(i) The resistive of a material is dependent on temperature. The resistivity of a conductor increase with increases in temperature according to the expression,
`rho_(T)=rho_(0)[1+alpha(T-T_(0)) " "...(1)`
(ii) Where `rho_(T)` is resistivity of the conductor at some reference temperature `T_(0)` (usually at `20^(@)C)` and `alpha` is the temperature coefficient of resistivity.
(iii) It is defined as the ratio of increases in resistivity per degree rise in temperature to its resistivity at`T_(0)`
From the equation (1), we can write
`rho_(T)-rho_(0)= alpha rho_(0)(T-T_(0))`
`:. alpha=(rho_(T)=rho_(0))/(rho_(0)(T-T_(0)))=(Delta rho)/(rho_(0)DeltaT)`
where `Delta rho= rho_(T)-rho_(0)` is change in reistivity for a change in temperature `Delta T=T-T_(0)`
Its unit is per `""^(@)C`.
`alpha` of conductor :
(iv) For conductors `alpha` is positive. if the temperature of a conductor increases, the average kinetic energy of electrons in the conductor increass. This results in more frequent collisions and hence the resistivity increases.
(v) The graph of the Even though, the resistivity of conductors like metal varies linearly for wide range of temperatures, there also exists a nonlinear region at very low temperatures.
(vi) The resistivity apporaches some finite value as the temperature apporaches absolute zero.
(vii) As the resistance is directly proportional to resistivity of the material, we can also write the also write the resistance of a conductor at temperature `T^(@)C` as
`R_(T)=R_(0)[1+(T-T_(0)]`
`alpha=(R_(T)-R_(0))/(R_(0)(T-T_(0)))=(1)/(R_(0))(Delta R)/(Delta T)`
`alpha =(1)/(R_(0))(Delta R)/(Delta T)`
where `DeltaR=R_(T)-R_(0)` is change in resistance during the change in temperature `Delta T=T-T_(0)`
(viii) `alpha` of semiconductors For semiconductors, the resistivity decreases with increases in temperature. As teh temperature increases, more electrons will be liberated from their atoms. Hence the current in increases and therefore the resistivity decreases. A semiconductor with a negative temperature coefficient of resistance is called a thermistor.
Temperature dependence of resistivity for a semiconductor
