The resonant frequency of an $L-C$ circuit is

An inductor of inductance $2 \mu H$ is connected in series with a resistance,a variable capacitor and an a.c. source of frequency $5 \text{ kHz}$. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x} \text{ F}$,where the value of '$x$' is (Take $\pi^2 = 10$).

In an $LCR$ resonant circuit,the phase difference between the current and the voltage is:

An a.c. e.m.f. of peak value $230 \ V$ and frequency $50 \ Hz$ is connected to a circuit with $R=11.5 \ \Omega, L=2.5 \ H$ and a capacitor all in series. The value of capacitance is '$C$' for the current in the circuit to be maximum. The value of '$C$' and maximum current are respectively $(\pi^2=10)$

In the circuit shown,the $AC$ source has voltage $V=20 \cos (\omega t) \text{ V}$ with $\omega=2000 \text{ rad/s}$. The magnitude of the amplitude current will be nearly

The $Q$ factor of a series $\text{LCR}$ circuit with $L=2 \text{ H}$,$C=32 \mu\text{F}$ and $R=10 \Omega$ is :-