Question

C3 C1 S2 CA S1

In the figure, battery B supplies 18 V. Take C1 = 1.3 ?F, C2 = 2.7 ?F, C3 = 3.6 ?F, and C4 = 4.4 ?F.

(A) Find the charge Q3 on capacitor C3 when ONLY switch S1 is closed.

(B) Find the charge Q₃ on capacitor C₃ when switch S2 is ALSO closed.

(C) What is the charge Q₄ on capacitor C₄ when switch S2 is ALSO closed?

Answer 1

Here ,

A) when only S1 is closed

Voltage of battery , V = 18 V

for the capacitors C1 and C3 in series

1/Ceq = 1/1.3 + 1/3.6

Ceq = 0.96 uF

Charge on Q3 = Ceq * V

Charge on Q3 = 0.96 * 18 V

Charge on Q3 = 17.2 uC

B)

when S2 is also closed

for the equivalent for capacitor

1/Ceq = 1/(1.3 + 2.7) + 1/(3.6 + 4.4)

Ceq = 2.67 uF

charge on C3 = Ceq * V * C3/(C3 + C4)

charge on C3 = 2.67 * 18 * 3.6/(3.6 + 4.4)

charge on C3 = 21.7 uC

C)

for the charge on C4

charge on C4 = Ceq * V * C4/(C3 + C4)

charge on C4 = 2.67 * 18 * 4.4/(3.6 + 4.4)

charge on C4 = 26.4 uC