If $C$ and $L$ denote capacitance and inductance respectively,then the dimensions of $LC$ are

$A$ circuit consists of a coil with inductance $L$ and an uncharged capacitor of capacitance $C$. The coil is in a constant uniform magnetic field such that the flux through the coil is $\phi$. At time $t=0$,the magnetic field is abruptly switched $OFF$. Let $\omega_{0}=1 / \sqrt{L C}$ and ignore the resistance of the circuit. Then,

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.

The switch is in position $A$ for a long time. At time $t=0$,it is shifted to position $B$. Find the maximum charge that will accumulate on the capacitor.

$A$ $60\,\mu F$ capacitor is charged to $100\,V$. This charged capacitor is connected across a $15\,mH$ coil,so that $LC$ oscillations occur. The maximum current in the coil is:

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