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

$\begin{array}{l} \tan ϕ = \frac{X_{L}}{R} = \frac{X_{C}}{R} \Rightarrow \tan 60^{\circ} = \frac{X_{L}}{R} = \frac{X_{C}}{R} \\ \Rightarrow X_{L} = X_{C} = \sqrt{3} R i.e. Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = R So average power P = \frac{V^{2}}{R} = \frac{200 \times 200}{100} = 400 W, \end{array}$

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