Question

derive an expression for the resistivity of material​

Answer 1

if you want simple expression for resistivity,then follow below procedure...

EXPRESSION FOR RESISTIVITY  OF MATERIAL

we know that the resistance of material body is directly proportional to its length

                      R ∝ L

also,the resistance is depend inversly on area of cross-section of body.

 

                     R ∝ A

COMBINNIG ABOVE TWO FACTORS,WE GET,

                   R ∝ L/A

           

                  R=ρ× L/A

where rho{ρ} is proportionality constant called specific resistance or   resistivity  

so we say,

                    →  ρ= R×A/L   ←

         

                   

           

                 

Answer 2

Explanation:

let n = number density of free electrons

A = Cross sectional area of conductor

e = electrons charge

Number of free electrons present in l length of conductor = nAl

Total charge contained in length l which can contribute in current

q = (n A l)e

The time taken by free electron to cross the l length of conductor is

t = l/vd

where, vd = drift speed of electron

current through the conductor

I = q/t

I = ( n A l )e/ t

= ( n A l ) e / ( l/vd )

=n e A vd

current density(i) = i/A = n e A vd/A = n e vd

( j= n e vd i.e. j ∞ vd )

thus current density of conductor is proportional to drift speed.

FOLLOW ME "B"