In an $LC$ circuit,the angular frequency at resonance is $\omega$. What is the new angular frequency when the inductance is made four times and the capacitance is made eight times its original value?

$A$ charged $30 \mu\text{F}$ capacitor is connected to a $27 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit (in $\text{ rad/s}$)?

$A$ transmitter transmits at a wavelength of $300\ m$. $A$ capacitor of capacitance $9.6\ \mu F$ is being used. The value of the inductance for the resonant circuit is approximately.

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

$A$ $2\,\mu F$ capacitor is charged to $100\,V$. After disconnecting the battery,a $20\,mH$ coil is connected across the charged capacitor. The capacitor discharges through the inductor and the current in the circuit is oscillatory. Assuming the resistance of the coil is zero,the maximum current in the circuit is.....$A$

$A$ 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.