Practice portal › Alternating Current › Power in AC Circuits

In an a.c. circuit the applied voltage is E=E₀ sin ω t and the current is I=I₀ sin (ω t-π/2). The power consumed is

Asked in AIEEE 2007 · Wattless current

(1) P=√2 E₀ I₀
(2) P=(E₀ I₀)/(√2)
(3) P=zero
(4) P=(E₀ I₀)/2

Answer: (3) P=zero

Step-by-step solution

P=1/2 E₀ I₀ cos φ with φ=π/2.

cos π/2=0, so P=0 (wattless).

Why the other options are wrong

(1) Ignores the power factor cos 90°=0.
(2) Uses r.m.s. product but forgets cos φ=0.
(4) Drops the cos φ factor.

More Power in AC Circuits questions

All Power in AC Circuits questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer