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

$A$ $LC$ circuit is in the state of resonance. If $C = 0.1 \mu F$ and $L = 0.25 \ H$. Neglecting the ohmic resistance of the circuit,what is the frequency of oscillations in $Hz$?

Consider an $LC$ circuit,with inductance $L = 0.1 \ H$ and capacitance $C = 10^{-3} \ F$,kept on a plane. The area of the circuit is $1 \ m^2$. It is placed in a constant magnetic field of strength $B_0$ which is perpendicular to the plane of the circuit. At time $t = 0$,the magnetic field strength starts increasing linearly as $B = B_0 + \beta t$ with $\beta = 0.04 \ T \ s^{-1}$. The maximum magnitude of the current in the circuit is . . . . $mA$.

The charge in an $LC$ circuit with negligible resistance oscillates as given by the equation $\frac{d^2q}{dt^2} + 16\pi^2q = 0$. If the charge is maximum equal to $24\,\mu C$ at $t = 0$,find the charge at $t = \frac{1}{12}\,s$ in $\mu C$.

Initially,the key was placed on $(1)$ until the capacitor got fully charged. Now,the key is placed on $(2)$ at $t = 0$. Find the minimum time when the energy in both the capacitor and the inductor will be the same.

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is: