Four capacitors are connected to battery in the manner shown at bottom. All capa

Question

Four capacitors are connected to battery in the manner shown at bottom. All capacitances are given in the table next in the figure, but the voltage V delivered by the battery is unknown. When connected to the network, the capacitor C acquires a charge of magnitude |Q_1| = 15 n C = 15 Times 10^-9 C on each of its plates. Q_1 = 15 nC C_1 = 8 p F C_2 = 6 p F C_3 = C_4 = 5 p F How much energy is stored in the capacitor C, when the network is connected? What is the voltage V supplied by the battery? What is the charge Q_4 on capacitor C_4?

Explanation / Answer

a) E1 = Q12/2C1 = (15 * 10-9)2 / (2 * 8 * 10-12) = 1.41 * 10-5 J

b) C3 and C4 are in parallel. Their equivalent capacitance is C34 = C3 + C4 = 10 pF

C1, C2 and C34 are in series. Their equivalent capacitance is given by,

1/Ceq = 1/8 + 1/6 + 1/10

=> Ceq = 120/47 pF

The charges on each of C1, C2 and C34 will be same as in Ceq since they are connected in series.

So, V = Qeq/Ceq = Q1/Ceq = (15 * 10-9) / [(120 / 47) * 10-12] = 5875 V

c) Since charge on C34 = Q1 and C3 = C4, we have, Q4 = Q1/2 = 7.5 * 10-9 C

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