Alternating Current Question 6
Question 6 - 2024 (29 Jan Shift 2)
In an a.c. circuit, voltage and current are given by : $\mathrm{V}=100 \sin (100 \mathrm{t}) \mathrm{V}$ and $I=100 \sin \left(100 t+\frac{\pi}{3}\right) \mathrm{mA}$ respectively.
The average power dissipated in one cycle is :
(1) $5 \mathrm{~W}$
(2) $10 \mathrm{~W}$
(3) $2.5 \mathrm{~W}$
(4) $25 \mathrm{~W}$
Show Answer
Answer: (3)
Solution:
$\mathrm{P}{\mathrm{avg}}=\mathrm{V}{\mathrm{mms}} \mathrm{I}_{\mathrm{ms}} \cos (\Delta \phi)$
$=\frac{100}{\sqrt{2}} \times \frac{100 \times 10^{-3}}{\sqrt{2}} \times \cos \left(\frac{\pi}{3}\right)$
$=\frac{10^{4}}{2} \times \frac{1}{2} \times 10^{-3}$
$=\frac{10}{4}=2.5 \mathrm{~W}$
