JEE Main · 2007 · 29 Apr 2007 · Offline · Capacitance

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A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

(A)1
(B)2
(C) $\frac{1}{4}$
(D) $\frac{1}{2}$ ✓ Correct

Answer: (D)

Solution

While the battery raises the plate potential to its emf, it drives a total charge

q

through the potential difference

V

and so does work

W = q V

. The energy that finally resides in the capacitor is

U = \frac{1}{2} q V

. The ratio of the two is

\frac{U}{W} = \frac{\frac{1}{2} q V}{q V} = \frac{1}{2}

, the missing half having been dissipated in the circuit resistance during the charging.

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

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