Problem 24.61 Three capacitors having capacitances of 8.9 ? F , 8.8 ? F , and 4.

Question

Problem 24.61

Three capacitors having capacitances of 8.9?F , 8.8?F , and 4.2?F are connected in series across a 33-V potential difference.

PART A= Q=7.1E-5 C

Part B

What is the total energy stored in all three capacitors?

Part C

The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination?

Explanation / Answer

when connected in series ,

1/ Cnet = 1/C1 + 1/C2 + 1/C3

so ,

1/ Cnet = 1/8.9 +1/8.8+ 1/4.2

Cnet = 2.155 mu F

so ,

A)
Q = CV= 2.155*33 *10^-6 = 7.1 *10^-5 C

B )
Energy stored = Q^2 /2 * ( 1/C1 + 1/C2 + 1/C3 )

E = (7.1 *10^-5 )^2/2 * ( 1/2.155)

E = 1.173*10^-3 J = 1.173 mJ

C) V1 = Q/C1 = 7.1*10^-5 /(8.9*10^-6) = 7.977 V

V2 = Q/C2 = 7.1*10^-5 /(8.8*10^-6) = 8.068 V

V3 = Q/C3= 7.1*10^-5 /(4.2*10^-6) = 16.905 V

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