Each transducer's name contains its measurand or its principle: (A)-(III), (B)-(I), (C)-(IV), (D)-(II), option 3.

(B) Resistance hygrometer and relative humidity. "Hygro-" means moisture, so the pairing is settled by the word itself. The device uses a hygroscopic film — lithium chloride or a conductive polymer — whose resistance falls sharply as it absorbs water vapour from the air. The dependence is strongly non-linear, typically several decades of resistance across the humidity range, so the reading is linearised electronically.

(A) Potentiometric device and displacement. A wiper slides along a resistive track, and the output is a simple ratio:

\(V_{out}=V_{in}\dfrac{x}{L}\)

Because it is a ratio of resistances, the reading is independent of supply variation and of the track's absolute resistance and its temperature coefficient — which is why the arrangement is so robust. It is the simplest displacement transducer there is, needing no excitation electronics at all, though the sliding contact wears and generates noise.

(D) Moving coil generator and velocity. A coil moving in a magnetic field generates an EMF by Faraday's law:

\(e=-N\dfrac{d\phi}{dt}=Blv\)

The output is proportional to velocity, not to position — the derivative is built into the physics. It is self-generating, needing no excitation, which is why it is used in vibration pick-ups and geophones.

(C) Dielectric gauge and thickness. A capacitance depends on the geometry of its plates:

\(C=\dfrac{\varepsilon A}{d}\)

Pass a sheet of material between two plates and the capacitance changes with the sheet's thickness, since the dielectric now fills a known fraction of the gap. The measurement is non-contact, which makes it suitable for moving webs of paper, plastic film or coated strip.

Note the contrast between (A) and (D), which is the pairing most easily confused: one measures where something is and needs an excitation supply; the other measures how fast it is moving and generates its own signal. Choosing between them amounts to choosing which quantity the instrument should measure directly rather than by differentiating or integrating.

Hence, the correct code is (A)-(III), (B)-(I), (C)-(IV), (D)-(II).