Question

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

Answer 1

Frequency of alternating current, f = 50 Hz
Alternation current $\left(i\right)$ is given by,
i = i₀sinωt ...(1)
Here, i₀ = peak value of current
Root mean square value of current $\left(i_{rms}\right)$ is given by,
$i_{\mathrm{rms}}=\frac{i_0}{\sqrt{2}}...\left(1\right)$
On substituting the value of the root mean square value of current in place of alternating current in equation (1), we get:
$$\begin{gathered} \frac{i_0}{\sqrt{2}}=i_0\sin \omega t \\ \Rightarrow \frac{1}{\sqrt{2}}=\sin \omega t\mathit{}=\sin \frac{\mathrm{\pi }}{4} \\ \Rightarrow \frac{\mathrm{\pi }}{4}=\mathrm{\omega }t \\ \Rightarrow t\mathit{}\mathit{=}\frac{\mathrm{\pi }}{4\omega }\mathit{}=\frac{\mathrm{\pi }}{4\times 2\mathrm{\pi }f}\left(\because \omega =2\mathrm{\pi }f\right) \\ =\frac{1}{8f}=\frac{1}{8\times 50} \\ =\frac{1}{400}=0.0025\mathrm{s} \\ =2.5\mathrm{ms} \end{gathered}$$