$A$ $60\,\mu F$ capacitor is charged to $50\, V$. This charged capacitor is connected across a $1.5\, mH$ coil,so that $LC$ oscillations occur. The max current in the coil is......$A$

Write the differential equation for an $LC$ circuit.

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

In an $LC$ oscillator,if values of inductance and capacitance become twice and eight times,respectively,then the resonant frequency of the oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ 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.

$A$ capacitor of capacitance $2 \mu F$ is charged to a potential difference of $12 \, V$. It is then connected across an inductor of inductance $0.6 \, mH$. The current in the circuit when the potential difference across the capacitor is $6 \, V$ is :