A resistor of resistance $ R $, inductor of inductive reactance $ 2R $ and a capacitor of capacitive reactance $ X_C $ are connected in series to an A.C. source. If the series LCR circuit is in resonance, then the power factor of the circuit and the value $ X_C $ are respectively:

Question

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Step 1: Resonance Condition At resonance, inductive reactance equals capacitive reactance: $$ X_L = X_C $$ Step 2: Compute $ X_C $ $$ X_C = 2R $$ Step 3: Compute Power Factor At resonance, power factor is given by: $$ \cos \phi = 1 $$ Thus, the correct answer is $ 1 $ and $ 2R $.

Answer

$ 0.5 $ and $ 4R $

Answer

$ 1 $ and $ 2R $

Answer

$ 0.5 $ and $ 2R $

Answer

$ 1 $ and $ 4R $

A resistor of resistance \( R \), inductor of inductive reactance \( 2R \) and a capacitor of capacitive reactance \( X_C \) are connected in series to an A.C. source. If the series LCR circuit is in resonance, then the power factor of the circuit and the value \( X_C \) are respectively:

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The Correct Option is B

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