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The power in an AC circuit is given by P=VᵣₘₛIᵣₘₛ cos δ. The power factor at the resonant frequency of a series L-C-R circuit will be _______.

Asked in GSEB Board July 2015 · 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 inductive or purely capacitive circuit, where δ=90°. At resonance the circuit behaves as a pure resistance, the opposite extreme.
• (3) cos δ=1/2 means δ=60°, which needs a net reactance of √3 R. At resonance the net reactance is zero, so δ=0.
• (4) 1/(√2) is the power factor at the half-power frequencies, where the net reactance equals R and δ=45° — not at resonance itself.

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