GATE 2026 EE Q.17: solution and answer

GATE 2026 · EEQ.17 · 1 mark · MCQ

A 15 kVA, 1100 V/220 V, single-phase two-winding transformer is configured as a 1.32 kV/1.1 kV autotransformer. What will be the rating of the autotransformer?

(A)
60 kVA
(B)
75 kVA
(C)
90 kVA
(D)
100 kVA

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Answer and solution

ANSWER

The rating of the autotransformer is 90 kVA — option (C).

Official answer: CSource: Official answer key, GATE 2026 EE (IIT Guwahati)

Two-winding transformer rated currents: $I_{1100} = \frac{15000}{1100} = 13.64 A$ (in the 1100 V winding), $I_{220} = \frac{15000}{220} = 68.18 A$ (in the 220 V winding).
Autotransformer connection: the 1100 V winding becomes the common winding and the 220 V winding becomes the series winding, connected so that the high terminal is $1100 V + 220 V = 1320 V$ and the low (tapped) terminal is $1100 V$ — matching the stated $1.32 kV /1.1 kV$ autotransformer.
Since the volts/turn and flux in each physical winding are unchanged by the reconnection, each winding still carries its own two-winding rated current: $68.18 A$ in the series (220 V) winding and $13.64 A$ in the common (1100 V) winding.
By KCL at the tap, the high-side line current equals the series-winding current ( $68.18 A$ ), and the low-side line current is $I_{L V} = I_{H V} + I_{common winding} = 68.18 + 13.64 = 81.82 A$ .
Autotransformer rating $= V_{L V} \times I_{L V} = 1100 \times 81.82 \approx 90, 000 VA = 90 kVA$ (checks out on the high side too: $1320 \times 68.18 \approx 90, 000 VA$ ).
Equivalently, using the standard conversion formula $S_{a u t o} = S_{2 -winding} \times \frac{V _{H}}{V _{H} - V _{L}}$ with $V_{H} = 1320 V$ , $V_{L} = 1100 V$ : $S_{a u t o} = 15 \times \frac{1320}{1320 - 1100} = 15 \times \frac{1320}{220} = 15 \times 6 = 90 kVA$ .
Both derivations agree: the autotransformer rating is $90 kVA$ , option (C).

KEY IDEA

Converting a two-winding transformer into an autotransformer (by electrically joining the two windings in series) multiplies its VA rating by the factor $\frac{V _{H}}{V _{H} - V _{L}}$ , because the same physical windings now also carry a conductively-transferred (not just transformed) component of power.

WATCH OUT FOR

Assuming the autotransformer rating equals the original two-winding rating (15 kVA) because "it's the same transformer," ignoring that autotransformer action lets the common winding carry more net through-current than pure transformer action alone.

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GATE 2026 EE Q.17: solution and answer

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