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A lamp consumed only 50 % of the maximum power applied in an A.C. circuit. What will be the phase difference between the applied voltage and the circuit current?

Asked in GUJCET 2014 · Power factor

• (1) π/6 rad
• (2) π/3 rad
• (3) π/4 rad
• (4) π/2 rad

Step-by-step solution

Why the other options are wrong

• (1) Uses sin φ = 1/2 instead of cos φ = 1/2. The power factor is the cosine of the phase difference.
• (3) Sets cos²φ = 1/2, as if the power went as the square of the power factor. That would need the current itself to shrink as the phase grows; here the comparison is at the same voltage and current, so P = VᵣₘₛIᵣₘₛ cos φ is linear in cos φ.
• (4) A phase difference of π/2 makes cos φ = 0: the lamp would take no power at all, not half.

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