An alternating e.m.f. having voltage V = V_0 | vedclass

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(C) The impedance of the series $L-C-R$ circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Given $|X_L - X_C| = R$,we substitute this into the imped

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$\frac{V_0}{2 R \omega C}$

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(C) The impedance of the series $L-C-R$ circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Given $|X_L - X_C| = R$,we substitute this into the impedance formula:$Z = \sqrt{R^2 + R^2} = \sqrt{2R^2} = R\sqrt{2}$.The peak current in the circuit is $I_0 = \frac{V_0}{Z} = \frac{V_0}{R\sqrt{2}}$.The potential difference across the capacitor is $V_C = I_0 X_C$.The r.m.s. value of the potential difference across the capacitor is $V_{C,rms} = I_{rms} X_C$.Since $I_{rms} = \frac{I_0}{\sqrt{2}} = \frac{V_0}{R\sqrt{2} \cdot \sqrt{2}} = \frac{V_0}{2R}$,we have:$V_{C,rms} = \frac{V_0}{2R} \cdot \frac{1}{\omega C} = \frac{V_0}{2R\omega C}$.

An alternating e.m.f. having voltage $V = V_0 \sin \omega t$ is applied to a series $L-C-R$ circuit. Given: $|X_L - X_C| = R$. The r.m.s. value of potential difference across the capacitor will be:

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