question_answer

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?

A)  10 A, 0.005s   

B)  15 A, 0.05s

C)  12 A, 0.05s    

D)  8 A, 0.01s

Correct Answer: A

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 \[=\frac{1}{frequency}=\frac{1}{50}s\] Time taken to rise from zero to maximum value is \[T=\frac{T}{4}=\frac{1}{50\times 4}=\frac{1}{200}s=0.005\,s\].