                     
                                                                                                                   K
   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                       
‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                   W‫א‬‫א‬‫א‬
                       
‫א‬‫א‬ R S ‫א‬‫א‬،‫א‬‫א‬                            ♦
      KShort Circuit‫א‬‫א‬
‫א‬‫א‬، R S ‫א‬‫א‬،‫א‬‫א‬               ♦
Open-Circuit‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬،E٨J ٧F‫א‬‫א‬‫א‬
                                                                                                      K




                                                          - ١٣٠ -
     ‫א‬‫א‬                               ‫٠٤١ א‬                                    ‫א‬
   ‫א‬‫א‬‫א‬                        ١-                       



                                                                                                         
                                           R١                      R2
                                                     a                                                   
                           +                                                     +                       
                           VS1                                                   VS2                     
                                                         R3
                           −                                                     −
                                                                                                         
                                                                                                         
                                                   b
                        K‫א‬E٨J ٧F
                                                                                                         
                                                         
‫א‬‫א‬‫א‬‫א‬E R 3 ‫א‬Fab‫א‬‫א‬‫א‬‫א‬
، I1 ‫א‬‫א‬،E٩J ٧F‫א‬
،‫א‬ab‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ I 2
‫א‬ab‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                         K‫א‬
                                                                                                         
                                                                                                         
                I1                                                                          I2
                                 a                                           a                           
    +                      R١             R2                            R١                             +

                                                    +
                                                                                      R2
    VS1                                                                                                 
                                                                                                       VS2
                                     R3                                          R3
                                                                                                         
                                                                                                         
                                 b                                           b                           
              K‫א‬‫א‬‫א‬E٩J ٧F




                                                   - ١٣١ -
    ‫א‬‫א‬                                ‫٠٤١ א‬                                  ‫א‬
   ‫א‬‫א‬‫א‬                       ١-                       



                                                                                      E٤J ٧F
                    K‫א‬‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬

                                                      a
                                                                                                       

                                        R1 = 100Ω            R 3 = 100Ω
                                                                                                        
                           +
                                                                                 +                      
                           10V
                                                             R 2 = 100Ω          5V
                           −                                                                            
                                                                                 −
                                                                                                        
                                                      b                                                 
                        KE٤J ٧F‫א‬‫א‬‫א‬E١٠J ٧F
                                                                                                  ‫א‬
           K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
        KE١١J ٧F١٠ V‫א‬‫א‬W‫א‬‫א‬‫א‬

                                                              a
                                 +            R1 = 100Ω           R 3 = 100Ω
                                 10V
                                                                  R 2 = 100Ω
                                 −


                                                              b
 KE٣J ٧F‫א‬‫א‬‫א‬١٠ V‫א‬‫א‬E١١J ٧F
                                              W‫א‬‫א‬ R 2 ‫א‬

                       R2 * R3
              RT =             + R1
                       R2 + R3

                       100 * 100
              RT =               + 100 = 150Ω
                       100 + 100

                      VS   10
              IT =       =    = 66.7mA
                      R T 150


                                                  - ١٣٢ -
    ‫א‬‫א‬                                  ‫٠٤١ א‬                               ‫א‬
   ‫א‬‫א‬‫א‬                         ١-                    



                              W‫א‬‫א‬ab‫א‬‫א‬‫א‬

                                100
              Iab = 66.7 *              = 33.3mA
                              100 + 100

             KE١٢J ٧F٥ V‫א‬‫א‬W‫א‬‫א‬‫א‬
                                                                                                       
                                                                                                       
                                                      a
                                                                                                       
                                         R1 = 100Ω          R 3 = 100Ω
                                                                                +                      
                                                           R 2 = 100Ω           5V                     
                                                                                −
                                                                                                       
                                                      b                                                
 KE٣J ٧F‫א‬‫א‬‫א‬٥ V‫א‬‫א‬E١٢J ٧F
                                                                                                       
                            W R T ‫א‬‫א‬‫א‬ab‫א‬‫א‬‫א‬
                               R 1R 2
              RT = R3 +
                              R + R 21

                              100 * 100
              R T = 100 +               = 150Ω
                              100 + 100

                      VS   5
              IT =       =    = 33.3mA
                      R T 150

                                                           Wab‫א‬‫א‬‫א‬
                         ⎛ R1        ⎞
              I ab = I T ⎜
                         ⎜R + R      ⎟
                                     ⎟
                         ⎝ 1    2    ⎠
                                100
              I ab = 33.3 *             = 16.7 mA
                              100 + 100


                                                    - ١٣٣ -
    ‫א‬‫א‬                                 ‫٠٤١ א‬                                   ‫א‬
   ‫א‬‫א‬‫א‬                         ١-                       



                                                  W‫א‬‫א‬

              ITab = 33.3 + 16.7 = 50mA

                 
،‫א‬ ‫א‬‫א‬
                            K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                        E٥J ٧F
     KE١٣J ٧F‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬
                                                              a                                           
                           +               R1 = 220Ω
                           10V
                                                                  R 2 = 100Ω     A     i S = 100mA
                           −


                                                              b
                        KE٥J ٧F‫א‬‫א‬‫א‬E١٣J ٧F
                                                                                                    ‫א‬
                                                                       K‫א‬‫א‬‫א‬
  KE١٤J ٧F١٠ V‫א‬‫א‬W‫א‬‫א‬‫א‬
                                                          a
                                                                                                          
                +                      R 1 = 220Ω
                                                                                                          
                10V
                                                                  R 2 = 100Ω                              
                 −
                                                                                                          
                                                                                                          
                                                          b
     KE٥J ٧F‫א‬‫א‬‫א‬‫א‬E١٤J ٧F
                                                      K‫א‬‫א‬‫א‬‫א‬
                                W R T ‫א‬‫א‬‫א‬‫א‬

              R T = 220 + 100 = 320Ω

                                 10
              iT = i ↓R2 =           = 31.2mA
                                 320
                                                    - ١٣٤ -
     ‫א‬‫א‬                                    ‫٠٤١ א‬                                         ‫א‬
    ‫א‬‫א‬‫א‬                            ١-                            



                     K 31.2mA 10V ‫א‬ R 2 ‫א‬‫א‬‫א‬∴ 
  KE١٥J ٧F١٠٠ mA‫א‬‫א‬W‫א‬‫א‬‫א‬
                                                                                                                    
                                                       a                                                            
                                    R1 = 220Ω                                                                       
                                                                                                                    
                                                               R 2 = 100Ω        A        i S = 100mA
                                                                                                                    
                                                                                                                    
                                                       b                                                            
      KE٥J ٧F‫א‬‫א‬‫א‬‫א‬E١٥J ٧F

                                             W‫א‬‫א‬ab‫א‬‫א‬

                          ⎛ 220 ⎞
               i ↓ R = iS ⎜           ⎟
                    2
                          ⎝ 220 + 100 ⎠

‫א‬ i s ،‫א‬ R 2 ‫א‬‫א‬‫א‬ i ↓ R 2 
                                                                                      W‫א‬،‫א‬
                            ⎛ 220 ⎞
               i ↓ R 2 = 100⎜     ⎟ = 68.8mA
                            ⎝ 320 ⎠

               ∴ i ↓ R 2 = 68.8mA

             K 68.8mA ‫א‬‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬
               W‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬
               i = 31.2 + 68.8 = 100mA




