The natural frequency of an $L-C$ circuit is equal to:

$A$ $2 \mu F$ capacitor is charged to $50 V$ by a battery. The battery is removed after the capacitor is fully charged. At time $t=0$,a $10 mH$ coil is connected in series with the capacitor. The maximum rate at which the current changes in the circuit is (in $A s^{-1}$)

Write the differential equation for an $LC$ circuit.

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is:

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