A capacitor of capacitance $C$ is charged to a potential $V$ and then connected to an inductor of inductance $L$. The maximum current in the resulting LC circuit is given by which of the following?

Solution

1. Initial energy stored in the capacitor is $U=(1/2)C{V}^2$.
2. At maximum current, all energy is stored in the inductor as $U=(1/2)L{I}_{max}^2$.
3. Equating the energies: $(1/2)C{V}^2=(1/2)L{I}_{max}^2$.
4. Solving for $I_{max}$ gives $I_{max}=V\sqrt{C/L}$.
5. Hence the answer is (B).