GATE EE 2016 Set 1 — Question 56
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Electrical Machines → Single-Phase Transformers → Losses & Max Efficiency
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Question
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 ______.
Correct answer
1.4 to 1.5
Solution
Iron loss is the sum of hysteresis loss and eddy current loss . Given that is constant (, , and ), the maximum flux density remains constant.
Under this condition, and .From the given data:
1) At 50 Hz: (Eq. 1)
2) At 25 Hz: (Eq. 2)Subtracting Eq. 2 from Eq. 1:
Substituting in Eq. 2:
Now, at 52 Hz:
W
WThe ratio of hysteresis loss to eddy current loss is:
Under this condition, and .From the given data:
1) At 50 Hz: (Eq. 1)
2) At 25 Hz: (Eq. 2)Subtracting Eq. 2 from Eq. 1:
Substituting in Eq. 2:
Now, at 52 Hz:
W
WThe ratio of hysteresis loss to eddy current loss is:
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