GATE 2026 IN Q.17: solution and answer

GATE 2026 · INQ.17 · 1 mark · MCQ

A single phase step-down transformer has a high voltage primary winding and a low voltage secondary winding. The secondary winding is connected to a load impedance $Z_{2}$ . The impedance $Z_{2}$ when referred to the primary winding is denoted by $Z_{2}^{'}$ . Which of the following conditions is true?

(A)
$Z_{2}^{'} = Z_{2}$
(B)
$0.5 Z_{2} < Z_{2}^{'} < Z_{2}$
(C)
$Z_{2}^{'} > Z_{2}$
(D)
$Z_{2}^{'} \leq 0.5 Z_{2}$

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Answer and solution

ANSWER

The correct answer is (C): $Z_{2}^{'} > Z_{2}$ .

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

Let the turns ratio be $a = \frac{N _{1}}{N _{2}}$ (primary turns to secondary turns).
In a step-down transformer, the primary is the high-voltage winding and the secondary is the low-voltage winding. Since voltage is proportional to the number of turns, the primary must have more turns than the secondary: $N_{1} > N_{2}$ , so $a > 1$ .
For an ideal transformer, the primary and secondary voltages and currents are related by $V_{1} = a V_{2}$ and $I_{1} = \frac{I _{2}}{a}$ .
The secondary-side impedance is $Z_{2} = \frac{V _{2}}{I _{2}}$ . Referred to the primary side, the impedance is $Z_{2}^{'} = \frac{V _{1}}{I _{1}} = \frac{a V _{2}}{I _{2} / a} = a^{2} \frac{V _{2}}{I _{2}} = a^{2} Z_{2}$
Since $a > 1$ , it follows that $a^{2} > 1$ , and therefore $Z_{2}^{'} > Z_{2}$ .
This matches option (C).

KEY IDEA

When an impedance is referred from one side of an ideal transformer to the other, it scales by the square of the turns ratio between the side it is being referred TO and the side it originally sits on: $Z_{2}^{'} = a^{2} Z_{2}$ , where $a = N_{1} / N_{2}$ .

WATCH OUT FOR

Confusing which winding has more turns in a step-down transformer (thinking the primary of a step-down transformer has fewer turns because "step-down" sounds like a reduction), or forgetting the transformation is by $a^{2}$ , not $a$ , and concluding $Z_{2}^{'} = Z_{2}$ or $Z_{2}^{'} < Z_{2}$ .

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GATE 2026 IN Q.17: solution and answer

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