Explain qualitative dependence of resistivity with temperature.

Explanation

`rArr` Conductivity of material `sigma = ("ne"^(2) tau)/(m)`
resitivity `rho = (1)/(sigma)`
`therefore rho = (m)/("ne"^(2) tau)`
If m and e are constant then,
`rho prop (1)/(n) and rho = (1)/(tau)`
Thus, resistivity is inversely proportional to number density and inversely proportional to relaxation time.
` rArr` With increase in temperature (average ) speed of electron increase hence relaxation time `tau` decrease and resistivity increase.
`rArr` IN a metal number density (n ) is not dependent on temperature.
`rArr` In semiconductor and insulator number density .n. increase with temperature. Hence, in such material with increase in temperature resistivity decreases.