Q. In an a.c. circuit the e.m.f. (e) and the current (i) at any instant are given respectively by e = E₀ sin ωt i = I₀ sin(ωt − φ) The average power in the circuit over one cycle of a.c. is
A) E₀I₀
B) E₀I₀/2
C) (E₀I₀/2) sin φ
D) (E₀I₀/2) cos φ
Explanation
[Solution from source] Average power = Erms × Irms × cos φ = (E₀/√2)(I₀/√2) cos φ = (E₀I₀/2) cos φ. E₀I₀/2 holds only when current and emf are in phase (φ = 0), and the sin φ form gives the wattless (reactive) component. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.