Temperature Coefficient of Resistance

Details of the temperature coefficient of resistance along with the formula and calculations and a table of common materials.

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The resistance and electrical resistivity of all materials is affected by temperature.

The change in electrical resistance has a bearing on electrical and electronic circuits. In some it can give rise to significant changes. As a result the temperature coefficient of resistance is an important parameter for many applications.

As a result of its importance the temperature coefficient of resistance is quoted for materials, the commonly used materials being widely available.

Towards the bottom of this page there is a temperature coefficient of resistance table for many common materials used within the electrical and electronics industries.

Temperature coefficient of resistance: the basics

There are two main reasons why the resistance of materials is dependent upon temperature.

One affect results from the the number of collisions that occur between the charge carriers and atoms in the material. As the temperature increases so do the number of collisions and therefore it can be imagined that there will be a marginal increase in resistance with temperature.

This may not always be the case because some materials have a negative temperature coefficient of resistance. This can be caused by the fact that with increasing temperature further charge carriers are released which will result in a decrease in resistance with temperature. As might be expected, this effect is often seen in semiconductor materials.

When looking at the resistance temperature dependence, it is normally assumed that the temperature coefficient of resistance follows a linear law. This is the case around room temperature and for metals and many other materials. However it has been discovered that the resistance effects resulting from the number of collisions is not always constant, particularly at very low temperatures for these materials.

The resistivity has been shown to be inversely proportional to the mean free path between collisions, i.e. this results in increasing resistivity / resistance with increasing temperature. For temperatures above about 15°K (i.e. above absolute zero), this is limited by thermal vibrations of the atoms and this gives the linear region which we are familiar. Below this temperature, the resistivity is limited by impurities and available carriers.

Resistance temperature graph, showing how temperature coefficient of resistance is flat at low temperatures — Resistance temperature graph

Temperature coefficient of resistance formula

The resistance of a conductor at any given temperature can be calculated from a knowledge of the temperature, its temperature coefficient of resistance, its resistance at a standard temperature, and the temperature of operation. The formula for this resistance temperature dependence can be expressed in general terms as:

R = R_{ref} (1 + α (T - T_{ref}))

Where
R = the resistance at temperature, T
R_ref = the resistance at temperature Tref
α = the temperature coefficient of resistance for the material
T = the material temperature in ° Celcius
T_ref = is the reference temperature for which the temperature coefficient is specified.

The temperature coefficient of resistance is normally standardised in relation to a temperature of 20°C. This temperature is typically taken to be normal "room temperature." As a result the formula for the temperature coefficient of resistance normally takes this into account:

R = R_{20} (1 + α_{20} (T - 20))

Where
R₂₀ = the resistance at 20°C
α₂₀ is the temperature coefficient of resistance at 20°C

Temperature coefficient of resistance table

The table below gives the temperature coefficient of resistance for a variety of substances including the copper temperature coefficient of resistance, as well as the temperature coefficient of resistance for aluminium and many other materials.

Temperature Coefficient of Resistance Table for Different Substances
Substance	Temperature Coefficient °C^-1
Aluminium	43 x 10^-4 (18°C - 100°C)
Antimony	40 x 10^-4
Bismuth	42 x 10^-4
Brass	~10 x 10^-4
Cadmium	40 x 10^-4
Cobalt	7 x 10^-5
Constantan (Alloy)	33 x 10^-4
Copper	40 x 10^-4
Gold	34 x 10^-4
Carbon (Graphite)	-5.6 x 10^-4
Germanium	-4.8 x 10^-2
Iron	56 x 10^-4
Lead	39 x 10^-4
Manganin	~2 x 10^-5
Molybdenum	46 x 10^-4
Nichrome	1.7 x 10^-4
Nickel	59 x 10^-4
Platinum	38 x 10^-4
Silicon	-7.5 x 10²⁴
Silver	40 x 10^-4
Tantalum	33 x 10^-4
Tin	45 x 10^-4
Tungsten	45 x 10^-4
Zinc	36 x 10^-4

It will be seen that most materials but not that are widely used within the electrical and electronics industry have a temperature coefficient of resistance that is very approximately around 30 to 50 x 10^-4, except semiconductors which are widely different.