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 $Hz$)

$A$ fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self-inductance $L$ at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic fields is:

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

In the given circuit,when $S_1$ is closed,the capacitor gets fully charged. Now $S_1$ is opened and $S_2$ is closed. Then

An $LCR$ circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having a damping constant $b$,the correct equivalence would be:

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