Why resistivity of metal decreases with increase in temperature..

Explanation

`rArr` Conductivity of metals,
`sigma = ("ne"^(2) tau)/(m)`
Here, n ,`e^(2)` , m are same.
`therefore sigma prop tau `
where `tau` = relaxation time.
`rArr` With increase in temperature relaxation time `(tau)` decreases hence, condcutivity decreases.
`rArr` Resistivity `rho prop (1)/(sigma) ` hence resitivity will increase. or `rho prop (m)/("ne"^(2) tau)` Hence with increase in temperature `.tau.` decreases hence resistivity will increase.