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

$A$ series $LCR$ circuit with inductance $L = 10\,H$,capacitance $C = 10\,\mu F$,and resistance $R = 50\,\Omega$ is connected to an $AC$ source of voltage $V = 200 \sin(100t)\,V$. If the resonant frequency of the $LCR$ circuit is $\nu_{0}$ and the frequency of the $AC$ source is $\nu$,then:

Obtain an equation for the sharpness of resonance in an $L-C-R$ series $AC$ circuit. What is the quality factor $Q$? Explain bandwidth.

In a non-resonant $LCR$ series circuit,what will be the nature of the circuit for frequencies higher than the resonance frequency?

In an $LCR$ circuit, the resonant frequency is $600 \ Hz$ and the half-power points are at $650 \ Hz$ and $550 \ Hz$. The quality factor is:

The tuning circuit of a radio receiver has a resistance of $50\,\Omega$,an inductor of $10\,mH$ and a variable capacitor. $A$ $1\,MHz$ radio wave produces a potential difference of $0.1\,mV$. The value of the capacitor to produce resonance is.......$pF$ (Take $\pi^2 = 10$).