Temperature Coefficient of Resistance
 formula as well as table of values for the temperature coefficient of resistance for various substances  the resistance temperature dependence.
Resistance & Resistivity includes
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.
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:
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:
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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