Question

A three phase induction motor is driving full-load torque which is independent of
speed. If the line voltage drops to 90% of the rated value, % increase in motor copper
losses

Answer 1

If the line voltage drops to 90% of the rated value, % increase in motor copper losses will be 23 %

Explanation :

For an induction motor, when the torque is constant then,

sV² = constant

=> s₁V₁² = s₂V₂²

=>  s₂V₂/s₁V₁ = V₁/V₂ = 1/0.9 = 1.11

we know that current is proportional to product of slip and voltage

=> I ∝ sV

=> I₂/I₁ = s₂V₂/s₁V₁ = 1.11

We know that the copper loss of an induction motor is directly proportional to square of the current

=> C₂/C₁ = (I₂/I₁)² = 1.11² = 1.23

Hence increase in copper loss = 0.23 = 23 %