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

The natural frequency of an $LC$ circuit is $120 \ kHz$. When the capacitor in the circuit is totally filled with a dielectric material,the natural frequency of the circuit decreases by $20 \ kHz$. The dielectric constant of the material is:

In an $LC$ oscillator,if values of inductance and capacitance become twice and eight times,respectively,then the resonant frequency of the oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is:

If $L = 1.00 \, mH$ and $C = 1.00 \, nF$,find the resonant frequency in $rad/s$.

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

If maximum energy is stored in the capacitor at $t = 0$,find the time after which the current in the circuit will be maximum. Given $L = 25 \, mH$ and $C = 10 \, \mu F$.