                                                        - ١٣٥ -
     ‫א‬‫א‬                                    ‫٠٤١ א‬                                         ‫א‬
    ‫א‬‫א‬‫א‬                            ١-                            




                                                               Thevinen's Theorem ٤J ٧
                    
‫א‬‫א‬
                                                            KThevinen's TheoremEF
 R Th ‫א‬‫א‬ VTh ‫א‬‫א‬
                                                                                 KE١٦J ٧F
                                                                                                                    
                                                            R Th
                                                                                        A

                            VTh                                                                                     
                                                               I                            r
                                                                                                                    
                                                                                                                    
                                                                                        B
                                   K??‫א‬E١٦J ٧F

‫א‬‫א‬‫א‬ R Th ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                    W‫א‬‫א‬‫א‬ r ‫א‬‫א‬ I ‫א‬
                       VTh
               I=                                                                                             E٦J ٧F
                     R Th + r
                                                                             W‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١
                                                                                 K VTh ‫א‬
EZF‫א‬‫א‬‫א‬‫א‬ E٢
F R Th ‫א‬‫א‬‫א‬Short Circuit‫א‬‫א‬
               KE‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R Th 



                                                        - ١٣٦ -
     ‫א‬‫א‬                                  ‫٠٤١ א‬                                       ‫א‬
    ‫א‬‫א‬‫א‬                          ١-                           



                   
 R Th ‫א‬‫א‬ VTh E‫א‬F E٣
‫א‬‫א‬KE١٦J ٧F‫א‬‫א‬‫א‬‫א‬
                                                                  W‫א‬‫א‬‫א‬
                      VTh
               I=
                    R Th + r

KComplex Circuit‫א‬‫א‬‫א‬W
‫א‬Output‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                   
                                                                                        
                                   W‫א‬،‫א‬‫א‬ ‫א‬
‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬Open E١
                                                                      K VTh ‫א‬
                                                                      
‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫ א‬E٢
        K‫א‬‫א‬ R Th 
Series Circuit‫א‬‫א‬E‫א‬F E٣
                                                      K‫א‬ R L  R Th ، VTh 
                                                                                            E٦J ٧F
                                      K‫א‬a،b‫א‬‫א‬‫א‬‫א‬‫א‬
                                                           a
                            +              R 1 = 4Ω            R 2 = 8Ω
                                                                                       +
                            10V
                                                               R 3 = 6Ω               5V
                            −
                                                                                       −


                                                           b
                                                       
                         KE٦J ٧F‫א‬‫א‬‫א‬E١٧J ٧F




                                                      - ١٣٧ -
    ‫א‬‫א‬                               ‫٠٤١ א‬                                  ‫א‬
   ‫א‬‫א‬‫א‬                    ١-                         



                                                                                                ‫א‬
                                                  
‫א‬Open‫א‬‫א‬‫א‬ab‫א‬‫א‬W‫א‬‫א‬
                                                                                        
                                                                        K VTh b،a‫א‬
                                                     a
                                                                                                       
                           +           R 1 = 4Ω             R 2 = 8Ω
                                                                                +                      
                           10V
                                                                                5V                     
                           −
                                                             I                  −                      

                                                     b
            Kab‫א‬E٦J ٧F‫א‬‫א‬‫א‬E١٨J ٧F
       W،‫א‬‫א‬‫א‬‫א‬‫א‬

             10 − 5 = I(4 + 8)

                      10 − 5 5
             ∴I =           = A
                       12    12
                                                             W‫א‬‫א‬ Va 
             ∴ Va = 10 − I * 4
                            5
              Va = 10 −       * 4 = 8.33V
                           12
             ∴ VTh = 8.33V

‫א‬‫א‬‫א‬‫א‬a‫א‬‫א‬
                                                            
‫א‬‫א‬‫א‬‫א‬‫א‬ ٥V ‫א‬‫א‬a
                                                                    W Va ‫א‬
              Va = 5 + I * 8

                            8
              Va = 5 +        *8
                           12

              Va = 5 + 3.33 ≈ 8.33V


                                                  - ١٣٨ -
  ‫א‬‫א‬                               ‫٠٤١ א‬                             ‫א‬
 ‫א‬‫א‬‫א‬                      ١-                  



                     K‫א‬‫א‬‫א‬ Va ‫א‬‫א‬
                                      K‫א‬Short R Th W‫א‬‫א‬

            R Th = R ab

  KE١٩J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                
                                      R 1 = 4Ω                 R 2 = 8Ω
                                                                                                
                                                           a
                                                                                                
                                                          b                                     
                                                                                                
 K‫א‬‫א‬E٦J ٧F‫א‬‫א‬‫א‬E١٩J ٧F
                                                  KE٢٠J ٧F‫א‬‫א‬‫א‬‫א‬
                                                                                                
                                     R 1 = 4Ω              R 2 = 8Ω
                                                       a
                                                                                                
                                                                                                
                                                      b
                                                                                                
                                                                                                
               KE١٩J ٧F‫א‬‫א‬‫א‬E٢٠J ٧F

                                                      WRTH‫א‬

                              4*8
           ∴ R Th = R ab =        = 2.66Ω
                              4+8




                                                - ١٣٩ -
    ‫א‬‫א‬                                 ‫٠٤١ א‬                                         ‫א‬
   ‫א‬‫א‬‫א‬                         ١-                             



              KE٢١J ٧F‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
                                                        R Th = 2.66Ω                                            
                                                                                   A                            
                                                                                                                
            VTh = 8.33V
                                                          I                            6Ω                       
                                                                                                                
                                                                                   B                            
                            KE٦J ٧FE٢١J ٧F

                                                                  Wab‫א‬‫א‬
                          VTh      8.33
              I ab =            =         = 0.96A
                       R Th + 6Ω 2.66 + 6

                                                                                         E٧J ٧F
                                             K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                           ‫א‬
                            
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                             K‫א‬
            KE٢٢J ٧F، E1 ‫א‬‫א‬W‫א‬‫א‬‫א‬
                                           IT١
                                                                                                                
                                                                    a
                                                                                                                
                                 +               R 1 = 4Ω               R 2 = 8Ω
                                                                                                                
                                 10V
                                                          Iab١          R 3 = 6Ω                                
                                 −
                                                                                                                
                                                    
                                                                    b
                                                    
 KE٧J ٧F‫א‬‫א‬‫א‬١٠ V‫א‬‫א‬E٢٢J ٧F

                                                                           WIab١‫א‬

                                                    - ١٤٠ -
    ‫א‬‫א‬                                   ‫٠٤١ א‬                                 ‫א‬
   ‫א‬‫א‬‫א‬                         ١-                       


                            8*6
              RT = 4 +          = 7.43Ω
                            8+6
                        10
              i T1 =        = 1.345A
                       7.43
                                 8
              i ab1 = 1.345 *       = 0.77 A
                                8+6
                                                                                                          
              KE٢٣J ٧F، E 2 ‫א‬‫א‬W‫א‬‫א‬‫א‬
                                                                                                          
                                                                    IT٢
                                                        a                                                 
                                         R 1 = 4Ω           R 2 = 8Ω                                      
                                                                                   +
                                               Iab٢         R 3 = 6Ω               5V                     
                                                                                   −                      
                                                                                                          
