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. $2 C V^{2}$
• 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
$C'=C+\frac{C}{2}=\frac{3 C}{2}$
Work done in charging the equivalent capacitor is stored in the form of potential energy.
$W =U=\frac{1}{2} C' V^{2}$
$=\frac{1}{2} \times \frac{3 C}{2} \times V^{2}$
$=\frac{3}{4} C V^{2}$