Question

An alternating current is given by the following equation,$I=3\sqrt{2}\sin (100\pi t+\frac{\pi }{4})$
Find the frequency and $rms$ value of the current over a full cycle.

• A. $50\text{Hz},3\text{A}$
• B. $50\text{Hz},3\sqrt{2}\text{A}$
• C. $50\text{Hz},\frac{3}{\sqrt{2}}\text{A}$
• D. $25\text{Hz},3\text{A}$

Answer 1

The correct option is A $50\text{Hz},3\text{A}$

Given:

$I=3\sqrt{2}\sin (100\pi t+\frac{\pi }{4})$

Over a full cycle, $rms$ value of current is given by,

$I_{rms}=\frac{I_{peak}}{\sqrt{2}}=\frac{3\sqrt{2}}{\sqrt{2}}=3\text{A}$

Also, $2\pi f=100\pi$

$\Rightarrow f=\frac{100\pi }{2\pi }=50\text{Hz}$

$\therefore$ Frequency, $f=50\text{Hz}$

Hence, option $\left(A\right)$ is correct.