Why does the resistivity of metal increase with an increase in temperature ?

Explanation

When temperature of conductor increases then vibrations of positive ions increases and it results in more chaos and hence more frequent collisions of electrons with ions. Time interval between two successive collisions is called relaxation time. We can say that relaxation time decreases with increases in temperature. Resistivity of metals can be written as
`rho=m/(ne^2tau)`
Here, `tau` is relaxation time. Hence, the resistivity of metals increases with an increase in temperature.