GATE 2025 IN Q.14: solution and answer

GATE 2025 · INQ.14 · 1 mark · MCQ

The primary coil of a linear variable differential transformer (LVDT) is supplied with AC voltage as shown in the figure. The secondary coils are connected in series opposition and the output is measured using a true RMS voltmeter. The displacement x of the core is indicated in mm on a linear scale. At the null position x = 0, the voltmeter reads 0 V. If the voltmeter reads 0.2 V for a displacement of x = +2 mm, then for a displacement of x = -3 mm, the voltmeter reading, in V, is

GATE 2025 IN question 14: An AC source drives the primary coil of an LVDT (primary on the left, dotted top terminal). — Figure from the GATE 2025 IN paper. It is part of the question.

(A)
-0.3
(B)
-0.1
(C)
0.3
(D)
0.5

Answer and solution

ANSWER

The voltmeter reads 0.3 V, which is option (C).

Official answer: CSource: Official answer key, GATE 2025 IN (IIT Roorkee)

The secondary coils are in series opposition, so the net output is $v_{o} = v_{s 1} - v_{s 2}$ . At null ( $x = 0$ ) the two induced voltages are equal and $v_{o} = 0$ V.
Within the linear range the output amplitude is proportional to the core displacement from null: $∣ V_{o} ∣ = k ∣ x ∣$ .
From the given reading, $k = \frac{0.2 V}{2 mm} = 0.1 V/mm$ .
For $x = - 3 mm$ the amplitude is $∣ V_{o} ∣ = 0.1 V/mm \times 3 mm = 0.3 V$ .
Moving the core to the other side of null reverses the phase of the output by $18 0^{\circ}$ . The sign of the displacement is carried only by this phase.
A true RMS voltmeter reads the RMS value of the waveform. This value is never negative and does not show the phase. So it reads $+ 0.3 V$ , not $- 0.3 V$ , and option (C) is correct.

KEY IDEA

An LVDT output amplitude is proportional to the core's distance from null. The side of null shows up only as a 180 degree phase change. A true RMS voltmeter cannot show phase, so it reads the magnitude, which is always positive.

WATCH OUT FOR

Treating the output as a signed DC-like quantity and picking -0.3 V for a negative displacement. Another slip is using only the magnitude scaling and choosing -0.1 V or 0.5 V by adding or subtracting readings.

From the GATE 2025 IN paper. Every question of this paper · Download the full paper · All 2 Motion & force questions, with notes