The carrier frequency generated by a tank circuit containing $1 \,nF$ capacitor and $10 \, \mu H$ inductor is

$A$ capacitor of capacitance $500\,\mu F$ is charged completely using a dc supply of $100\,V$. It is now connected to an inductor of inductance $50\,mH$ to form an $LC$ circuit. The maximum current in $LC$ circuit will be $.........A$.

$A$ condenser of capacity $6 \ \mu F$ is fully charged using a $6 \ V$ battery. The battery is removed and a resistanceless $0.2 \ mH$ inductor is connected across the condenser. The current flowing through the inductor when one-third of the total energy is in the magnetic field of the inductor is.....$A$

The frequency of an $L-C$ circuit is $f_{1}$. If a resistance $R$ is also added to it,the frequency becomes $f_{2}$. The ratio $\frac{f_{2}}{f_{1}}$ will be:

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

In an oscillating $LC$ circuit, the maximum charge on the capacitor is $Q$. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes: