How does one cane understand the temperature dependence resistivity of a conductor ?

Explanation

(i) For conductors `alpha` is positive. If the temperature of a conductor increases, the average kinetic energy of electrons in the conductor increases. This results in more frequent collisions and hence the resistivity increases.
(ii) 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.
(iii) The resistivity approaches some finite value as the temperature approaches absolute zero.
(iii) As the resistance is directly proportional to resistivity of the material, we can also write the resistance of a conductor at temperature `T^(@)C` as
`R_(T)=R[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 `Delta =R_(T)-R_(0)` is change in resistance during the change in temperature `Delta T=T-T_(0)`