Question

Find the time required for $50\text{Hz}$ sinusoidal alternating current to change its value from $zero$ to $rms$ value.

• A. $1.5\text{ms}$
• B. $2.0\text{ms}$
• C. $2.5\text{ms}$
• D. $3.5\text{ms}$

Answer 1

The correct option is C $2.5\text{ms}$

Alternating current $I$ is given by

$I=I_0\sin \omega t$

And, $rms$ value of current, $I_{rms}=\frac{I_0}{\sqrt{2}}$

$\therefore \frac{I_0}{\sqrt{2}}=I_0\sin \omega t$

$\Rightarrow \sin \omega t=\frac{1}{\sqrt{2}}$

$\Rightarrow \omega t=\frac{\pi }{4}$

$\Rightarrow \left(2\pi \nu \right)t=\frac{\pi }{4}$

$\Rightarrow t=\frac{1}{8\nu }=\frac{1}{8\times 50}\text{s}=2.5\text{ms}$

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