Question

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 energy stored in the capacitor and work done by the battery will be?

• A. $\frac{2}{1}$
• B. $1$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{2}$

Suppose Q amount of charge flows through the battery.
$W=QV=C{V}^2------\left(1\right)E=\frac{1}{2}C{V}^2--------\left(2\right)\frac{E}{W}=\frac{\frac{1}{2}C{V}^2}{C{V}^2}=\frac{1}{2}$