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The power in an A.C. circuit is given as P=VᵣₘₛIᵣₘₛ cos δ. The power factor at the resonance frequency of a series L–C–R circuit will be .........

Asked in RS Academy GUJCET booklet · Power factor

• (1) zero
• (2) 1
• (3) 1/2
• (4) 1/(√2)

Step-by-step solution

Why the other options are wrong

• (1) Zero is the power factor of a purely reactive circuit, a pure L or pure C with δ=90°. At resonance the reactances cancel instead.
• (3) cos δ=1/2 means δ=60°, which nothing at resonance produces; there δ=0.
• (4) 1/(√2) is the power factor at the half-power frequencies, where |X_L-X_C|=R and δ=45°, not at resonance itself.

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