Question

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

Answer 1

$I=I_o\sin \omega t$

And , $\omega =2\pi f=100\pi$

And $I_{rms}=\frac{I_o}{\sqrt{2}}$

$⟹\frac{I_o}{\sqrt{2}}=I_o\sin \omega t$

$⟹\sin \omega t=\frac{1}{\sqrt{2}}$

$⟹\omega t=\frac{\pi }{4}$

$⟹t=\frac{\pi }{4\times 100\pi }$

$⟹t=2.5ms$