Question

Two condensers, one of capacity C and the other of capacity $\frac{C}{2}$, are connected to a V-volt battery, as shown. the work done in charging fully both the condensers is?

• A. $C{V}^2$
• B. $\frac{1}{4}C{V}^2$
• C. $\frac{3}{4}C{V}^2$
• D. $\frac{1}{2}C{V}^2$

Answer 1

The correct option is C $\frac{3}{4}C{V}^2$

The two condensers in the circuit are in parallel order, hence $C^{\prime }=C+\frac{C}{2}=\frac{3C}{2}$
The work done in charging the equivalent capacitor is stored in the form of potential energy
Hence, $W=U=\frac{1}{2}{C}^{\prime }{V}^2=\frac{1}{2}\left(\frac{3C}{2}\right)V^2=\frac{3}{4}C{V}^2$.