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  • 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 vo

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^{\circ} . When only the inductor is removed the current leads the voltage by 60^{\circ} . The average power dissipated is

Option: 1

50 W


Option: 2

100 W


Option: 3

200 W


Option: 4

400 W


Answers (1)

best_answer

\mathrm{\begin{aligned} & \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 \end{aligned}}

\mathrm{\text { i.e. } \mathrm{Z}=\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}=\mathrm{R}}

\mathrm{\text { So average power } \mathrm{P}=\frac{\mathrm{V}^2}{\mathrm{R}}=\frac{200 \times 200}{100}=400 \mathrm{~W}}

Posted by

sudhir kumar

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