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In LCR series a.c. circuit at resonance the value of power factor will be _________.

Asked in GUJCET 2024 · Power factor

• (1) 1
• (2) 0
• (3) -1
• (4) ∞

Step-by-step solution

Why the other options are wrong

• (2) Zero is the power factor of a pure reactance — an inductor or a capacitor on its own, where φ=±90°. At resonance X_L and X_C cancel, so φ=0 and the circuit behaves as a plain resistor.
• (3) cos φ=-1 needs φ=180°, which a series R–L–C circuit can never reach: tan φ=(X_L-X_C)/R keeps φ between -90° and +90°, and a passive circuit cannot return net power to the source.
• (4) Confuses the power factor with the current. cos φ cannot exceed 1 by definition; what peaks at resonance is Iᵣₘₛ=(Vᵣₘₛ)/R, because the impedance drops to its minimum Z=R.

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