1. Tardigrade
  2. Question
  3. Physics
  4. An L C R 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°. When only the inductor is removed the current leads the voltage by 60°. The average power dissipated is

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Q. An $L C R$ 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

Alternating Current

Solution:

$\tan \phi=\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., $Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}=R$
So average power, $P=\frac{V^{2}}{R}$
$=\frac{200 \times 200}{100}=400\,W$