                                                        b
                                                                                                          
 KE٧J ٧F‫א‬‫א‬‫א‬ ٥ V‫א‬‫א‬E٢٣J ٧F

                                                                           WIab٢‫א‬
                            4*6
              RT = 8 +          = 10.4Ω
                            4+6
                       5
              iT =         = 0.48A
                      10.4
                                4
              i ab = 0.48 *        = 0.192A
                               4+6

                                                                                   
،‫א‬ab‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
                                              W‫א‬‫א‬‫א‬‫א‬‫א‬

              i ab = 0.77 + 0.192 = 0.962A

                                              
                                              
                            K ‫א‬‫א‬ ‫א‬‫א‬

                                                      - ١٤١ -
    ‫א‬‫א‬                              ‫٠٤١ א‬                                     ‫א‬
   ‫א‬‫א‬‫א‬                      ١-                         



                                                                                      E٨J ٧F
                 W‫א‬E٢٤J ٧F‫א‬‫א‬‫א‬ R L ‫א‬‫א‬‫א‬
                                                                      K‫א‬EF
                                                                                   KEF
                                                                 12kΩ                                    
                                                        a
                                                                                                         
                                                  
                                                                                    R L = 8kΩ
                           2mA     I                       10kΩ         
                                                                                                         
                                                         b                                               
                        KE٨J ٧F‫א‬‫א‬‫א‬E٢٤J ٧F
                                                                                                     ‫א‬
‫א‬‫א‬12KΩ ، 8KΩ ‫א‬‫א‬‫א‬‫א‬‫א‬W
                                                                                         
                                                                                 K10KΩ ‫א‬‫א‬
                              10
             ∴i ↓ = 2 *
                  RL        10 + 20

                       1 2
              i ↓ = 2 * = mA
               RL      3 3




                                                 - ١٤٢ -
     ‫א‬‫א‬                                   ‫٠٤١ א‬                                    ‫א‬
    ‫א‬‫א‬‫א‬                           ١-                        



                                                                                                       
                                                                                K‫א‬W
 KEJ ٢٥J ٧F‫א‬‫א‬ VTh  R L ‫א‬W‫א‬‫א‬
                                                                                                              
                                                                  12kΩ
                                                       a                                                      
                                                                         I=0
                                                                                                              
                                                                                   VTh
                                                                                                              
                  2mA              I                        10kΩ
                                                                                   ⇐                          
                                                                                                              
                                                        b
                                                                                                              
              KRLE٨J ٧F‫א‬‫א‬‫א‬EJ ٢٥J ٧F

               ∴ VTh = 2mA * 10KΩ = 20V

‫א‬‫א‬‫א‬W‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                             
                                              KEJ ٢٥J ٧F‫א‬‫א‬‫א‬EF
                                                                                                              
                                                                       12kΩ
                                                             a                                                
                                                                       I=0                                    
                                                                                    R Th
                            open                                  10kΩ
                                                                                    ⇐                         
                                                                                                              
                                                                                                              
                                                              b
                                                                                                              
       K‫א‬E٨J ٧F‫א‬‫א‬‫א‬EJ ٢٥J ٧F

                                                                        WRTh

               ∴ R Th = 10 + 12 = 22KΩ

                                        KE٢٦J ٧FW‫א‬‫א‬

                                                       - ١٤٣ -
     ‫א‬‫א‬                                ‫٠٤١ א‬                                      ‫א‬
    ‫א‬‫א‬‫א‬                        ١-                          



                                                                                                             
                                                     R Th = 22kΩ                                             
                                                                                  A                          
                                                                                                             
       VTh = 20V
                                                        I                             R L = 8kΩ              
                                                                                                             
                                                                                                             
                                                                                  B
                                                    
                             KE٨J ٧FE٢٦J ٧F
                                                                                                             
                                      W‫א‬‫א‬‫א‬
                          VTh
              ∴I =
                       R TH + R L
                     20     20V  2
               I=         =     = mA
                    22 + 8 30KΩ 3
                                         K‫א‬‫א‬‫א‬‫א‬

                                                        ‫א‬‫א‬           ١J ٤J ٧
،Bridge Circuit‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬Thevinen's Theorem،‫א‬‫א‬
        K‫א‬‫א‬‫א‬‫א‬،‫א‬
B،A‫א‬‫א‬W‫א‬‫א‬،E٢٧J ٧F‫א‬‫א‬
                           
                                            K R L ‫א‬D،COutput‫א‬

                         
‫א‬‫א‬D،C‫א‬‫א‬‫א‬
                                                  
                                             KSource‫א‬‫א‬B،A‫א‬‫א‬



                                                    - ١٤٤ -
 ‫א‬‫א‬                                ‫٠٤١ א‬                                     ‫א‬
‫א‬‫א‬‫א‬                       ١-                          



                                                               A
                                                                                                        
                                                    R1                 R2                               
                                                                                                        
                                                             RL
                        VS                  C                                D                          
                                                
                                                R 3                    R4
                                                
                                                              B

                                 K‫א‬‫א‬E٢٧J ٧F
                                                                                     E٩J ٧F
                                              W‫א‬،E٢٨J ٧F‫א‬‫א‬‫א‬
                                            KD،C‫א‬ R L ‫א‬‫א‬EF
                                                                       K R L ‫א‬‫א‬‫א‬EF
                                                 A
                                                                                                        
                                  R 3 = 330Ω                       R 2 = 680Ω
                                                                                                        
                                                R L = 1kΩ                                               
 VS = 24V                             C                                D                                
                                                                                                        
                                  R 3 = 680Ω                       R 4 = 560Ω
                                                                                                        
                                                                                                        
                                                         B
                                                
                         KE٩J ٧F‫א‬‫א‬E٢٨J ٧F




                                                - ١٤٥ -
     ‫א‬‫א‬                                        ‫٠٤١ א‬                                   ‫א‬
    ‫א‬‫א‬‫א‬                               ١-                        



                                                                                                              ‫א‬
                                                                              W‫א‬
‫א‬‫א‬‫א‬‫א‬D،C‫א‬ R L ‫א‬W‫א‬‫א‬
                                                                                     
                                                                                   W VTh D،C

               VTh = VC − VD

                     ⎛ R3 ⎞      ⎛ R4 ⎞
               VTh = ⎜     ⎟VS − ⎜
                     ⎜R +R ⎟     ⎜ R + R ⎟VS
                                         ⎟                                                                  E٧J ٧F
                     ⎝ 1  3⎠     ⎝ 2    4⎠


،K‫א‬‫א‬ R L ‫א‬‫א‬‫א‬‫א‬‫א‬
            
                                                                                        KE٢٩J ٧F
                                                                                                         W

                VC = I1R 3
                          VS
                I1 =
                        R1 + R 3

                VD = I 2 R 4
                          VS
                I2 =
                        R2 + R4

                                                                                                                  
                                                                      I1         I2
                                                                                                                  
                                             R 1 = 330Ω                                  R 2 = 680Ω
                            +
                            24V
                                                        C                  VTh           D
                            −
                                                                                                                  
                                             R 3 = 680Ω                                  R 4 = 560Ω
                                                                      VC         VD                               
                                                                                                                  
