Two capacitors of capacitance $2C$ and $C$ are connected in series across a battery of voltage $V$.

Question

Two capacitors of capacitance $2C$ and $C$ are connected in series across a battery of voltage $V$. The total electrostatic energy stored in the combination is

Professor PC Thomas Classes · Answer

(a) : When two capacitors $2C$ and $C$ are connected in series, their equivalent capacitance $C_{eq}$ is given by $\frac{1}{C_{eq}} = \frac{1}{2C} + \frac{1}{C} = \frac{3}{2C}$. Therefore, $C_{eq} = \frac{2C}{3}$. The total energy stored in the combination is $U = \frac{1}{2} C_{eq} V^2 = \frac{1}{2} \left(\frac{2C}{3}\right) V^2 = \frac{1}{3} C V^2$.