Question

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

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

Answer 1

Answer: (B)

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