A battery is used to charge a parallel plate capacitor till the potential differece 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

Options

A. 1
B. `1/2`
C. `2`
D. `1/4`

Answer

B

Explanation

When it is fully charged, energy stored in the capacitor
`E_(1)=(1)/(2)CV^(2)` and the work done by the battery `W=QV ` or `W=CVxxV=CV^(2)`
`because V=(W)/(Q) and C=(Q)/(V)" "Q=CV`
`therefore (E_(1))/(W)=((1)/(2)CV^(2))/(CV^(2))=(1)/(2)`