Alternating Current

The capacitor of capacitance $C$ can be charged (with the help of a resistance R ) by a voltage source V , by closing switch $\mathrm{S}_1$ while keeping switch $\mathrm{S}_2$ open. The capacitor can be connected in series with an inductor L by closing switch $\mathrm{S}_2$ and opening $\mathrm{S}_1$.

Initially, the capacitor was uncharged. Now, switch $S_1$ is closed and $S_2$ is kept open. If time constant of this circuit is $\tau$, then