Given below are two statements :Statement I : | vedclass

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(C) Statement-$I$: The current in an $LCR$ series circuit is given by $I = \frac{V}{\sqrt{R^2 + (X_L - X_C)^2}}$. At resonance,$X_L = X_C$,which makes

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Both Statement $I$ and Statement $II$ are true.

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(C) Statement-$I$: The current in an $LCR$ series circuit is given by $I = \frac{V}{\sqrt{R^2 + (X_L - X_C)^2}}$. At resonance,$X_L = X_C$,which makes the impedance $Z = R$ (minimum). Since impedance is minimum,the current $I = \frac{V}{R}$ is maximum. Thus,Statement-$I$ is true.Statement-$II$: In a purely resistive circuit,the current is $I_{res} = \frac{V}{R}$. In a series $LCR$ circuit,the current is $I_{LCR} = \frac{V}{\sqrt{R^2 + (X_L - X_C)^2}}$. Since $\sqrt{R^2 + (X_L - X_C)^2} \geq R$,it follows that $I_{LCR} \leq I_{res}$. Therefore,the current in a purely resistive circuit is always greater than or equal to the current in an $LCR$ circuit for the same voltage source. Thus,Statement-$II$ is true.

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