In a series LCR circuit R = 200 Ω and the voltage and the frequency… | JEE Main 2010 (AIEEE)

Q73JEE Main 2010 · AIEEEDifficult

Power, Power Factor & Wattless Current

In a series $LCR$ circuit $R = 200\ \Omega$ and the voltage and the frequency of the main supply are $220\text{ V}$ and $50\text{ Hz}$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^\circ.$ On taking out the inductor from the circuit the current leads the voltage by $30^\circ.$ The power dissipated in the $LCR$ circuit is

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Answer: (d)

Without C: $\tan 30^\circ = X_L/R$ . Without L: $\tan 30^\circ = X_C/R$ .
So $X_L = X_C$ : resonance, $Z = R$ .
$P = V^2/R = 220^2/200 = 242$ W, so the answer is (d).

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