Question

An AC source rated 100 V (rms) supplies a current of 10 A (rms) to a circuit. The average power delivered by the source

(a) must be 1000 W
(b) may be 1000 W
(c) may be greater than 1000 W
(d) may be less than 1000 W

Answer 1

(b) may be 1000 W
(d) may be less than 1000 W

The average power delivered by an AC source is given by,
$P_{avg}=V_{rms}{I}_{rms}\cos \varphi$
Given:
V_rms = 100 V
I_rms = 10 A
$\Rightarrow P_{avg}=1000\cos \varphi$
$\because \varphi \in \left(-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2}\right)$
$\Rightarrow \cos \varphi \in \left(0,1\right)$
$\therefore 0\le P_{avg}\le 1000$