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Question

Determine the rms value of a semi-circular current wave which has a maximum value of a Ampere. The y axis denotes current in Ampere and x axis denotes time. 

  1. (12)a
  2. 32a
  3. 23a
  4. 13a


Solution

The correct option is C 23a
We know,
Irms =I2dtdt

Since, x2+y2=a2
y2=a2x2
Now,
I2dtaay2dx 
aa(a2x2)dx=[a2xx33]aa
a3a33+a3a33=2a32a33

Therfore,
I2dt=4a33
dtaadx=2a
So,
Irms =23a2
Irms =23a

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