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 $\mu C$.

In an oscillation of $L-C$ circuit,the maximum charge on the capacitor is $Q$. The charge on the capacitor,when the energy is stored equally between the electric and magnetic field is

$A$ 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 given $L-C$ circuit,inductance is $80 \mu H$ and capacitance is $20 \mu F$. The maximum potential difference across the capacitor is $80 \ V$. The maximum current is (in $A$)

What is meant by $LC$ circuit? What are $LC$ oscillations?