d
In case of oscillatory discharge of a capacitor through an inductor, charge at instant \(t\) is given by

\(q=q_{0} \cos \omega t\)

where, \(\omega=\frac{1}{\sqrt{L C}}.........(i)\)

\(\therefore \cos \omega t=\frac{q}{q_{0}}=\frac{C V_{2}}{C V_{1}}=\frac{V_{2}}{V_{1}} \quad(\because q=C V)\)

Current through the inductor

\(I= \frac{d q}{d t}=\frac{d}{d t}\left(q_{0} \cos (v t)=-q_{0} \omega \sin \omega t\right.\)

\(|I|=C V_{1}-\frac{1}{\sqrt{L C}}\left[1-\cos ^{2} \omega t\right]^{1 / 2} \)

\(=V_{1} \sqrt{\frac{C}{L}}\left[1-\left(\frac{V_{2}}{V_{1}}\right)^{2}\right]^{1 / 2}=\left[\frac{C\left(V_{1}^{2}-V_{2}^{2}\right)}{L}\right]^{1 / 2}\)