Initially,the key was placed on $(1)$ until the capacitor got fully charged. Now,the key is placed on $(2)$ at $t = 0$. Find the minimum time when the energy in both the capacitor and the inductor will be the same.

An $LC$ circuit contains a $20 \; mH$ inductor and a $50 \; \mu F$ capacitor with an initial charge of $10 \; mC$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t=0$.
$(a)$ What is the total energy stored initially? Is it conserved during $LC$ oscillations?
$(b)$ What is the natural frequency of the circuit?
$(c)$ 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)?
$(d)$ At what times is the total energy shared equally between the inductor and the capacitor?
$(e)$ If a resistor is inserted in the circuit,how much energy is eventually dissipated as heat?

In the given $L-C$ circuit,inductance is $80 \mu H$ and capacitance is $20 \mu F$. The maximum potential difference across the capacitor is $80 \ V$. The maximum current is (in $A$)

In an oscillating $LC$ circuit,the total stored energy is $U$ and the maximum charge on the capacitor is $Q$. When the charge on the capacitor is $\frac{Q}{2}$,the energy stored in the inductor is:

In the given circuit,when $S_1$ is closed,the capacitor gets fully charged. Now $S_1$ is opened and $S_2$ is closed. Then

The carrier frequency generated by a tank circuit containing $1 \,nF$ capacitor and $10 \, \mu H$ inductor is