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 (in $Hz$)

In an oscillating $LC$ circuit,the maximum charge on the capacitor is $Q$. What is the charge on the capacitor when the energy is stored equally between the electric and magnetic fields?

$A$ charged $30\; \mu F$ capacitor is connected to a $27\; mH$ inductor. The initial charge on the capacitor is $6\; mC$. What is the total energy stored in the circuit initially? What is the total energy at a later time?

An ideal capacitor of capacitance $0.2\, \mu F$ is charged to a potential difference of $10\, V$. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self-inductance $0.5\, mH$. The current at a time when the potential difference across the capacitor is $5\, V$,is.....$A$

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.)

$A$ capacitor of capacitance $C$ is charged to a potential difference $V_0$. Now,this capacitor is connected to an ideal inductor. When $25\%$ of the energy of the capacitor is transferred to the inductor,what will be the potential difference across the capacitor?