                                                            
                    KRL‫א‬E٩J ٧F‫א‬‫א‬E٢٩J ٧F
                                                            - ١٤٦ -
    ‫א‬‫א‬                                  ‫٠٤١ א‬                               ‫א‬
   ‫א‬‫א‬‫א‬                          ١-                   



                                                                      WVTh

                      ⎛ 680 ⎞              ⎛ 560 ⎞
              ∴ VTh = ⎜           ⎟ * 24 − ⎜           ⎟ * 24
                      ⎝ 330 + 680 ⎠        ⎝ 680 + 560 ⎠

              VTh = 16.158 − 10.838 = 5.32V

                                                                                   
 R Th ‫א‬‫א‬‫א‬W‫א‬‫א‬
                       KE٣٠J ٧F‫א‬‫א‬‫א‬‫א‬D،C‫א‬‫א‬
                                                          R1

                                            A
                                                                            C
                                                          R3
                                                                            R Th

                                                          R2                ⇐
                                            B            R4                 D


                            KE٩J ٧FRTh‫א‬E٣٠J ٧F
                                                                           WRTh

                              R 1R 3   R 2R 4
              ∴ R Th =               +                                                           E٨J ٧F
                             R1 + R 3 R 2 + R 4

                           330 * 680 680 * 560
              R Th =                +
                           330 + 680 680 + 560

              R Th = 222.178 + 307.096 = 529.27Ω

                                   KE٣١J ٧FW‫א‬‫א‬




                                                     - ١٤٧ -
    ‫א‬‫א‬                                   ‫٠٤١ א‬                                     ‫א‬
   ‫א‬‫א‬‫א‬                           ١-                         



                                                                                                               
                                                     R Th = 529.27Ω
                                                                                  C                            
                                                                                                               
     VTh = 5.32V
                                                          I                           R L = 1kΩ                
                                                                                                               
                                                                                 D                             
                             KE٩J ٧FE٣١J ٧F

      W،‫א‬CD‫א‬‫א‬

                               VTh
              ∴ I CD =
                            R Th + R L

                               5.32
              I CD =                     = 3.5mA
                           529.27 + 1000

                                                                   ٣{٥ mACD‫א‬‫א‬‫ ∴א‬

                                                            J ‫א‬–‫א‬ ٥J ٧
                                 E Y ← ∆ F‫א‬‫א‬‫א‬‫١ א‬J ٥J ٧
                                                                          " Conversion From Delta → Star "
                                      
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                    KE٣٢J ٧F‫א‬ Y ← ∆ ‫א‬
                                                                                      A
                                    A
                                                      
                                                                                                               
                                                                  ≡
                                   R1
                                                                           RC                       RA         
                                    O                                                                          
                            R2                R3
                                                                                       RB
               B                                              C       B                                    C
                                                                                                               
                                    K Y ↔ ∆ E٣٢J ٧F
                                                      - ١٤٨ -
    ‫א‬‫א‬                                    ‫٠٤١ א‬                                    ‫א‬
   ‫א‬‫א‬‫א‬                            ١-                        



                                                    Kc،b،aC،B،A ∆ ‫א‬
                                                                    K٣،٢،١ Y ‫א‬
                                                  " Conversion From (Y←∆)" (Y←∆)‫א‬
،E٣٣J ٧F ∆ ‫א‬‫א‬ Y ‫א‬
                                               K‫א‬
                                                                                                              


                                                               A



                                                        R1
                                             RC                             RA                                
                                                  R2       O           R3
                                                                                                              
                                                                                                              
                                       B                                        C
                                                           RB
                                                       
                             ‫א‬‫א‬‫א‬E٣٣J ٧F

‫א‬= Y W‫א‬‫א‬‫א‬
                                                   
                            WK ∆ ‫א‬‫א‬ ∆ ‫א‬
                         R AR C
              R1 =                                                                              E٩J ٧F
                      RA + RB + RC
                          R BR C
              R2 =                                                                              E١٠J ٧F
                       RA + RB + RC
                         R CR A
              R3 =                                                                              E١١J ٧F
                      RA + RB + RC




                                                       - ١٤٩ -
     ‫א‬‫א‬                                    ‫٠٤١ א‬                                       ‫א‬
    ‫א‬‫א‬‫א‬                            ١-                          



                                 E ∆ ← Y F‫א‬‫א‬‫א‬                     ٢J ٥J ٧
                                                             W‫א‬‫א‬‫א‬
                                     R 1R 3
               R A = R1 + R 3 +                                                            E١٢J ٧F
                                      R2
                                     R 2R 3
               RB = R2 + R3 +                                                              E١٣J ٧F
                                      R1
                                     R 1R 2
               R C = R1 + R 2 +                                                            E١٤J ٧F
                                      R3

‫א‬ Y ‫א‬ ∆ ‫א‬‫א‬
                                 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                            E١٠J ٧F
                                   K‫א‬ Y ‫א‬E٣٤J ٧F‫א‬ ∆ ‫א‬ 
                                                                                                   
                                                            A
                                                        
                                                        
                                              220Ω                     560Ω



                                                            100Ω
                                         B                                       C
                             KE١٠J ٧F‫א‬E٣٤J ٧F
                                                                                                           ‫א‬
،E٣٥J ٧F ∆ ‫א‬‫א‬ Y ‫א‬
                                                                                   K Y ← ∆ ‫א‬




                                                        - ١٥٠ -
    ‫א‬‫א‬                                ‫٠٤١ א‬                              ‫א‬
   ‫א‬‫א‬‫א‬                       ١-                   



                                                                                                    
                                                         A                                          
                                                                                                    
                                                                                                    
                                                    R1                                              
                                      100Ω                             220Ω
                                                                                                        
                                                                                                        
                                              R2     O            R3                                    

                                                                                                    
                                  B                                           C                     
                                                   560Ω
             KE١٠J ٧F‫א‬‫א‬‫א‬E٣٥J ٧F

،E١١J ٧FJ E٩J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                          W

                         100 * 220
              R1 =                    = 25Ω
                      100 + 220 + 560

                         100 * 560
              R2 =                    = 63.6Ω
                      100 + 220 + 560

                         220 * 560
              R3 =                    = 140Ω
                      100 + 220 + 560




                                                   - ١٥١ -
 ‫א‬‫א‬                                  ‫٠٤١ א‬                                  ‫א‬
‫א‬‫א‬‫א‬                          ١-                      



                             KE٣٦J ٧F‫א‬‫א‬
                                                      A                                                
                                                  
                                            R 1 = 25Ω                                                  
                                                                                                       
                                                      O
                                    R 2 = 63.5Ω                   R 3 = 140Ω                           

                                    B                                    C
                                                                                                       
       KE١٠J ٧F‫א‬‫א‬‫א‬E٣٦J ٧F

                                                                                    E١١J ٧F

                                         KE٣٧J ٧F‫א‬‫א‬ ∆ ← Y ‫א‬ 
                                                                                                
                                                      A                                                
                                                                                                       
                                         R 1 = 1kΩ                                                     
                                                                                                       
                                                      O
                               R 2 = 2.2kΩ                        R 3 = 5.6kΩ                          
                                                                                                       
                                B                                              C
                                                                                                       
                         KE١١J ٧F‫א‬E٣٧J ٧F




                                                  - ١٥٢ -
     ‫א‬‫א‬                                 ‫٠٤١ א‬                                     ‫א‬
   ‫א‬‫א‬‫א‬                        ١-                           



