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Energy of a Capacitor

An initially ...

Question

An initially uncharged capacitor is connected across a battery, during charging work done by battery is X & energy stored in capacitor is Y, then X : Y is

A

2:1

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B

1:1

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C

1:2

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D

1:3

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Solution

The correct option is A 2:1
Work done by battery is, $W = q . V = C V . V = C V^{2}$
Energy stored in capacitor is,
$U = \frac{1}{2} C V^{2} W : U = C / V^{2} : \frac{1}{2} C / V^{2} = 2 : 1$

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