Question

An alternating current in circuit is given by $I=20\sin (100\pi t+0.005\pi )A$. The r.m.s value and the frequency of current respectively are:

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

Answer 1

Answer: (C)

$10\sqrt{2}A$ and $50Hz$

Given $I=20\sin (100\pi t+0.005\pi )A$
The root mean square value of alternating current
$=I_{rms}=\frac{I_0}{\sqrt{2}}=\frac{20}{\sqrt{2}}=10\sqrt{2}A$
Also, $\omega =100\pi$
$\Rightarrow 2\pi f=100\pi$
or $f=50Hz$