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Q.

An LCR circuit contains resistance of 100 $Ω$ and a supply of 200 V at 300 rad angular frequency. If only capacitor is taken out from the circuit and the rest of the circuit is joined, current lags behind the voltage by 60°. If, on the other hand. only inductor is taken out, the current leads by 60° with the applied voltage. The current flowing in the circuit is

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a

2.5 A

b

1 A

c

2 A

d

1.5 A

answer is C.

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Detailed Solution

According to the given question,

$\tan 60^{\circ} = \frac{ωL}{R} and \tan 60^{\circ} = \frac{1 / ωC}{R}$

$∴ ωL = (1 / ωC) (case of resonance)$

Now $Z = \sqrt{R^{2} + {(ωL - \frac{1}{ωC})}^{2}} = 100 Ω$

$∴ I_{rms} = \frac{E_{rms}}{Z} = \frac{200 V}{100 Ω} = 2 A$

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An LCR circuit contains resistance of 100Ω and a supply of 200 V at 300 rad angular frequency. If only capacitor is taken out from the circuit and the rest of the circuit is joined, current lags behind the voltage by 60°. If, on the other hand. only inductor is taken out, the current leads by 60° with the applied voltage. The current flowing in the circuit is