An LCR circuit contains resistance of 110 $Ω$ and a supply 220V at 300 rad/s angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by $45^{0}$ . If on the other hand, only inductor is removed the current leads by $45^{0}$ with the applied voltage. The rms current flowing in the circuit will be:

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2.5 A

1.5A

answer is C.

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Detailed Solution

$\begin{array}{l} R = 110 Ω \\ V_{r m s} = 220 V \\ ω = 300 rad / s \\ C a s e 1 : o n l y L a n d R p r e s e n t \\ \tan 45 ° = \frac{X_{L}}{R} \\ C a s e 2 : o n l y C a n d R p r e s e n t \\ \tan 45 ° = \frac{X_{C}}{R} \\ T h u s, X_{L} = X_{C} \\ ∴ Z = R \\ \Rightarrow I_{r m s} = \frac{V_{r m s}}{Z} = \frac{220}{110} \\ \Rightarrow I_{r m s} = 2 A \end{array}$