                                                                                                        ‫א‬
،E٣٨J ٧F، Y ‫א‬ ∆ ‫א‬
                                                                                 K ∆ ← Y ‫א‬
                                                            A                                                
                                                                                                             
                                                                                                             
                                                     1kΩ                                                     
                                          RB                             RA
                                                                                                             
                                                        O
                                               2.2kΩ               5 .6 k Ω                                  

                                     B                                           C
                                                        RC
             KE١٢J ٧F‫א‬‫א‬‫א‬E٣٨J ٧F
                                                                                                             
                                               
‫א‬H Y ‫א‬ ‫א‬‫א‬= ∆ ‫א‬
                                                                               K‫א‬ Y 
                                             W،E١٤J ٧FJ E١٢J ٧F‫א‬‫א‬

                                 1 * 5 .6
              R A = 1 + 5 .6 +            = 9.15KΩ
                                   2.2

                                 1 * 2 .2
              R B = 1 + 2.2 +             = 3.59KΩ
                                   5 .6

                                   2.2 * 5.6
              R C = 2.2 + 5.6 +              = 20.12KΩ
                                       1




                                                     - ١٥٣ -
     ‫א‬‫א‬                                 ‫٠٤١ א‬                                         ‫א‬
   ‫א‬‫א‬‫א‬                          ١-                             




K‫א‬‫א‬ ∆ ← Y  Y ← ∆ ‫א‬‫א‬‫א‬                              ٣J ٥J ٧

                                                                                            E١٢J ٧F
‫א‬،E٣٩J ٧F‫א‬‫א‬‫א‬ R L ‫א‬‫א‬‫א‬
                                                                                                       K∆ → Y
                                                               A                                                  
                                                                                                                  
                                        R 1 = 4.7kΩ                      R 2 = 3 .9 k Ω
                                                                                                                  
                                                            18kΩ                                                  
          VS = 120V                           C                                D
                                                                                                                  
                                                                                                                  
                                       R 3 = 2 .2 k Ω                     R 4 = 2 .7 k Ω
                                                     
                                                                B
                        KE١٢J ٧F‫א‬‫א‬‫א‬E٣٩J ٧F
                                                                                                            ‫א‬
     
D،C،A‫א‬‫א‬‫א‬ ∆ ‫א‬‫א‬‫א‬
                                                                
‫א‬ Y ‫א‬D،C،B‫א‬‫א‬‫א‬ ∆ ‫א‬
                      
‫א‬D،C،B‫א‬‫א‬‫א‬ ∆ ‫א‬‫א‬
                                   KE٤٠J ٧F Y ‫א‬‫א‬
                                                                                                                  
                                                                     C                                        D
                           18kΩ                                                  R١            R٢
           C                              D
                                                                                                                  

                                                               ≡
                                                                                           o
   R 3 = 2 .2 k Ω                     R 4 = 2.7kΩ                                             R٣


                             B                                                            B

          KE١٢J ٧F‫א‬‫א‬‫א‬E٤٠J ٧F

                                                     - ١٥٤ -
    ‫א‬‫א‬                                ‫٠٤١ א‬                                        ‫א‬
   ‫א‬‫א‬‫א‬                        ١-                            



                                                                          W R 3 ، R 2 ، R1 

                         18 * 2.2
              R1 =                   = 1.73KΩ
                      2.2 + 2.7 + 18

                          2.7 * 18
              R2 =                    = 2.12KΩ
                       2.2 + 2.7 + 18

                         2 .2 * 2 .7
              R3 =                   = 0.26KΩ
                      2.2 + 2.7 + 18

 R 3 ، R 2 ، R1 ‫א‬‫א‬‫א‬‫א‬
                                                                                      WE٤١J ٧F
                                                                                                              
                                                                                                             
                                                                   A
                                                                                                              
                                        R 1 = 4.7 kΩ                       R 2 = 3 .9 k Ω                    
                                                                                                              
             VS = 120V                       C                                   D                            
                                                1.73kΩ                    2.12kΩ                              
                                                                   o
                                                                       0.26kΩ                                 
                                                                                                              
                                                                   B
                                                                                                              
       K‫א‬‫א‬‫א‬‫א‬‫א‬E٤١J ٧F
                                                                                                              
                                                  WE٤٢J ٧F‫א‬‫א‬‫א‬‫א‬




                                                   - ١٥٥ -
     ‫א‬‫א‬                               ‫٠٤١ א‬                                            ‫א‬
   ‫א‬‫א‬‫א‬                        ١-                                



                                                              A                                                   
                                                                              I2                                  
                                                                   I1
                                                    4.7 kΩ                                                        
                                                                                     3 .9 k Ω
                                       +                                                                          
                                       120V               C                           D
                                                                                                                  
                                       −
                                                  1.73kΩ                             2.12kΩ                       
                                                                                                                  
                                                                                                                  
                                                                            0.26kΩ
                                                                                                                  
                                                                        B                                         
                            KE٤١J ٧F‫א‬E٤٢J ٧F

                    
‫א‬‫א‬ Υ ‫א‬ ∆ ‫א‬‫א‬‫א‬‫א‬
                        ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                              W‫א‬‫א‬
                                                                             K‫א‬ R T W
                                                                     K I T ‫א‬‫א‬W
                                              K‫א‬‫א‬ I 2 ، I1 W
                                                     K VC  C ‫א‬‫א‬W‫א‬
                                                  K VD  D ‫א‬‫א‬W
                                            K D ، C ‫א‬‫א‬‫א‬W
              VCD = VC − VD
         K R L  VCD ‫א‬‫א‬ CD ‫א‬‫א‬W
                           VCD
             ∴ ICD =
                           RL
                                                                             W‫א‬‫א‬‫א‬

                        (4.7 + 1.73) ⋅ (3.9 + 2.12)
              RT =                                  + 0.26 ≈ 3.37 KΩ
                       (4.7 + 1.73) + (3.9 + 2.12)

                                                   - ١٥٦ -
       ‫א‬‫א‬                                    ‫٠٤١ א‬                                          ‫א‬
      ‫א‬‫א‬‫א‬                            ١-                             


                 ∴ R T = 3.37 KΩ

                         120
                 IT ≈         ≈ 35.6mA
                         3.37

                                                                           W‫א‬‫א‬

                 I1 = I T *
                                     (3.9 + 2.12)
                              (3.9 + 2.12) + (4.7 + 1.73)
                 ∴ I1 = 17.2mA

                 I 2 = 18.38mA

                 VC ≈ 39.18V

                 VD = 48.32V

                                                                                 K D ، C ‫א‬‫א‬
                 ∴ VCD = VC − VD

                 VCD = 39.18 − 48.32 = −9.14V

 C ‫א‬‫א‬ D ‫א‬‫א‬EJ F‫א‬W
                                                                K ICD ‫א‬‫א‬ VD 〉 VC
                              9.14V
                ∴ ICD =             = 0.507mA
                              18KΩ

                    KE‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ٧
 ‫א‬‫א‬‫א‬‫א‬
                                                                
 ‫א‬،‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
                                                                                      
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                       
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  
 ‫א‬‫א‬‫א‬‫א‬‫א‬
                                     
 ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                                      K‫א‬‫א‬

                                                          - ١٥٧ -
    ‫א‬‫א‬                               ‫٠٤١ א‬                                ‫א‬
   ‫א‬‫א‬‫א‬                       ١-                    



                                           
‫א‬‫א‬‫א‬Mesh
                  K‫א‬b،a‫א‬‫א‬،E٤٣J ٧F‫א‬‫א‬‫א‬
                                     R١                                 R٢                            K
                      a                                     b                               d
                                                                                                      
            V١                                                                                    V٢ 
                                           a           R3                      b
                                                                                                      
                                                  

                                                            c
                                                                                           e          
                                    R5                                    R4                          
                   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤٣J ٧F
                                                                                                      
                                                       W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                KMesh‫א‬‫א‬‫א‬‫א‬             E١F
       KCL‫א‬ Meshes ‫א‬‫א‬       E٢F
                                                                                                K‫א‬‫א‬
                      K‫א‬‫א‬‫א‬KVL‫א‬                  E٣F
                               K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬            E٤F
                             Meshes.‫א‬‫א‬‫א‬‫א‬‫א‬             E٥F
                                          K‫א‬‫א‬‫א‬‫א‬‫א‬             E٦F




                                                  - ١٥٨ -
    ‫א‬‫א‬                                      ‫٠٤١ א‬                                         ‫א‬
   ‫א‬‫א‬‫א‬                             ١-                              



                                                                                               E١٣J ٧F
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                            KE٤٤J ٧F‫א‬
                                                                                                                     
                         I1                              I2                                   I3
                    a
                                               b                                 d                                   
                                 10Ω                     c            30Ω            20Ω                             
         10V                                       20V                                                      15V
                                       20Ω                                                                           
                                 I1                                     10Ω
                                                             I2                       I3                             
                                         I5                                 I4
                                                                                                                     
                                                                  f                                                  
                         KE١٣J ٧F‫א‬‫א‬‫א‬E٤٤J ٧F
                                                                                                                     
                                                                    
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬
                                                    K،‫א‬‫א‬
                                                          
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                            K I 5 ، I 4 ، I 3 ، I 2 ، I1 ‫א‬‫א‬‫א‬ I 3 ، I 2 ، I1 
                               EbF‫א‬‫א‬‫א‬ I 5 ، I 4 

               I 5 = I1 − I 2                                                                (a)

               I 4 = I 2 − I3                                                                (b)

                                                                                             
‫א‬‫א‬‫א‬ I 3 ، I 2 ، I1 ‫א‬‫א‬
                                                                                                             K‫א‬
                                                                          
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                               K‫א‬
                                                                                                                     
                                        Mesh E١F‫א‬‫א‬W‫א‬‫א‬
                                                                                                                     
               10 = 10I1 + 20I 5                                                             (c)
                                                         - ١٥٩ -
    ‫א‬‫א‬                               ‫٠٤١ א‬                                          ‫א‬
   ‫א‬‫א‬‫א‬                       ١-                              



                                                              I1 + I 2 EaF I 5 
                                                                I 2 ، I1  I 5 KW
              ∴10 = 10I1 + 20I1 − 20I 2
              10 = 30I1 − 20I 2                                                       (d)

                                                                        KEdF
                                                                                                               
                                   Mesh E٢F‫א‬‫א‬W‫א‬‫א‬
               20 = 30I 2 + 20I5 − 10I 4                                              (e)
                    WEeF I 5 ، I 4 ‫א‬
              20 = −30I 2 + 20(I1 − I 2 ) − 10(I 2 − I 3 )
              20 = −30I 2 + 20I1 − 20I 2 − 10I 2 + 10I 3
              20 = 20I1 − 60I 2 + 10I 3                                               (f)
                                                                                                               
                                      Mesh E٣F‫א‬‫א‬W‫א‬
              15 = −20I 3 + 10I 4                                                     (g)
                                                                   WEbF I 4 
               15 = −20I 3 + 10(I 2 − I 3 )
               15 = −20I 3 + 10I 2 − 10I 3
               15 = −30I 3 + 10I 2                                                    (h)
‫א‬ I 3 ، I 2 ، I1 EhF،EfF،EdF‫א‬
                                                  W‫א‬‫א‬‫א‬
              10 = 30I1 − 20I 2 − (0) I 3                                             (I)
              − 20 = −20I1 + 60I 2 − 10I 3                                            (II)
              − 15 = (0) I1 − 10I 2 + 30I 3                                           (III)
                               W(III, II, I)‫א‬‫א‬
                                                                                                               



                                                  - ١٦٠ -
      ‫א‬‫א‬                                 ‫٠٤١ א‬                                     ‫א‬
    ‫א‬‫א‬‫א‬                        ١-                           



                ⎡ 10 ⎤ ⎡+ 30          − 20    −0 ⎤      ⎡I1 ⎤
                ⎢− 20⎥ = ⎢− 20        + 60    − 10⎥     ⎢I ⎥                                    (IV)
                ⎢     ⎥ ⎢                         ⎥     ⎢ 2⎥
                ⎢− 15 ⎥ ⎢− 0
                ⎣     ⎦ ⎣             − 10     30 ⎥
                                                  ⎦     ⎢I 3 ⎥
                                                        ⎣ ⎦
                                                                                                              
                               WEIVF‫א‬‫א‬
                [V] = [R ] ⋅ [I]                                                        E١٥J ٧F
                                                                                                              
             K‫א‬‫א‬‫א‬‫א‬‫א‬، [I]‫א‬J
 MeshE٣F،MeshE٢F،MeshE١F‫א‬‫א‬‫א‬W [V ] ‫א‬J
                              
 ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
                                    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬W [R ] ‫א‬J
                       ⎡R11 R12 R13 ⎤
                [R ] = ⎢R 21 R 22 R 23 ⎥
                       ⎢               ⎥                                                E١٦J ٨F
                       ⎢R 31 R 32 R 33 ⎥
                       ⎣               ⎦
                                                                                                              
 ‫א‬‫א‬‫א‬ R 33 ، R 22 ، R11 ‫א‬‫א‬
                                                                     W،‫א‬
                                                       KMeshE١F‫א‬‫א‬ R11
                                                       KMeshE٢F‫א‬‫א‬ R 22
                                                       KMeshE٣F‫א‬‫א‬ R 33
                                                                                                              
  R12 ‫א‬‫א‬‫א‬‫א‬
           
 E٢F‫א‬‫א‬‫א‬ R 23 ‫א‬KMeshE٢F،MeshE١F‫א‬‫א‬
         K‫א‬‫א‬‫א‬،‫א‬MeshE٣F‫א‬،Mesh
  
 ‫א‬‫א‬‫א‬MeshE٣F‫א‬MeshE١F‫א‬
                                         K‫א‬R١٣


                                                      - ١٦١ -
    ‫א‬‫א‬                               ‫٠٤١ א‬                                      ‫א‬
   ‫א‬‫א‬‫א‬                       ١-                         



                                                                         
‫א‬‫א‬‫א‬‫א‬
                                                                                           K I 3 ، I 2 ، I1
                                                                        ‫א‬‫א‬‫א‬
                                                     W‫א‬E١
                      R 11   R 12      R 13
               ∆ = R 21 R 22          R 23                                         E١٧J ٧F
                      R 31   R 32      R 33
                                                                                     K‫א‬∆
                W‫א‬‫א‬‫א‬

