Displacement sensing — the device made from a transformer with a movable ferromagnetic core, one primary, and two secondaries connected in opposition is called a(n) ______.

Introduction / Context:
Precision position and displacement measurements in control systems often rely on inductive sensors. A widely used device employs a transformer structure whose coupling varies with a movable core, yielding an AC output proportional to position near the null. Engineers know this as a standard instrument in mechatronics and instrumentation.

Given Data / Assumptions:

• Construction: one primary, two secondary coils, movable core.
• Operation: AC excitation of the primary, differential secondary output.
• Application: linear displacement with high resolution.

Concept / Approach:
The Linear Variable Differential Transformer (LVDT) has two secondaries wired in series opposition. When the core is centered, induced voltages cancel (near-zero output). Displacement of the core increases coupling to one secondary and decreases coupling to the other, producing a differential voltage proportional to displacement and indicating direction by phase. The structure described precisely matches an LVDT.

Step-by-Step Solution:

Verification / Alternative check:
Data sheets show transfer characteristics with high linearity around the null region, low friction (no electrical contact), and excellent repeatability.

Why Other Options Are Wrong:

• Strain gauge: resistive foil sensor; not a transformer.
• Accelerometer: measures acceleration, often capacitive or piezoelectric.
• “Transformer displacement sensor”: a generic phrase; the standard specific name is LVDT.

Common Pitfalls:
Confusing LVDT with RVDT (rotary variant) or assuming potentiometric wipers; LVDT is contactless and uses AC coupling.

Final Answer:
LVDT.