The power factor of an $LCR$ circuit at resonance is:

An inductor of inductance $L$,a capacitor of capacitance $C$,and a resistor of resistance $R$ are connected in series to an $ac$ source. The quality factor of the circuit is

For a series $LCR$ circuit,the power loss at resonance is

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

$A$ telephone wire of length $200\, km$ has a capacitance of $0.014\, \mu F$ per km. If it carries an $AC$ of frequency $5\, kHz$,what should be the value of an inductor required to be connected in series so that the impedance of the circuit is minimum? (in $mH$)

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