GATE 2026 IN – Question 58
A single-phase transformer has a rating of 10 kVA, 50 Hz, 1100 V/220 V. In an open-circuit test with the high-voltage side open, the following are obtained:
Voltage applied to the low-voltage winding: 220 V.
Measured power: 363 W.
Measured current: 2.75 A.
The magnetizing reactance $X_m$ referred to the high-voltage winding is ________ Ω. (Rounded off to the nearest integer.)
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Correct answer: 2490 to 2510
Explanation
The core-loss current on the low-voltage side is $I_c=P/V=363/220=1.65\ \mathrm A$. The magnetizing current is $I_m=\sqrt{I_0^2-I_c^2}=\sqrt{2.75^2-1.65^2}=2.2\ \mathrm A$.
Thus $X_{m,LV}=220/2.2=100\ \Omega$. The turns ratio is $a=1100/220=5$. Referred impedance scales by $a^2$, so $X_{m,HV}=25\times100=$ **2500 Ω**.