### Alternating Current Question 6

#### Question 6 - 2024 (29 Jan Shift 2)

In an a.c. circuit, voltage and current are given by : $V=100 \sin (100 t) V$ and $I=100 \sin \left(100 t+\frac{\pi}{3}\right) mA$ respectively.

The average power dissipated in one cycle is :

(1) $5 W$

(2) $10 W$

(3) $2.5 W$

(4) $25 W$

## Show Answer

#### Answer: (3)

#### Solution:

$P _{avg}=V _{mms} I _{ms} \cos (\Delta \phi)$

$=\frac{100}{\sqrt{2}} \times \frac{100 \times 10^{-3}}{\sqrt{2}} \times \cos \left(\frac{\pi}{3}\right)$

$=\frac{10^{4}}{2} \times \frac{1}{2} \times 10^{-3}$

$=\frac{10}{4}=2.5 W$