Temperature sensors — a thermistor's resistance–temperature characteristic (R vs T) is best described as which type of relationship for practical engineering use (note: most thermistors are NTC or PTC with strongly curved R–T behavior rather than straight-line)?

Introduction / Context:
Thermistors are widely used temperature sensors in electronics and control systems. Unlike resistance temperature detectors (RTDs) that are designed for near-linear behavior over moderate spans, thermistors exhibit a strongly curved resistance–temperature (R–T) characteristic. This item checks whether you recognize the essential shape of that characteristic in practical design terms.

Given Data / Assumptions:

• The device in question is a thermistor (either NTC or PTC).
• We are describing the general R–T dependence, not a tiny trimmed range with linearization circuitry.
• Focus is on intrinsic sensor behavior as supplied by manufacturers.

Concept / Approach:
In an NTC (negative-temperature-coefficient) thermistor, resistance falls rapidly as temperature rises; in a PTC thermistor, resistance increases with temperature, often sharply around a knee. Both cases are decidedly non-linear. While engineers frequently fit NTC data with the “Beta” equation or the Steinhart–Hart equation (which involve logarithms of resistance), those are curve-fitting formulas. The core takeaway is that the R–T curve is not a straight line and its slope changes with temperature.

Step-by-Step Solution:

Verification / Alternative check:
Look at manufacturer R–T tables: resistance halves or quarters over relatively small temperature intervals. No single linear gain captures behavior across a wide span; linearization usually requires resistor networks or digital compensation in microcontrollers.

Why Other Options Are Wrong:

• Linear: thermistors are not intrinsically linear over wide ranges.
• Logarithmic: models use logarithms, but the device itself is not “pure logarithmic.”
• Geometric: not a standard description for sensor R–T curves.

Common Pitfalls:
Confusing the mathematical forms used to fit data (which include logs) with the sensor’s fundamental behavior; also assuming “calibrated” equals “linear.”

Final Answer:
Nonlinear.