$A$ charged $30\; \mu F$ capacitor is connected to a $27\; mH$ inductor. What is the angular frequency of free oscillations of the circuit?

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

If $L$ and $C$ are inductance and capacitance respectively,then the dimensional formula of $(LC)^{-\frac{1}{2}}$ is

$A$ capacitor of capacitance $C$ is charged to a potential difference $V_0$. Now,this capacitor is connected to an ideal inductor. When $25\%$ of the energy of the capacitor is transferred to the inductor,what will be the potential difference across the capacitor?

$A$ 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,

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.