Question

Two capacitors $C$ and $\frac{C}{2}$ are connected to a battery of $V$ volts, as shown below

The work done in charging both the capacitors fully is

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

Answer 1

Answer: (B)

The two capacitors are in parallel. The equivalent capacitance
$C^{\prime }=C+\frac{C}{2}=\frac{3C}{2}$
Work done in charging the equivalent capacitor is stored in the form of potential energy.
$W=U=\frac{1}{2}{C}^{\prime }{V}^2$
$=\frac{1}{2}\times \frac{3C}{2}\times V^2$
$=\frac{3}{4}C{V}^2$