Two condensers, one of capacity `C` and the other of capacity `C//2` are connected to a `V` volt battery, as shown.

The work done in charging fully both the condensers is

Options

A. `2CV^(2)`
B. `(1)/(4)CV^(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 equilvalent capacitor is stored in the from of potential energy.
Hence, `W = U = (1)/(2)C'V^(2)`
`= (1)/(2) ((3C)/(2))V^(2)`
`= (3)/(4)CV^(2)`