Question

Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.

Answer 1

Given f = 50 Hz, i =$i_{0}sin\omega t$

Peak value i =$\frac{i_2}{\sqrt{2}}$

$\frac{i_0}{\sqrt{2}}=i_{0}sin\omega t$

$\Rightarrow \frac{1}{\sqrt{2}}=sin\omega t=-sin\frac{\pi }{4}$

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

or t = $\frac{\pi }{4\omega }=\frac{\pi }{4\times 2\pi f}$

= $\frac{1}{8f}=\frac{1}{8\times 50}$

= $\frac{1}{400}$ = 0.0025 s

=2.5 ms