In an oscillating $LC$ circuit, the maximum charge on the capacitor is $Q$. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes:

$A$ capacitor of capacity $C$ is charged to a potential difference of $V_1$. The plates of the capacitor are then connected to an ideal inductor of inductance $L$. The current through the inductor when the potential difference across the capacitor reduces to $V_2$ is

$A$ capacitor of capacitance $C$ has an initial charge $Q_0$ and is connected to an inductor $L$ as shown. At $t = 0$,the switch $S$ is closed. What is the current through the inductor when the energy in the capacitor is three times the energy of the inductor?

Solve the differential equation of $L-C$ circuit and obtain the expression of current.

Explain how $LC$ oscillations take place in the circuit.

The natural frequency of an $L-C$ circuit is $125 \ kHz$. When the capacitor is totally filled with a dielectric material,the natural frequency decreases by $25 \ kHz$. The dielectric constant of the material is nearly