For a series LCR circuit,R = X_L = 2X_C. The | vedclass

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

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$\frac{\sqrt{5}R}{2}, 	an^{-1}\left(\frac{1}{2}ight)$

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(B) Given: $R = X_L$ and $X_L = 2X_C$,which implies $X_C = \frac{R}{2}$.The impedance $Z$ of a series $LCR$ circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Substituting the values: $Z = \sqrt{R^2 + (R - \frac{R}{2})^2} = \sqrt{R^2 + (\frac{R}{2})^2} = \sqrt{R^2 + \frac{R^2}{4}} = \sqrt{\frac{5R^2}{4}} = \frac{\sqrt{5}R}{2}$.The phase difference $\phi$ is given by $	an \phi = \frac{X_L - X_C}{R}$.Substituting the values: $	an \phi = \frac{R - R/2}{R} = \frac{R/2}{R} = \frac{1}{2}$.Therefore,$\phi = 	an^{-1}\left(\frac{1}{2}ight)$.Thus,the impedance is $\frac{\sqrt{5}R}{2}$ and the phase difference is $	an^{-1}\left(\frac{1}{2}ight)$.

For a series $LCR$ circuit,$R = X_L = 2X_C$. The impedance of the circuit and the phase difference between $V$ and $i$ will be:

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