The $Q$-value of a series $LCR$ circuit with $L=2 \ H$,$C=32 \ \mu F$,and $R=20 \ \Omega$ is:

For the $LCR$ circuit shown here,the current is observed to lead the applied voltage. An additional capacitor $C'$,when joined with the capacitor $C$ present in the circuit,makes the power factor of the circuit unity. The capacitor $C'$ must have been connected in

The inductance $L$,capacitance $C$,and resistance $R$ are the values of the components connected in series to an $AC$ source of angular frequency $\omega$. The inductive and capacitive reactances are $X_L$ and $X_C$ respectively. If the circuit is purely resistive,then

Obtain the equation of bandwidth for an $L-C-R$ series $AC$ circuit and deduce the equation of $Q$ factor.

An alternating $e.m.f.$ of frequency $v = \frac{1}{2\pi \sqrt{LC}}$ is applied to a series $LCR$ circuit. For this frequency of the applied $e.m.f.$:

$L, C, R$ represent physical quantities inductance,capacitance,and resistance respectively. The combinations which have the dimensions of frequency are