Question

An $L C$ circuit consists of a $20.0- mH$ inductor and a $0.500-\mu F$ capacitor. If the maximum instantaneous current is $0.100 \,A$, the greatest potential difference across the capacitor (in $V$) is

Answer 1

At different times, the maximum energy stored in the capacitor is equal to the maximum energy stored in the inductor.
${\left[\frac{1}{2} C(\Delta V)^{2}\right]_{\max }=\frac{1}{2} L I_{i}^{2}}$
$\text { So }\left(\Delta V_{c}\right)_{\max }=\sqrt{\frac{L}{C}} I_{i}$
$=\sqrt{\frac{20.0 \times 10^{-3}}{0.500 \times 10^{-6}}(0.100)}=20.0 \,V$