explain how does the resistivity of a conductor depends on

Resistivity is inversely proportional to the relaxation time, because smaller value of t will mean more frequent collisions and hence larger resistivity. The relaxation is dependent on temperature of the given substance. An increase in temperature will mean that ions and atoms are vibrating more vigorously about their mean position and thus the frequency of collision increases. Hence a rise in temperature for conductors result in increase in resistivity of material.