Question

Derive an expression for the resistivity of a material of a conductor alao prove the unit of resistivity​

Answer 1

Explanation:

Relation between the resistivity and relaxation time : We know that drift velocity of electron is given by

vd=

eE

m

τbutE=

V

l

∴Vd=

e

m

.

V

l

.Tau⇒V=

vd.ml

eτ

∴ According to Ohm's law

R=

V

I

=

vdml/eτ

I

=

vdml/e.τ

neAvd

⇒R=

vdml

eτ.neAvd

=

m

ne2τ

.

l

A

...(i)

But the resistivity is given by R=ρ

l

A

Comparing (i) and (ii), we get ρ=

m

ne2τ