GATE EE 2026 Set 1 — Question 42
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Electric Circuits → AC Power & Three-Phase → RMS & Average Values
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Question
An electrical component has voltage drop , when the current through it is . What is the average power dissipated over a half cycle corresponding to ?
Correct answer
(C) (Vₘ Iₘ)/(2) cos θ
Solution
The instantaneous power is the product of instantaneous voltage and current:Using the trigonometric identity , we get:The average power over a half cycle is:Since and , the sine terms cancel out:This is the same as the average power over a full cycle.
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