The frequency of oscillation of the current in the given circuit is:

At a moment $t = 0$ when the charge on capacitor $C_1$ is zero, the switch $S$ is closed. If $I_0$ is the current through the inductor at that instant, then for $t > 0$,

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:

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:

$A$ 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 $.........A$.

$A$ capacitor of capacity $20 \mu F$ is charged to a potential of $35 \text{ V}$. The battery is then disconnected. $A$ pure inductor coil of $200 \text{ mH}$ is connected across the capacitor so that $LC$ oscillations are set up. The maximum current in the coil is: (in $\text{ A}$)