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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 to the work done by the battery will be

Asked in JEE Main 2007 · Energy stored and energy density

Answer: (1) 1/2

Step-by-step solution

The battery pushes a total charge Q=CV through a constant emf V, so the work it does is W=QV=CV².

The energy that ends up stored in the capacitor is U=1/2CV².

U/W=(1/2CV²)/(CV²)=1/2.

The missing half is dissipated as heat in the resistance of the charging circuit, whatever that resistance may be.

Why the other options are wrong

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