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

Answer 1

Answer: (C)

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

An alternating current is given as $I=20\sin (100\pi t+0.05x)$ A

Comparing it with $I=I_o\sin (wt+\varphi )$

We get, $I_o=20$ A and $w=100\pi$

R.m.s value of current $I_{rms}=\frac{I_o}{\sqrt{2}}=\frac{20}{\sqrt{2}}=10\sqrt{2}$ A

Frequency of current $\nu =\frac{w}{2\pi }=\frac{100\pi }{2\pi }=50$ Hz