              ∆ = R11{R 22 R 33 − R 32 R 23 } − R12 {R 21R 33 − R 31R 23 } + R13 {R 21R 32 − R 31R 22 }

                                                K∆‫א‬‫א‬‫א‬
                                                                    W I1 ‫א‬
                     V1 R12 R13
                   1
              I1 =   V2 R 22 R 23                                                   E١٨J ٧F
                   ∆
                     V3 R 32 R 33
                                                                   W I 2 ‫א‬
                     R11        V1      R13
                   1
              I2 =   R 21       V2      R 23                                        E١٩J ٧F
                   ∆
                     R 31       V3      R 33
                                                                   W I 3 ‫א‬
                     R11        R12      V1
                   1
              I3 =   R 21       R 22     V2                                         E٢٠J ٧F
                   ∆
                     R 31       R 32     V3

                        W‫א‬ I 3 ، I 2 ، I1 ‫א‬ ∆ ‫א‬‫א‬
                                                                                 W ∆ ‫א‬
                   + 30 − 20            −0
               ∆ = − 20 +60             − 10
                   −0   − 10            + 30
                                                  - ١٦٢ -
    ‫א‬‫א‬                                ‫٠٤١ א‬                               ‫א‬
  ‫א‬‫א‬‫א‬                         ١-                   



،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                       W‫א‬
                                                                                                     
              ∆ = 30(60 * 30 − (−10) * (−10 )) − (−20) * (− 20 * 30 − 0) + 0(KK) = 39000
                                         W‫א‬‫א‬‫א‬، I1 
                     + 10          − 20 − 0
                   1
              I1 =   − 20          + 60 − 10
                   ∆
                     − 15          − 10 +30
                                                                    W‫א‬

                            1
             ∴ I1 =             {10 * (60 * 30 − 100) − (−20) * (− 20 * 30 − 15 * 10)} = 0.05128A
                          39000
                                                                                   W
                    + 30 + 10 − 0            + 30 +10    0
                  1                    1
             I2 =   − 20 − 20 − 10 =       ⋅ − 20 − 20 − 10
                  ∆                  39000
                    −0   − 15 + 30           −0   − 15 + 30

                                                       W‫א‬‫א‬‫א‬
                        1
             I2 =           {30 * ((−20) * (30) − (−15) * (−10)) − (10) * ((−20) * (30) − (0))}
                      39000
             I 2 = −0.423A

                                           K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                   W
                     + 30 − 20 + 10
                   1
              I3 =   − 20 + 60 − 20
                   ∆
                     − 0 − 10 − 15
                       WI٣‫א‬ ∆ ‫א‬‫א‬‫א‬
              1
     I3 =         { 30 * ((60) * (−15) − (−10) * (−20)) − (−20) * ((−20) * (−15)
            39000
                    − (−10) * (10)) =
             I 3 = −0.641A
                                                   - ١٦٣ -
     ‫א‬‫א‬                                ‫٠٤١ א‬                                    ‫א‬
   ‫א‬‫א‬‫א‬                         ١-                       



                                           K‫א‬‫א‬‫א‬‫א‬‫א‬
                        W I 5 ، I 4  I 3 ، I 2 ، I1 ‫א‬‫א‬‫א‬‫א‬

               I 4 = I 2 − I 3 = 0.218A

               I 5 = I1 − I 2 = 0.05128 + 0.42300 = 0.47428A

‫א‬‫א‬‫א‬W
              K‫א‬‫א‬‫א‬‫א‬‫א‬
                                                                                  "Summary"‫א‬
      
    K‫א‬‫א‬‫א‬‫א‬ KCL  E١F
‫א‬‫א‬ KVL  E٢F
                                                                                                
                                                                                              K‫א‬
   K E٣F
                                    K‫א‬‫א‬‫א‬‫ א‬E٤F
       K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٥F
                                                         
 ‫א‬‫א‬‫א‬‫א‬‫א‬ E٦F
                                                                    
،‫א‬‫א‬‫א‬‫א‬‫א‬
              
 ‫א‬‫א‬‫א‬‫א‬
                                             K‫א‬‫א‬‫א‬‫א‬‫א‬
                              
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٧F
                                                            K‫א‬‫א‬‫א‬
                                                                
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٨F
            K‫א‬‫א‬‫א‬‫א‬ R Th ‫א‬‫א‬ VTh 
                                                                                                          
                                                                                                          




                                                    - ١٦٤ -
  ‫א‬‫א‬                                     ‫٠٤١ א‬                                        ‫א‬
 ‫א‬‫א‬‫א‬                             ١-                            



                                          ‫א‬‫א‬
                                                                                                                 
                       K R S = 50Ω ، VS = 300V E١F
                                                                                                                 
                           K‫א‬‫א‬‫א‬‫א‬‫א‬E٢F
                                                                                                                 
                            100Ω                                                      2 .2 Ω
                                                                                                                 
              5kV                                                         12V
                                                                                                                 
                                                                                                                 
                                                                                                                 
                                                                                                                 
          K R S = 1.2KΩ ، iS = 600mA ‫א‬‫א‬E٣F
                                                                                                                 
                                   K‫א‬‫א‬‫א‬‫א‬E٤F
                                                                                                                 
                                                                                                                 
0.01A        I           2.7 kΩ                        10mA           I    4 .7 k Ω                              
                                                                                                                 
                                                                                                                 
                          K‫א‬‫א‬‫א‬ R 5 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥F

                                   R1 = 1kΩ            R 3 = 1kΩ                                                 
                                                                                                                 
                 2V
                                                                                                                 
                                  R 2 = 2 .2 k Ω          R 4 = 1kΩ
                                                                                               R5                
                                                                                                                 
                                                              3V                                                 

                                                      - ١٦٥ -
 ‫א‬‫א‬                                     ‫٠٤١ א‬                                  ‫א‬
‫א‬‫א‬‫א‬                             ١-                      



                             W‫א‬‫א‬ R 3 ‫א‬‫א‬‫א‬‫א‬‫א‬E٦F
                                                                        R 3 = 330Ω                        
                                                                                                          
                               R 1 = 680Ω             R 2 = 220Ω
           100mA        I                                                            R 4 = 470Ω           
                                                         20V                                              
                                                                                                          
                                                                                                          
                                                                                                          
                                              K R L ‫א‬‫א‬‫א‬‫א‬ E٧F
                                                                                                          
                               1kΩ                   8.2kΩ                560Ω                            
               40V
                                                                                                          

                                0 .5 A        I                                      R 5 = 1 .5 k Ω



                                                       60V
                                                                                                          
                              1kΩ
                                                                                                          
                                                                                                          
                                                    ‫א‬‫א‬ R L ‫א‬‫א‬‫א‬E٨F
                                                           A

                                     R 1 = 1kΩ                       R 2 = 820Ω

                                                      R L = 1kΩ
                                         C
 VS = 12V                                                                 D


                                 R 3 = 2.2kΩ                          R 4 = 1.2kΩ


                                                         B
                                                     - ١٦٦ -
 ‫א‬‫א‬                  ‫٠٤١ א‬                                 ‫א‬
‫א‬‫א‬‫א‬          ١-                     




                             W‫א‬‫א‬‫א‬ AB ‫א‬E٩F
                                                                                      
                                                                                      
                          R 1 = 10Ω                               R 2 = 15kΩ          
                    +                                                                 
                    10V               A                       B                       
                    −
                                                                                      
                           R 3 = 12kΩ             I = 0.2mA   R4
                                                                                      
                                                                                      
                                                                                      




                           


                                  - ١٦٧ -
‫א‬‫א‬                           ‫٠٤١ א‬                                 ‫א‬
                              ١-                     



                          (References) ‫א‬‫א‬
                                      
[١] Thomas L. Floyed, Electrical Engineering Fundamentals, Prentice, Inc, sixth
    edition, ٢٠٠٠.
[٢] B. L. Theraja, A. K. Theraja, " Electrical Technology", published by Ninja
    Construction development Co. Ltd. Ram Nagar, New Delhi, ١١٠٠٥٥, ١٩٩٥.
[٣] M. A. PAI, "Introduction to Electric Circuits and Machines", Affiliated east west
    presses private limited, ١٩٧٥.




