For an $LCR$ series $AC$ circuit, $L = 25 \, mH$, $R = 3 \, \Omega$, and $C = 62.5 \, \mu F$. What is the frequency of the source at which resonance occurs (in $Hz$)?

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

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 $\pi^2 = 10$).

An $LCR$ circuit is at resonance for a capacitor $C$,inductance $L$,and resistance $R$. If the value of the resistance is halved while keeping all other parameters the same,the current amplitude at resonance will be:

At resonance frequency,the impedance in a series $LCR$ circuit is

In the circuit shown in the figure,an a.c. source gives voltage $V = 20 \cos (2000 t)$. The impedance and r.m.s. current respectively will be: