First slide

Phasors and Phasor Diagrams

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

Moderate

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

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

Solution

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

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