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:

Consider the following circuit. By keeping $S_1$ closed,the capacitor is fully charged and then $S_1$ is opened and $S_2$ is closed,then

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

An $LC$ circuit contains a $20 \; mH$ inductor and a $50 \; \mu F$ capacitor with an initial charge of $10 \; mC$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t=0$.
$(a)$ What is the total energy stored initially? Is it conserved during $LC$ oscillations?
$(b)$ What is the natural frequency of the circuit?
$(c)$ At what time is the energy stored $(i)$ completely electrical (i.e.,stored in the capacitor)? $(ii)$ completely magnetic (i.e.,stored in the inductor)?
$(d)$ At what times is the total energy shared equally between the inductor and the capacitor?
$(e)$ If a resistor is inserted in the circuit,how much energy is eventually dissipated as heat?

In $L-C$ oscillation,the maximum charge on the capacitor is $Q$. If at any instant,the electric energy and magnetic energy associated with the circuit are equal,then the charge on the capacitor at that instant is:

An oscillator circuit consists of an inductance of $0.5 \, mH$ and a capacitor of $20 \, \mu F$. The resonant frequency of the circuit is nearly (in $Hz$)