We connect a charge capacitor to an inductor the electric current and charge on the capacitor in the circuit undergoes LC oscillations.

An LC circuit contains a $20 \mathrm{mH}$ inductor and a $50 \mathrm{\mu F}$ capacitor with an initial charge of $10 \mathrm{mC}$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t=0$. At what times is the total energy shared equally between the inductor and the capacitor?

The switch in figure is connected to position a for a long time interval. At $t=0$ the switch is thrown to position $b$. After this time,

After the switch is closed in the $LC$ circuit, shown in the figure, the charge on the capacitor is sometimes zero, but at such instants, the current in the circuit is not zero. How is this behavior possible?

An LC circuit contains a $20 \mathrm{mH}$ inductor and a $50 \mathrm{\mu F}$ capacitor with an initial charge of $10 \mathrm{mC}$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t=0$. At what time is the energy stored (i) completely electrical (i.e., stored in the capacitor)? (ii) completely magnetic (i.e., stored in the inductor)?

An LC circuit contains a $20 \mathrm{mH}$ inductor and a $50 \mathrm{\mu F}$ capacitor with an initial charge of $10 \mathrm{mC}$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t=0$. What is the natural frequency of the circuit?

An inductor and two capacitors are connected in the circuit as shown in figure. Initially capacitor $\mathrm{A}$ has no charge and capacitor $\mathrm{B}$ has $\mathrm{C}\mathrm{V}$ charge. Assume that the circuit has no resistance at all. At $\mathrm{t}=0,$ switch $\mathrm{S}$ is closed, then given $\left[ \mathrm{L}\mathrm{C}=\frac{2}{{\mathrm{\pi }}^2\times {10}^4}{\mathrm{s}}^2 \& \mathrm{C}\mathrm{V}=100 \mathrm{m}\mathrm{C}\right]$