Consider the circuit consisting of two capacitors having capacitances `3 mu F` and `6 mu F` and an ideal battery of emf e = 4 volts as shown. The switch S is open for a long time and then closed. After the switch is closed. The work done by the battery is :

Options

A. 16 m J
B. 32 m J
C. 64 m J
D. 128 m J

Answer

C

Explanation

Initial charge on 6 mF capacitor
`= (3 xx 6)/(3+6) xx 4 = 8 mC`
final charge on 6mF capacitor `= 6 xx 6 = 25 mC` charge passing through cell (in direction aided by cell) `= q_(f) -q_(i) = Dq = 24 - 8 = 16 mC` work done by cell = Dqe `= 16 xx 4 = 64 mJ`