GATE 2020 EE – Question 31

Electrical Machines · Single phase transformer: equivalent circuit, phasor diagram, open circuit and short circuit tests, regulation and efficiency · 1 mark · Numerical answer

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 source, the no-load losses will be ________ W (rounded off to 2 decimal places).

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Correct answer: 162.41 to 162.59

Explanation

In all three cases $V/f=4$, so the flux is constant and the iron loss is $P=Af+Bf^2$. From $450=50A+2500B$ and $320=40A+1600B$, we get $B=0.1$ and $A=4$. At 25 Hz, $P=4\times25+0.1\times625=162.5$ W.