Obtain the resonant frequency $\omega_{r}$ of a series $LCR$ circuit with $L=2.0 \;H, C=32\; \mu F$ and $R=10\; \Omega$. What is the $Q$-value of this circuit?

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:

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

$A$ resonance circuit having inductance and resistance $2 \times 10^{-4} \ H$ and $6.28 \ \Omega$ respectively oscillates at $10 \ MHz$ frequency. The value of the quality factor of this resonator is .........
$[\pi = 3.14]$

In an $LCR$ series circuit at resonance:

$A$ series $LCR$ circuit is designed to resonate at an angular frequency $\omega_{0} = 10^{5} \, rad/s$. The circuit draws $16 \, W$ power from a $120 \, V$ source at resonance. The value of resistance $R$ in the circuit is ...... $\Omega$.