Two condenser, one of capacity C and the other of capacity ` (C )/(2)`, are connected to a V volt battery, as shown in figure. The work done in charging fully both the condensers is

Options

A. `2 C V ^ 2 `
B. ` (1 )/( 4 ) C V ^ 2 `
C. ` ( 3 ) /( 4 ) CV ^ 2 `
D. ` ( 1 ) /( 2 ) CV ^ 2 `

Answer

C

Explanation

The two condensers in the circuit are in parallel order, hence
` C' = C + ( C) /( 2) = ( 3C)/( 2 ) `
The work done in charging the equivalent capacitor is stored in the form to potential energy.
Hence, ` W = U = ( 1 ) /( 2 ) C'V^ 2 `
` = ( 1 ) /( 2 ) ( ( 3C)/( 2 ) ) V ^ 2 = ( 3 )/( 4 ) CV^ 2 `