$A$ $4 \mu F$ capacitor is charged to $10 \ V$. The battery is then disconnected and a pure $10 \ mH$ coil is connected across the capacitor so that $LC$ oscillations are set up. The maximum current in the coil is (in $A$)

$A$ charged $30 \mu\text{F}$ capacitor is connected to a $27 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit (in $\text{ rad/s}$)?

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.

$A$ 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 oscillating $LC$ circuit consists of a $75\,mH$ inductor and a $1.2\,\mu F$ capacitor. If the maximum charge on the capacitor is $2.7\,\mu C$,the maximum current in the circuit will be $...........\,mA$.

$A$ $1 \, \mu F$ capacitor is charged to $50 \, V$. The charging battery is then disconnected and a $10 \, mH$ coil is connected across the capacitor so that $LC$ oscillations occur. What is the maximum current in the coil (in $, A$)? Assume that the circuit contains no resistance.