Question

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

• A. $\frac{\sqrt{5} R}{2}, \tan ^{-1}(2)$
• B. $\frac{\sqrt{5} R}{2}, \tan ^{-1}\left(\frac{1}{2}\right)$
• C. $\sqrt{5} X_C, \tan ^{-1}(2)$
• D. $\sqrt{5} R, \tan ^{-1}\left(\frac{1}{2}\right)$

Answer 1

Answer: (B)

$X_L=R, X_C=R / 2$
$ \therefore \tan \phi=\frac{X_L-X_C}{R}=\frac{R-\frac{R}{2}}{R}=\frac{1}{2} $
$\Rightarrow \phi=\tan ^{-1}(1 / 2)$
Also, $Z=\sqrt{R^2+\left(X_L-X_C\right)^2}$
$=\sqrt{R^2+\frac{R^2}{4}}=\frac{\sqrt{5}}{2} R$