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
Magnetizing reactance referred to the high voltage winding is __________ Ω.
(rounded off to the nearest integer)
ANSWER
The magnetizing reactance referred to the HV side is Xm = 2500 Ω.
Official answer: 2490 to 2510Source: Official answer key, GATE 2026 IN (IIT Guwahati)
Open-circuit test is performed with the LV winding energized and the HV side open, so V0 = 220 V, I0 = 2.75 A, and P0 = 363 W are all LV-side quantities.
Working (core-loss) component of no-load current: .
Magnetizing component: .
Magnetizing reactance on the LV side (the side where the test was done): .
Turns ratio (HV/LV): .
Refer to the HV side by multiplying by : .
KEY IDEA
In an open-circuit test performed from a given winding, the no-load current I0 splits into an in-phase (core-loss) component Iw = P0/V0 and a quadrature (magnetizing) component Im = sqrt(I0² − Iw²); the magnetizing reactance on the test side is V0/Im, and to refer any impedance/reactance from the LV side to the HV side it is multiplied by the square of the turns ratio a = (HV rated voltage / LV rated voltage).
WATCH OUT FOR
Forgetting to refer the LV-side magnetizing reactance to the HV side (i.e., stopping at 100 Ω), or applying the turns ratio the wrong way (dividing by a² instead of multiplying), since the OC test was performed from the LV side but the question asks for Xm referred to the HV side.
From the GATE 2026 IN paper. Every question of this paper · Download the full paper · All 14 Transformers questions, with notes
