Capacitance and Capacitors

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							                 Capaticance



                                                      2
                               • Capacitor

                                                1
                               • Connecting capacitors
0011 0010 1010 1101 0001 0100 1011




                                            4
                               • Dielectrics and capacitors
                               • Energy stored in a capacitor
                     Reading Questions
       I read ____ per cent of the text for class today.
0011 0010 1010 1101 0001 0100 1011
         1.   Less than 20
         2.   20 to 40
         3.   40 to 60
         4.   60 to 80


                                                           1
                                                               2
         5.   More than 80




                                                     4
                       EMF or Battery
0011 0010 1010 1101 0001 0100 1011




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                       EMF or Battery
0011 0010 1010 1101 0001 0100 1011




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                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




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                                     You should do this one.
                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




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                           Class Question
      A wire connects the positive and
      negative terminals of a battery.
0011 0010 1010 1101 0001 0100 1011
      Two identical wires connect the
      positive and negative terminals of
      an identical battery. Rank in order,
      from largest to smallest, the


                                             1
                                                 2
      currents Ia to Id at points a to d.
                1.   Ia = Ib = Ic = Id




                                             4
                2.   Ia = Ib > Ic = Id
                3.   Ic = Id > Ia = Ib
                4.   Ic = Id > Ia > Ib
                5.   Ia > Ib > Ic = Id
                           Class Question
      A wire connects the positive and
      negative terminals of a battery.
0011 0010 1010 1101 0001 0100 1011
      Two identical wires connect the
      positive and negative terminals of
      an identical battery. Rank in order,
      from largest to smallest, the


                                             1
                                                 2
      currents Ia to Id at points a to d.
                1.   Ia = Ib = Ic = Id




                                             4
                2.   Ia = Ib > Ic = Id
                3.   Ic = Id > Ia = Ib
                4.   Ic = Id > Ia > Ib
                5.   Ia > Ib > Ic = Id
                                    Resistance
      Resistivity
0011 0010 1010 1101 0001 0100 1011
          T  
                    1          m
                        
                           ne2 (T )




                                                  1
                                                      2
                                  L          l
             A                          R
                                             A




                                                  4
                    J  E
                           Resistivity
0011 0010 1010 1101 0001 0100 1011




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                                         4
                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




                                           1
                                               2
                                 R
                                      l
                                      A

                                           4
                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




                                        1
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                              V  IR

                                       4
                         Class Question
       Resistance is
0011 0010 1010 1101 AL 0100 1011
            1. R  0001
                     A
            2.   R
                    L
                    L
            3.   R


                                          1
                                              2
                     A
                    A
            4.   R
                     L




                                          4
            5. None of the above
                         Class Question
       Resistance is
0011 0010 1010 1101 AL 0100 1011
            1. R  0001
                     A
            2.   R
                    L
                    ρL
            3.   R


                                          1
                                              2
                     Α
                    A
            4.   R
                     L




                                          4
            5. None of the above
             Capacitance and Capacitors
       Capacitors are used everywhere!
0011 0010 1010 1101 0001 0100 1011




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             Capacitance and Capacitors
        Even in the life sciences!
0011 0010 1010 1101 0001 0100 1011




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             Capacitance and Capacitors
0011 0010 1010 1101 0001 0100 1011
                                        Q
                                     C
                                        V



                                            1
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                                        4
             Capacitance and Capacitors
      Parallel Plate Capacitor
0011 0010 1010 1101 0001 0100 1011
      • First we would like to
        calculate the capacitance for a
        parallel plate capacitor. You
        will recall that a capacitor is


                                               1
                                                   2
        formed with two conducting
        plates, each with area A and       +Q.A
        separated by a distance d,




                                          4
        small compared to plate size.
        The two plate have equal
        charge but with opposite          -Q
        signs.
             Capacitance and Capacitors
    • Write the capacitance for a parallel plate capacitor.
0011 0010 1010 1101 0001 0100 1011
                 0 A
           C   
                  d
    • Now let’s derive this from the definition for capacitance.


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      What is the definition?
              Q
           C




                                                   4
              V
    • The electric field is constant in magnitude and direction
      between the plates and the magnitude is
                Q
           E  
              0 0 A
             Capacitance and Capacitors
      • Write 1101 0001 0100 1011
0011 0010 1010 the general relationship (an integral) that allows you to
        calculate the potential difference from the electric field.
                                          
               V  V                 E  dl
                                    path AB




                                                         1
                                                                 2
     • The electric field between the plates is constant in magnitude
       and direction. Write the relationship for potential again for a
       constant electric field.




                                                    4
                                
              V             E  dl   E             dl
                         path AB                  path A B


                                                 Ed  Ed
              Capacitance and Capacitors
      • Finally, use the definition for capacitance and substitute in
        the potential difference you just found.
0011 0010 1010 1101 0001 0100 1011



            Q A A  0 A
          C      
            V  Ed       d

                                                         1
                                                                 2
                      d
                   0




                                                    4
             Capacitance and Capacitors
     • The flash on your camera uses a capacitor to store the
0011 0010 1010 1101 0001 0100 1011
       energy for the flash. If the voltage across the capacitor is 9
       volts (from a battery) and the capacitance is 5,000 mF,
       what is the charge on the plates?
           Q
        C   Q  CV  5,000 mF9V
           V
                      45mC
                                                        1
                                                                2
                                                   4
            1    1
         U  QV  0.045C 9V  2.0mJ
            2    2
             Capacitance and Capacitors
     • The capacitance for a coaxial cable       electric field lines
0011 0010 1010 1101 0001 0100 1011
                                                            
             Q                                             E
         C
            V
         Q  L                                       +Q


