Question

An alternating current in a circuit is given by $I=20$ sin $(100\pi t+0.05\pi )$ A. The r.m.s. value and the frequency of current respectively are

• A. 10A and 100 Hz
• B. 10A and 50 Hz
• C. 10 $\sqrt{2}$ A and 50Hz
• D. 10 $\sqrt{2}$ A and 100 Hz

Answer 1

Answer: (C)

Given, $l=20\sin (100\pi t+0.05\pi )$
The root mean square value of alternating current
$=I_{ms}=\frac{I_0}{\sqrt{2}}=\frac{20}{\sqrt{2}}=10\sqrt{2}A$
Also, $\omega =100\pi$
$\Rightarrow 2\pi f=100\pi$ or $f=50Hz$