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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 voltage by $60^{0}$ . When only the inductor is removed the current leads the voltage by $60^{0}$ . If all elements are connected, the current in the circuit is

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2 A

4 A

1 A

answer is D.

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Detailed Solution

$\tan ϕ = \frac{X_{L}}{R} = \frac{X_{C}}{R} \Rightarrow \tan 60^{o} = \frac{X_{L}}{R} = \frac{X_{C}}{R}$

$\Rightarrow X_{L} = X_{C} = \sqrt{3} R$

i.e. $Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = R$

So, $i_{r m s} = \frac{{V_{r m s}}^{}}{R} = \frac{200}{100} = 2 A$

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