                                                         1
                                                                 2
                                                      -Q
         V           E  dl 
                   path AB




                                                   4
                                 b dr    
                                                lnb  a 
               b
                    r  rdr 
                      ˆ ˆ              
              a 2 r           2 0 a r 2 0
                    0


           Q                   L      2 0 L
         C                        
           V             
                           lnb a    lnb a 
                       2 0
             Capacitance and Capacitors
   Energy Stored in Capacitors
0011 0010 1010 1101 0001 0100 1011
   • One definition of a capacitor is a device that will store
      electrical energy. Write the expression for the energy that is
      in a capacitor in terms of the charge Q and the capacitance C.
                1     1 Q2

                                                       1
                                                               2
             U  QV 
                2     2C
   • Use the definition of capacitance to change the expression for




                                                   4
     the energy to one in terms of voltage V and capacitance C.
                1    1
             U  QV  CV 2
                2    2
             Capacitance and Capacitors
    • A parallel plate capacitor made from two metal pie pans (10
       inches in diameter) places 2 mm apart is charged to 100
0011 0010 1010 1101 0001 0100 1011

       volts. What is the electrical energy stored in the two pie
       pans? Discuss this problem in your group before you work
       the problem.


                                                             1
                                                                     2
        First find C.
        Use parallel plate




                                                        4
               A  r  3.14(2.45cm10in)  0.19m2
                         2


              0 A
                      8.85 X 10         C 2 Nm 2 0.19m 2 
                                    12
         C                                                     8.7 X 1010 F
             d                            2mm
            1    1
         U  CV  (45mC)(100V )2  2.8mJ
               2

            2    2
             Capacitance and Capacitors
      Capacitors in parallel
0011 0010 1010 1101 0001 0100 1011




                                              1
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                     C  C1  C2  C3  
             Capacitance and Capacitors
      Capacitors in series
0011 0010 1010 1101 0001 0100 1011




                                      1
                                          2
                       1 1 1 1
                            
                       C C1 C2 C3    4
             Capacitance and Capacitors
       A problem
0011 0010 1010 1101 0001 0100 1011




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             Capacitance and Capacitors
0011 0010 1010 1101 0001 0100 1011




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             Capacitance and Capacitors
      • Discuss the circuit in your group. Where should you start?
        Which capacitors are in series or parallel?
0011 0010 1010 1101 0001 0100 1011

        C1 = 3.0 mF, C2 = 2.0 mF, C3 = 1.0 mF, C4 = 6.0 mF, and
        C5 = 4.0 mF,
                           C1



                                                      1
                                                              2
                  A
                                                 C4




                                                 4
                                                 C5
                           C2       C
                                     3

                  B


     • Which two capacitors should you start with?
             Capacitance and Capacitors
    • Start with C and C5.
0011 0010 1010 110140001 0100 1011            C1
    • C4 and C5 are in series.           A
      1/C45 = 1/C4 +1/C5                                       C4

            = 1/6.0 + 1/4.0 = 2/12 + 3/12                      C5
                                              C2       C




                                                   1
                                                           2
      C45 = 12/5 mF
                                                       3

                                         B
    • Now look at C2, C3, C45.               C1

    • C2, C3, and C45 are in parallel. A
        – C’ = C2 + C3 + C45
        – = 2.0 + 1.0 +12/5 = 5 2/5 mF
    • FinallyC1 and C’ are in series. B
           1/C = 1/C4,5 +1/C1
                                             C2




                                                   4
                                                   C
                                                   3       C
                                                               4,5
             Capacitance and Capacitors
0011 0010 1010 1101 0001 0100 1011




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             Capacitance and Capacitors
0011 0010 1010 1101 0001 0100 1011




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             Capacitance and Capacitors
      Capacitors and Dielectrics
0011 0010 1010 1101 0001 0100 1011
      • When a dielectric in placed between the plates of a
        capacitor the capacitance increases. What is the
        relationship between the capacitance with the dielectric, C,
        to the capacitance without the dielectric, C0?


                                                        1
                                                                2
                
             C  C0  C0
                0




                                                   4
     • What is the capacitance for a
       parallel plate capacitor with a
       dielectric?
                   A  0 A
              C        
                    d       d
             Capacitance and Capacitors
     • Capacitors and Dielectrics
0011 0010 1010 1101 0001 0100 1011
                 
              C  C0  C0
                 0



                                     1
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             Capacitance and Capacitors
0011 0010 1010 1101plate capacitor with
      • A parallel 0001 0100 1011      a capacitance 3.0 mF (for air
        in between) has Teflon placed between the plates. What is
        the capacitance with the Teflon?

             C = 0A/d = C0 = 2.1*3.0mF = 6.3mF


                                                        1
     • The capacitor above is connected to a 10 volt supply
       without the dielectric. What is the energy stored in the

                                                                  2
                                                   4
       capacitor?

             U = 1/2CV2 = ½ (3.0mF)(10V)2 = 0.15mJ
                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




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                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




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                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




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                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




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                     Student Workbook
0011 0010 1010 1101 0001 0100 1011




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                        Class Question
0011 0010 1010 1101 0001 0100 1011




                                                            1
                                                                  2
        Rank in order, from largest to smallest, the equivalent
        capacitance (Ceq)a to (Ceq)d of circuits a to d.




                                                     4
                     1. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
                     2. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
                     3. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
                     4. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
                     5. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c
                        Class Question
0011 0010 1010 1101 0001 0100 1011




                                                            1
                                                                  2
        Rank in order, from largest to smallest, the equivalent
        capacitance (Ceq)a to (Ceq)d of circuits a to d.




                                                     4
                     1. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
                     2. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
                     3. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
                     4. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
                     5. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c