Q. The peak value of an alternating current frequency $50\, Hz$ is $14.14\, A$. Find the $rms$ value of current, and how much time will the current take in reaching from zero to maximum value?
Delhi UMET/DPMTDelhi UMET/DPMT 2002
Solution:
The root-mean-square (rms) value of an alternating current is defined as the square-root of the average of $ {{i}^{2}} $ during a complete cycle, where $i$ is the instantaneous value of alternating current.
$ \therefore i_{rms}=\frac{{{i}_{0}}}{\sqrt{2}} $
$ ({{i}_{0}}= $ peak value of current)
Given, $ {{i}_{0}}=14.14\,A $
$\therefore i_{rms}=\frac{14.14}{\sqrt{2}}=\frac{14.14}{1.414}=10\,A $
Also, time period $ =\frac{1}{\text{frequency}}=\frac{1}{50}s $
Time taken to rise from zero to maximum value is
$T=\frac{T}{4}=\frac{1}{50\times 4}=\frac{1}{200}s=0.005\,s $ .
