Temperature Coefficient of Resistance

- formula as well as table of values for the temperature coefficient of resistance for various substances - the resistance temperature dependence.

The resistance of all substances varies with temperature. This temperature resistance dependence has a bearing on electronic circuits in many ways.

In most cases the resistance increases with temperature, but in some it falls.

As a result it is often necessary to have an understanding of the resistance temperature dependence.

Temperature coefficient of resistance basics

The reason behind the temperature coefficient of resistance within a conductor can be reasoned intuitively.

The resistance of a material has a dependence upon a number of phenomena. One of these is 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.

Graph showing the resistance change with temperature
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 equation for this resistance temperature dependence can be expressed in general terms as:

The formula for the temeprature coefficient of resistance.

Where
    R = the resistance at temperature, T
    Rref = the resistance at temperature Tref
    α = the temperature coefficient of resistance for the material
    T = the material temperature in ° Celcius
    Tref = 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 as this is normal "room temperature." Accordingly the equation normally used in practical terms is:

Resistance temperature coefficient formula normalised to room temperature of 20C

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, etc..


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 10^24
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


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