Resistance and temperature

When a material is heated its resistance will change. This is due to the thermal motion of the atoms within the specimen

The equation for this variation is:


where R_q is the resistance of the specimen at some temperature q^oC and R_o the resistance at 0^oC. In this equation b is much less than a and so we can express the change by the following simplified equation as long as the temperature change is not too great.


Here a is called the temperature coefficient of resistance and is defined as the increase in resistance per degree rise divided by the resistance at 0^oC



Some values of the temperature coefficient of resistance (a)
copper 43 x10^{- 4}K^-1       tungsten 60 x10^-4K^-1    gold 36x10^-4K^-1
nichrome 0.88x10^{- 4}K^-1   carbon -5.1x10^-4K^-1     steel 33x10^-4K^-1

For a metal the temperature coefficient of resistance is positive - in other words and increase in the temperature gives an increase in resistance. This can be explained by the motion of the atoms and free electrons within the solid. At low temperatures the thermal vibration is small and electrons can move easily within the lattice but at high temperatures the motion increases giving a much greater chance of collisions between the conduction electrons and the lattice and so impeding their motion. In a light bulb the filament is at about 2700 ^oC when it is working and its resistance when hot is about ten times that when cold. (For a typical domestic light bulb the resistance measured at room temperature was 32W and this rose to 324W at its working temperature).


We can also define the change in the resistivity with temperature by an equation similar to that for resistance:


where b is the temperature coefficient of resistivity.
We require that the variation of resistance should be small so b should be as small as possible for thermal stability.

The following table gives the temperature coefficients of resistivity for a number of materials:


However in non-metals such as semiconductors an increase in temperature leads to a drop in resistance. This can be explained by electrons gaining energy and moving into the conduction band - in fact changing from being bound to a particular atom to being able to move freely - an increase in the number of free electrons. The temperature coefficient of resistance and also that of the temperature coefficient of resistivity is therefore negative.





(See also superconductivity)