$A$ $2 \mu F$ 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 $A s^{-1}$)

$A$ capacitor of capacitance $500\,\mu F$ is charged completely using a dc supply of $100\,V$. It is now connected to an inductor of inductance $50\,mH$ to form an $LC$ circuit. The maximum current in $LC$ circuit will be $.........A$.

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

In $L-C$ oscillation,the maximum charge on the capacitor is $Q$. If at any instant,the electric energy and magnetic energy associated with the circuit are equal,then the charge on the capacitor at that instant is:

An $L-C$ circuit contains a $196 \text{ pF}$ capacitor and a $441 \text{ } \mu\text{H}$ inductor. The frequency of electromagnetic radiation emitted by an antenna coupled to the $L-C$ circuit is:

In the $LCR$ circuit shown in the figure,the ac driving voltage is $V = V_m \sin \omega t$.
$(a)$ Write down the equation of motion for $q(t)$.
$(b)$ At $t = t_0$,the voltage source is removed and $R$ is short-circuited. Write down the energy stored in each of $L$ and $C$ at this instant.
$(c)$ Describe the subsequent motion of charges.