GATE EE 2020 Set 1 — Question 31
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Electrical Machines → Single-Phase Transformers → Losses & Max Efficiency
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Question
A single-phase, 4 kVA, 200 V/100 V, 50 Hz transformer with laminated CRGO steel core has rated no-load loss of 450 W. When the high-voltage winding is excited with 160 V, 40 Hz sinusoidal ac supply, the no-load losses are found to be 320 W. When the high-voltage winding of the same transformer is supplied from a 100 V, 25 Hz sinusoidal ac supply, the no-load losses will be __________ W (rounded off to 2 decimal places).
Correct answer
162.41 to 162.59
Solution
No-load losses consist of hysteresis loss and eddy current loss . If the ratio is constant, .
1.Check ratios:
- Case 1:
- Case 2:
- Case 3:
2.Set up equations from Case 1 and Case 2:
- (Eq. 1)
- (Eq. 2)
- Subtract Eq. 2 from Eq. 1:
- Substitute B into Eq. 2:
- .
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