                                      - ١٦٨ -
                     ‫א‬       ‫٠٤١ א‬                                        ‫א‬
                                 ١-                            



                                    ‫א‬

                    ‫א‬                                                             ‫א‬
                                                                                       
                                                      ‫א‬‫א‬‫א‬W‫א‬‫א‬
                                                                  ‫א‬‫א‬‫א‬‫א‬
                     ٢                                                      ١J ١
                     ٢                                      ‫א‬‫א‬‫א‬٢J ١
                     ٢                                          ‫א‬‫א‬١J ٢J ١
                     ٣           ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١
                     ٣                               ‫א‬‫א‬‫א‬٣J ١
                     ٤                                                   ‫א‬١J ٣J ١
                     ٤                                                    ‫א‬٢J ٣J ١
                     ٦                                                    ‫א‬٣J ٣J ١
                     ٧                                                  ‫א‬٤J ٣J ١
                     ٧                                    ‫א‬‫א‬٥J ٣J ١
                     ٩                                           ‫א‬‫א‬٦J ٣J ١
                     ١٠                                                 ‫א‬٧J ٣J ١
                     ١٢                                          ‫א‬‫א‬
                                                                    W‫א‬‫א‬
                     ١٤                                         ‫א‬‫א‬‫א‬‫א‬
                     ١٥                                                      ١J ٢
                     ١٥                                                    ٢J ٢
                     ١٥                                     ‫א‬EF١J ٢J ٢
                     ١٦                                           ‫א‬٢J ٢J ٢
                     ١٨                                         ٣J ٢J ٢
                     ‫א‬       ‫٠٤١ א‬                                         ‫א‬
                                 ١-                             


                     ١٨                                        ‫א‬١J ٣J ٢J ٢
                     ١٩                                        ‫א‬٢J ٣J ٢J ٢
                     ٢١                                           ‫א‬‫א‬
                                                                ‫א‬‫א‬W‫א‬‫א‬
                     ٢٤                                          ‫א‬‫א‬‫א‬‫א‬
                     ٢٥                                                      ١J ٣
                     ٢٥                                                        ‫א‬٢J ٣
                     ٢٨                                 ‫א‬‫א‬‫א‬‫א‬٣J ٣
                     ٣٢                                           ‫א‬‫א‬
                                    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬
                     ٣٣                                          ‫א‬‫א‬‫א‬‫א‬‫א‬
                     ٣٤                                                       ١J ٤
                     ٣٤                                 ‫א‬‫א‬‫א‬٢J ٤
                     ٣٥                                           ‫א‬‫א‬١J ٢J ٤
                     ٣٦                              ‫א‬‫א‬‫א‬٣J ٤
                     ٣٩                                   ‫א‬‫א‬‫א‬٤J ٤
                     ٤١                                        ٥J ٤
                     ٤٤                                         ٦J ٤
                     ٤٤                                                 ‫א‬٧J ٤
                     ٤٦                              ‫א‬‫א‬‫א‬١J ٧J ٤
                     ٤٩                                        ‫א‬‫א‬‫א‬‫א‬٨J ٤
                     ٥٢                                ‫א‬٩J ٤
                     ٥٦                                          ‫א‬‫א‬١٠J ٤
                     ٦٠                                          ‫א‬‫א‬‫א‬
                                   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
                     ٦٧                                         ‫א‬‫א‬‫א‬‫א‬
                      ‫א‬       ‫٠٤١ א‬                                        ‫א‬
                                  ١-                            


                     ٦٨                                                          ١J ٥
                     ٦٩                               ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥
                     ٧٠                                            ٣J ٥
                     ٧٢              ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٥
                     ٧٥                     ‫א‬‫א‬‫א‬‫א‬١J ٤J ٥
                     ٧٦                               ‫א‬‫א‬‫א‬٥J ٥
                     ٧٩                           ‫א‬‫א‬‫א‬‫א‬EF٦J ٥
                     ٨٦                                           ‫א‬‫א‬‫א‬‫א‬٧J ٥
                     ٨٩                                           ‫א‬‫א‬
                                                                ‫א‬‫א‬‫א‬W‫א‬‫א‬
                     ٩١                                          ‫א‬‫א‬‫א‬‫א‬
                     ٩٢                                                       ١J ٦
                     ٩٢                                        ‫א‬‫א‬–‫א‬‫א‬٢J ٦
                     ٩٧                                 ‫א‬‫א‬–‫א‬‫א‬‫א‬٣J ٦
                     ١٠١                  ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٦
                     ١٠٨                              ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ٦
                     ١١٨                                        ‫א‬‫א‬
                                                         ‫א‬‫א‬‫א‬W‫א‬‫א‬
                      ١٢٣                                        ‫א‬‫א‬‫א‬‫א‬
                     ١٢٤                                                      ١J ٧
                     ١٢٤                     ‫א‬‫א‬‫א‬‫א‬٢J ٧
                     ١٢٤                                      ‫א‬‫א‬١J ٢J ٧
                     ١٢٨                                         ٢J ٢J ٧
                     ١٢٨                                         ‫א‬٣J ٢J ٧
                     ١٣٠                                              ‫א‬٣J ٧
                     ١٣٦                                                  ٤J ٧
                     ‫א‬                          ‫٠٤١ א‬                                 ‫א‬
                                                    ١-                     


                     ١٤٤                                     ‫א‬‫א‬١J ٤J ٧
                     ١٤٨                                        J ‫א‬–‫א‬٥J ٧
                     ١٥٠             E Y ← ∆ F‫א‬‫א‬‫א‬‫א‬١J ٥J ٧
                     ١٥٠              E ∆ ← Y F‫א‬‫א‬‫א‬٢J ٥J ٧
                     ١٥٤        ∆ ← Y  Y ← ∆ ‫א‬‫א‬‫א‬٣J ٥J ٧
                                                                                          K‫א‬‫א‬
                     ١٥٧         ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٦J ٧
                                                                                                  KE‫א‬
                     ١٦٥                                                      ‫א‬‫א‬
                     ١٦٨                                                                          ‫א‬‫א‬
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               ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

            ‫א‬E‫א‬F‫א‬‫א‬

GOTEVOT appreciates the financial support provided by BAE SYSTEMS

								
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