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GATE 2021 EE – Question 43

Electrical Machines · Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency · 2 marks · Multiple choice

In a single-phase transformer, the total iron loss is 2500 W at nominal voltage of 440 V and frequency 50 Hz. The total iron loss is 850 W at 220 V and 25 Hz. Then, at nominal voltage and frequency, the hysteresis loss and eddy current loss respectively are

  1. 1600 W and 900 W
  2. 900 W and 1600 W
  3. 250 W and 600 W
  4. 600 W and 250 W

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Show answer and explanation

Correct answer: (B) 900 W and 1600 W

Explanation

The ratio $V/f$ is the same in both cases, so $B_{max}$ is constant and $P_i=Af+Bf^2$. Then $2500=50A+2500B$ and $850=25A+625B$, so $1700=50A+1250B$ and $1250B=800$, giving $B=0.64$. So the eddy loss is $0.64\times2500=1600$ W and the hysteresis loss is $900$ W.