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Lecture 16

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									PHY301 – Circuit Theory


                                              Virtual University
                                                   PHY 301
                                                 LECTURE 16

Example:        Calculate the voltage Vac .




Solution:          We want to calculate the voltage Vac. To solve this problem the circuit        can
be redrawn as




       Let the current I is flowing through the circuit. The KVL equation will be
                        1
                                    10kI + 20kI + 30KI -6 = 0
                                        1         1       1
                             10kI + 20kI + 30KI = 6
                                  1       1         1
                                              60kI = 6
                                                    1
                                                             I = 6/60k
                                                              1
                                                   I = 0.1mA
                                                    1
                          Now Vac will be equal to
                              Vac = (10k + 20k)I
                                                 1
                                   = 30k(0.1mA)
                              Vac = 3 Volts
Example:       Calculate the voltage Vac .




Virtual University of Pakistan                                                               Page 67
PHY301 – Circuit Theory

Solution:   We want to calculate the voltage V .First we will have to calculate the voltage across 40k resistor.
                                              bd
                Let the current I be flowing through the loop.
                                 1
                          Applying KVL
                                   10kI + 9 + 40kI + 10kI – 6 = 0
                                        1         1        1
                                                                 60kI = -3
                                                                      1
                                                                        I = - 3/60k
                                                                         1
                                                                            = - 0.05 mA
                          So, voltage across 40k resistor
                                                                  V      = (-0.05m)(40k)
                                                                    40k
                                                       = - 2 volts ---------- (A)
                We want to want to calculate Vbd we will redraw the circuit as




                  Now to calculate V     we take the path bdcb
                                      bd
                   Applying KVL
                                               V -V        -9 =0
                                                bd    40k
                  by putting the value of V     from equation (A) we have
                                            40k
                                   V – (–2) –- 9 =0
                                     bd
                                       V +2 –- 9 =0
                                        bd
                                                           V = 7 Volts
                                                             bd


Example:        Calculate the current I .
                                       0




Solution: We want to calculate the current I . The circuit can be redrawn as
                                            0




Virtual University of Pakistan                                                                        Page 68
PHY301 – Circuit Theory

                 KVL for mesh 1
                 Here
                           I = 120 mA
                            1
                 Applying KVL to mesh 2
                                    8kI + 4kI + 4k(I – I ) = 0
                                       2     2      2 1
                                    16kI – 4k I = 0
                                        2      1
                                         16kI = 480
                                             2
                                I = 480/16k
                                 2
                                 I = 30 mA
                                  2
                 So I will be
                     0
                                            I =I –I
                                             0   1 2
                                    I = 120 – 30
                                     0
                                  I = 90 mA
                                   0




Example:       Calculate the current I and the voltage V .
                                      0                 0




Solution: We want to calculate the current I and the voltage V The circuit can   be redrawn as
                                            0                 0.




                         Applying KVL to mesh 1
                                          2kI +6k(I – I )= 12
                                             1      1 2
                                               8kI – 6kI = 12
                                                  1     2

                         Applying KVL at mesh 2
                                   8kI + 4kI + 6k (I – I ) = 0
                                      2     2       2 1
                                                   18kI - 6kI = 0
                                                       2      1




Virtual University of Pakistan                                                        Page 69
PHY301 – Circuit Theory

Solving equations of mesh 1 and mesh 2
                                                   24kI  - 18kI = 36
                                                       1       2
                                                  -24kI + 72kI = 0
                                                       1       2
                                                54kI = 36
                                                    2
                                                                  I = 36/54k
                                                                   2
                                                                   I = 0.67mA ------------(A)
                                                                    2
                 Now V       will be equal to
                         0
                                                                  V = 4k I
                                                                   0       2
                           by putting the value of I2 from equation (A) we have
                                                                  V = 2.66 Volts
                                                                    0
Example:        Calculate the current I .
                                       0




Solution: We want to calculate the current I . To apply KVL the circuit can be                  redrawn as
                                            0




                 Here
                                        I = - 2mA
                                         1
        Negative value of I is due to this reason because the direction of I is going    opposite to the
                           1                                                1
Independent current source.
                                         I = 4mA
                                          3
                          KVL for mesh 2
                          4kI + 6k (I – I ) + 2k(I – I ) = 12
                             2        2 3          2 1
                                      12kI – 24 + 4 =12
                                            2
                                                              I = 32/12k
                                                               2
                                                                 = 8/3 mA
                                                                  = 2.66 mA
                                              I = I = 2.66mA
                                               0 2
Example:       Calculate the current I .
                                      0




Virtual University of Pakistan                                                                        Page 70
PHY301 – Circuit Theory

Solution:       We want to calculate the current I .The circuit can be redrawn as
                                                  0




                         Here
                         I = - 2mA
                          1
                         I = 4mA
                          3
                         Apply KVL on the mesh 2
                                 2kI + 1k(I – I ) = 12
                                    2      2 1
                                           3KI + 2 =12
                                              2
                                                     I = 10/3 mA
                                                      2
                                                      I = 3.33mA
                                                       2
                Now
                                           I =I –I
                                            0 1 2
                                    = - 2 – 3.33
                                            I = - 5.33 mA
                                             0




Virtual University of Pakistan                                                      Page 71

								
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