Two condensers, one of capacity `C` and the other of capacity `C//2`, are connected to a `V` volt battery, as shown
The heat produced in connecting wires

Options

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

Answer

C

Explanation

The charge supplied by battery `Q=(3C)/(2)V`
Work done by battery `W_(b)=QV=(3CV^(2))/(2)`
Change in stored energy in capacitors
`DeltaU=(1)/(2)CV^(2)+(1)/(2).(c)/(2)V^(2)=(3)/(4)CV^(2)`
`W_(b)=DeltaU+H`
`H=(3)/(4)CV^(2)` OR
Heat produced `H=(1)/(2)C(V-0)^(2)+(1)/(2)(c)/(2)(V-0)^(2)`
`=(3)/(4)CV^(2)`