First slide

AC Circuits

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

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

$\sqrt{5} X_{C}, \tan^{- 1} (2)$
D

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

Solution

$X_{L} = R, X_{C} = R / 2$
$∴ tanφ = \frac{X_{L} - X_{C}}{R} = \frac{R - \frac{R}{2}}{R} = \frac{1}{2}$
$\Rightarrow φ = \tan^{- 1} (1 / 2)$
Also $Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = \sqrt{R^{2} + \frac{R^{2}}{4}} = \frac{\sqrt{5}}{2} R$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App