GATE 2016 EE – Question 56
A single-phase 400 V, 50 Hz transformer has an iron loss of 5000 W at the rated condition. When operated at 200 V, 25 Hz, the iron loss is 2000 W. When operated at 416 V, 52 Hz, the value of the hysteresis loss divided by the eddy current loss is ________.
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Correct answer: 1.4 to 1.5
Explanation
With the ratio $V/f$ constant, hysteresis loss is proportional to $f$ and eddy current loss to $f^2$, so the iron loss is $Af + Bf^2$. From $50A + 2500B = 5000$ and $25A + 625B = 2000$ we get $B = 0.8$ and $A = 60$. At 416 V and 52 Hz the ratio $V/f$ is 8, the same as before, so the same constants apply. The hysteresis loss is $60 \times 52 = 3120$ W and the eddy current loss is $0.8 \times 52^2 = 2163$ W, so the ratio is $\frac{3120}{2163} = 1.44$.