) If you have five capacitors with capacitances 1.3 × 10 -6 F, 3.4 × 10 -6 F, 5.

Question

) If you have five capacitors with capacitances 1.3 × 10-6 F, 3.4 × 10-6 F, 5.1 × 10-6 F, and two 6.3 × 10-6 F in series. What is the equivalent capacitance of all five?

C =  F     

b) Initially the capacitors are uncharged. Now a 14 V battery is attached to the system. How much charge is on the positive plate of the 5.1 × 10-6 F capacitor?

Q =  C     

c)What is the potential difference between the plates of the 5.1 × 10-6 F capacitor?

V =  V     

d) How much energy is stored in the entire capacitor system?

PE =  J     

e) If you have five capacitors with capacitances 1.3 × 10-6 F, 3.4 × 10-6 F , 5.1 × 10-6 F, and two 6.3 × 10-6 F in parallel. What is the equivalent capacitance of all five?

C =  F     

f) If one attaches a 14 V battery to the system, how much charge is on the positive plate of the 5.1 × 10-6 F capacitor?

Q =  C     

g)What is the potential difference between the plates of the 5.1 × 10-6 F capacitor?

V =  V     

h) How much energy is stored in the entire capacitor system?

Explanation / Answer

We use the expressions for capacitors

. a) 1/Ceq = 1/C1+ 1/C2+1/C3+1/C4+1/C5      1/Ceq = 1/1.3+1/3.4+/5.1+1/6.3+1/6.3

       1/Ceq= (3.4 5.1 6.3 + 1.3 5.1 6.3 + 1.3 3.4 6.3 +1.3 3.4 5.1 + 1.3 3.4 5.1)/( 1.3 3.4 5.1 6.3)

       1/ Ceq= (109.242+ 41.769+ 27.846+ 22.542+ 22.542)/(142.0146 10-6)= 223.941/ 142.0146 10-6

       Ceq= 142.0146 10-6 / 223.941

          Ceq= 0.634 10-6 F

. b) V= 14 V  

Qt = Ceq V        Qt = 0.634 10-6 14    Qt = 8.876 10-6 C

In a circuit of series capacitors is charged all capacitors equals    Q5 = Qt

Q5 = 8.876 10-6 C

. c)   V5 = Q/C5    V5= 8.876 10-6 C / 5.1 10-6 F      V5 =1.74 V

. d) energy

     U = ½ Ceq V2        U = ½ 0.634 10-6 142        U= 62.132 10-6 J

. e)   parallel capacitors

        Ceq = C1+C2+C3+C4+C5      Ceq= (1.3 +3.4+5.1+6.3+6.3) 10-6 F       Ceq= 22.4 10-6 F

. f)    V= 14 V      Q5 = C5 V  

In parallel the voltages applied to all capacitors are equal

           Q5 = 5.1 10-6   14               Q5= 71.4 10-6 C

.g) In a parallel circuit voltages they are equal     V5=V = 14V

.h)      U = ½ Ceq V2        U= ½ 22.4 10-6   142       U= 2195.2 10-6 J

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