A series L C R circuit with 100 Ω resistance is connected to an ac source of 200 V with an angular frequency of 300 rad s - 1 . If only the capacitor is removed, the current lags behind the voltage by

Question

A series L C R circuit with 100 Ω resistance is connected to an ac source of 200 V with an angular frequency of 300 rad s - 1 . If only the capacitor is removed, the current lags behind the voltage by a phase of 60 ∘ . If only the inductor is removed, the current leads the voltage by a phase of 60 ∘ . The current and the power dissipated in the circuit is

TestHub · Accepted Answer

From given condition circuit is at resonance

For LR circuit,

$\tan 60 = \frac{X_{L}}{R} \Rightarrow X_{L} = \sqrt{3} R$

For CR circuit

$\tan 60 = \frac{X_{C}}{R} \Rightarrow X_{C} = \sqrt{3} R$ $\Rightarrow X_{L} = X_{C} = \sqrt{3} R$

$I_{rms} = \frac{V_{rms}}{R} = \frac{200}{100} = 2 Amp$

$P = I^{2} R = 4 \times 100 = 400 Watt$

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