Q180 / 200 · WBJEE 2013 · Physics
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$10 \mathrm{A}$ and $100 \mathrm{Hz}$
- B$10 \mathrm{A}$ and $50 \mathrm{Hz}$
- Correct answerC$10 \sqrt{2} \mathrm{A}$ and $50 \mathrm{Hz}$
- D$10 \sqrt{2}$ A and $100 \mathrm{Hz}$
Solution
Given, $I=20 \sin (100 \pi t+0.05 \pi)$
The root mean square value of alternating
$$
\text { current }=l_{\mathrm{ms}}=\frac{l_{0}}{\sqrt{2}}=\frac{20}{\sqrt{2}}=10 \sqrt{2} \mathrm{A}
$$
Also, $\quad \omega=100 \pi$
$\Rightarrow \quad 2 \pi f=100 \pi$ or $f=50 \mathrm{Hz}$
Hence, the correct answer is option: 'C'.