Question

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

• A. $0.050s$
• B. $0.025s$
• C. $0.0025s$
• D. $0.0075s$

Answer 1

The correct option is C $0.0025s$

Consider the frequency of alternating current $f=50HZ$

Alternation current $\left(i\right)$ is

$i=i_0\sin \omega ------\left(1\right)$

$i_0=peakvalueofcurrent$

Root mean square value of current $\left(i_{rms}\right)$ is

$i_{rms}=\frac{i_0}{\sqrt{2}}$

Now,

Substituting the value of the root mean square value of current in place of alternating current in equation $\left(1\right)$

Get,

$\begin{array}{c}\frac{i_0}{\sqrt{2}}=i_0\sin \omega t\\ \Rightarrow \frac{1}{\sqrt{2}}=\sin \omega t=\sin \frac{\pi }{4}\\ \Rightarrow \frac{\pi }{4}=\omega t\\ \Rightarrow t=\frac{\pi }{4\omega }=\frac{\pi }{4\times 2\pi f}\left(\because \omega =2\pi f\right)\\ =\frac{1}{8f}=\frac{1}{8\times 50}\\ =\frac{1}{400}=0.0025s\end{array}$

Hence, The option $C$ is the correct answer $0.0025s$