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√2)a√32a√23a√13a

Solution

## The correct option is C √23aWe know, Irms =√∫I2dt∫dt Since, x2+y2=a2 ⇒y2=a2−x2 Now, ∫I2dt→∫a−ay2dx  ⇒∫a−a(a2−x2)dx=[a2x−x33]a−a ⇒a3−a33+a3−a33=2a3−2a33 Therfore, ∫I2dt=4a33 ∫dt⇒∫a−adx=2a So, Irms =√23a2 Irms =√23a

Suggest corrections