Question

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

• A. 50 W
• B. 100 W
• C. 200 W
• D. 400 W

Answer 1

The correct option is B 100 W

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