An oscillator circuit consists of an inductance of $0.5 \ mH$ and a capacitor of $20 \ \mu F$. The resonant frequency of the circuit is nearly......$Hz$

$A$ $1 \mu F$ capacitor is charged to $50 \ V$ and is then discharged through a $10 \ mH$ inductor of negligible resistance. The maximum current in the inductor is (in $A$)

In the circuit given below,the capacitor $C$ is charged by closing the switch $S_1$ and opening the switch $S_2$. After charging,the switch $S_1$ is opened and $S_2$ is closed. Find the maximum current in the circuit.

At a moment $t = 0$ when the charge on capacitor $C_1$ is zero,the switch $S$ is closed. If $I_0$ is the current through the inductor at that instant,then for $t > 0,$

Show that in the free oscillations of an $LC$ circuit,the sum of energies stored in the capacitor and the inductor is constant in time.

The charge of the capacitor in an $LC$ oscillatory circuit,when the energy associated with the inductor and capacitor are equal,is . . . . . . . ($Q_{0}$ is the initial charge on the capacitor.)