For the series LCR circuit,R = frac{X_L}{2} = | vedclass

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(B) The impedance $Z$ of a series $LCR$ circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Given $R = \frac{X_L}{2}$,we have $X_L = 2R$.Given $R = 2

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$\frac{\sqrt{13}}{2} R, 	an^{-1}\left(\frac{3}{2}ight)$

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(B) The impedance $Z$ of a series $LCR$ circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Given $R = \frac{X_L}{2}$,we have $X_L = 2R$.Given $R = 2X_C$,we have $X_C = \frac{R}{2}$.Substituting these values into the impedance formula:$Z = \sqrt{R^2 + (2R - \frac{R}{2})^2} = \sqrt{R^2 + (\frac{3R}{2})^2} = \sqrt{R^2 + \frac{9R^2}{4}} = \sqrt{\frac{13R^2}{4}} = \frac{\sqrt{13}}{2} R$.The phase difference $\phi$ is given by $	an \phi = \frac{X_L - X_C}{R}$.Substituting the values: $	an \phi = \frac{2R - R/2}{R} = \frac{3R/2}{R} = \frac{3}{2}$.Therefore,$\phi = 	an^{-1}(\frac{3}{2})$.

For the series $LCR$ circuit,$R = \frac{X_L}{2} = 2 X_C$. The impedance of the circuit and the phase difference between $V$ and $I$ will be

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