The quality factor of an $LCR$ circuit having resistance $(R)$ and inductance $(L)$ at resonance frequency $(\omega)$ is given by:

In a series $LR$ circuit,$X_{L} = R$ and the power factor of the circuit is $P_{1}$. When a capacitor with capacitance $C$ such that $X_{L} = X_{C}$ is put in series,the power factor becomes $P_{2}$. The ratio $\frac{P_{1}}{P_{2}}$ is

The power factor in an $L-C-R$ circuit at resonance is

$A$ resistor of $R=6 \Omega$,an inductor of $L=1 \text{ H}$,and a capacitor of $C=17.36 \mu \text{F}$ are connected in series with an $AC$ source. Find the $Q$ factor.

An $LCR$ series circuit with $100 \Omega$ resistance is connected to an $AC$ source of $200 V$ and angular frequency $300 \text{ rad/s}$. When only the capacitor is removed,the current lags behind the voltage by $60^{\circ}$. When only the inductor is removed,the current leads the voltage by $60^{\circ}$. The power dissipated in the $LCR$ circuit will be:

Power delivered by the $ac$ source of the circuit becomes maximum when