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(D) In a series $LCR$ circuit at resonance,the inductive reactance $X_L$ is equal to the capacitive reactance $X_C$ $(X_L = X_C)$.At resonance,the pha

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Power factor is zero.

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(D) In a series $LCR$ circuit at resonance,the inductive reactance $X_L$ is equal to the capacitive reactance $X_C$ $(X_L = X_C)$.At resonance,the phase difference $\phi$ between voltage and current is $0^{\circ}$.$1$. The power factor is $\cos \phi = \cos 0^{\circ} = 1$. Thus,option $D$ is incorrect.$2$. Average power $P_{avg} = V_{rms} I_{rms} \cos \phi = V_{rms} I_{rms} (1) = V_{rms} I_{rms}$,which is equal to the apparent power. Thus,option $B$ is true.$3$. Peak energy stored in the capacitor is $\frac{1}{2} C V_0^2$ and in the inductor is $\frac{1}{2} L I_0^2$. At resonance,these values are equal. Thus,option $A$ is true.$4$. Wattless current is $I_{rms} \sin \phi$. Since $\phi = 0^{\circ}$,$\sin 0^{\circ} = 0$,so wattless current is zero. Thus,option $C$ is true.Therefore,the statement that is not true is that the power factor is zero.

List-$I$	List-$II$
$(a)$ $\omega L > \frac{1}{\omega C}$	$(i)$ Current is in phase with $emf$
$(b)$ $\omega L = \frac{1}{\omega C}$	$(ii)$ Current lags behind the applied $emf$
$(c)$ $\omega L < \frac{1}{\omega C}$	$(iii)$ Maximum current occurs
$(d)$ Resonant frequency	$(iv)$ Current leads the $emf$

For a series $LCR$ circuit at resonance,the statement which is not true is:

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