First slide

Power in a.c. circuit

Question

An LCR series circuit with a resistance of 100 ohm is connected to an ac source of 200 V (r.m.s.) and angular frequency 300 rad/s. When only the capacitor is removed, the current lags behind the voltage by 60^o . When only the inductor is removed the current leads the voltage by 60^o . The average power dissipated is

Moderate

A

50 W
B

100 W
C

200 W
D

400 W

Solution

$\tan \varphi = \frac{{{X_L}}}{R} = \frac{{{X_C}}}{R} \Rightarrow \tan {60^o} = \frac{{{X_L}}}{R} = \frac{{{X_C}}}{R}$
$\Rightarrow {X_L} = {X_C} = \sqrt 3 \;R$
$i.e.,\,\,Z = \sqrt {{R^2} + {{({X_L} - {X_C})}^2}} = R$
$So{\text{ }}average{\text{ }}power\,\,P = \frac{{{V^2}}}{R} = \frac{{200 \times 200}}{{100}} = 400\,\,W$

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