In an LCR series circuit,if R = X_L = 2X_C,fi | vedclass

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

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

In an $LCR$ series circuit,if $R = X_L = 2X_C$,find the impedance and the phase difference between the current and the voltage.

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