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An LCR series circuit with 100 \(\Omega\) resistance is connected to an AC source of 200 V and angular frequency 300 rad/s. When only the capacitance is removed, the current lags behind the voltage by 60°. When only the inductance is removed, the current leads the voltage by 60°. Then the current and power dissipated in the LCR circuit are respectively:

1. 1 A, 200 watt.
2. 1 A, 400 watt.
3. 2 A, 200 watt.
4. 2 A, 400 watt.

Correct answer: 2 A, 400 watt.

Solution

For the RL case, \(\tan 60^\circ=X_L/R\), so \(X_L=100\sqrt{3}\,\Omega\). For the RC case, \(\tan 60^\circ=X_C/R\), so \(X_C=100\sqrt{3}\,\Omega\). Thus \(X_L=X_C\), so the circuit is at resonance and \(Z=R=100\,\Omega\), giving \(I=200/100=2\,\text{A}\) and \(P=I^2R=400\,\text{W}\).

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