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Resistance-Temperature Relationship

The resistance-temperature (R-T) relationship plays a central role in resistance temperature detectors (RTDs). The R-T relationship of some common RTD materials are illustratrated in the following schematic where the y-axis is the normalized resistance with respect to resistance at 0 °C (32 °F), x-axis is the temperature.

Resistance-Temperature Relationship
for some RTD materials

For a given material, the resistance at any temperature can be obtained by curve-fitting the R-T curve. Suppose that a nth degree polynomial least-square curve-fit is used. The temperature function will then be,

Some references suggest to express the resistance as a function of temperature (rather than temperature as a function of resistance), i.e.,

Although such a relationship is mathematically correct, its usefulness is limited. After all, we are interested in determining temperature from a resistance measurement.

A Simplified Case

Some materials have an almost linear R-T relationship within a certain temperature range, T1 < T < T2. Such a linear function would take the form,

Rearranging to bring temperature out gives,

where a is the average temperature coefficient of resistance in the (T1,T2) temperature range, i.e., a is the slope of the R-T line.

Both the measured temperature and the reference temparature should be within the (T1,T2) temperature range,

T1 < {T, TRef} < T2
Glossary
Mechanical Engineers Outlook

Guide for those interested in becoming a mechanical engineer. Includes qualifications, pay, and job duties.

CNC Machining Design Guide

Optimize your designs, reduce machining time, and lower your costs.

Negotiate Your Salary

Learn the best principles to negotiate the salary you deserve!

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.