Question
Find the time required for a $50\ Hz$ alternating current to change its value from zero to the rms value.
✓
Answer
$ \text { Data }: f =50 Hz , i =\frac{i_0}{\sqrt{2}} \therefore \frac{i}{i_0}=\frac{1}{\sqrt{2}}$
$i = i _0 \sin \omega t$
$\therefore \sin \omega t =\frac{i}{i_0}=\frac{1}{\sqrt{2}}$
$\therefore \omega t =\frac{\pi}{4} rad$
$\therefore 2 ft =\frac{\pi}{4}$
$\therefore t =\frac{1}{8 f}=\frac{1}{8(50)}=\frac{1}{400}$
$=\frac{1000 \times 10^{-3}}{400}=2.5 \times 10^{-3} s $
This is the required time.
$i = i _0 \sin \omega t$
$\therefore \sin \omega t =\frac{i}{i_0}=\frac{1}{\sqrt{2}}$
$\therefore \omega t =\frac{\pi}{4} rad$
$\therefore 2 ft =\frac{\pi}{4}$
$\therefore t =\frac{1}{8 f}=\frac{1}{8(50)}=\frac{1}{400}$
$=\frac{1000 \times 10^{-3}}{400}=2.5 \times 10^{-3} s $
This is the required time.
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