$A$ charged $10 \mu F$ capacitor is connected to a $16 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit?

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?

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycle/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is

In the circuit shown below, the switch is kept in position $a$ for a long time and is then thrown to position $b$. The amplitude of the resulting oscillating current is given by

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......$Hz$

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