The plot given below shows the average power delivered to an $LRC$ circuit versus frequency. The quality factor of the circuit is

With the gradual increase in frequency of an $A.C.$ source,the impedance of an $LCR$ series circuit

The resonant frequency of a series $LCR$ circuit is $f$. The circuit is now connected to a sinusoidally alternating e.m.f. of frequency $2f$. The new reactance $X_{L}^{\prime}$ and $X_{C}^{\prime}$ are related as:

In a series $LR$ circuit with $X_L = R$, the power factor is $P_1$. If a capacitor of capacitance $C$ with $X_C = X_L$ is added to the circuit, the power factor becomes $P_2$. The ratio of $P_1$ to $P_2$ will be:

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:

In an $LCR$ circuit,the capacitance is changed from $C$ to $2C$. For the resonant frequency to remain unchanged,the inductance should be changed from $L$ to: