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(B) Let the capacitance of the capacitor be $C$ and the e.m.f. of the battery be $V$. When the capacitor is fully charged,the potential difference acr

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(B) Let the capacitance of the capacitor be $C$ and the e.m.f. of the battery be $V$. When the capacitor is fully charged,the potential difference across the plates is $V$. The charge stored on the capacitor is $q = CV$. The energy stored in the capacitor is $U = \frac{1}{2} CV^2 = \frac{1}{2} qV$. The work done by the battery in supplying charge $q$ is $W = qV = CV^2$. The ratio of the energy stored in the capacitor to the work done by the battery is $\frac{U}{W} = \frac{\frac{1}{2} qV}{qV} = \frac{1}{2}$.

$A$ battery is used to charge a parallel plate capacitor until the potential difference between the plates becomes equal to the e.m.f. of the battery. The ratio of the energy stored in the capacitor to the work done by the battery will be

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