Question

on the basis of electron theory what is expression for resistivity of conductor in terms of free electrons​

Answer 1

Answer:

On the basis of electron drift, derive an expression for resistivity of a conductor in terms of number density of free electrons and relaxation time. ... Electrons are accelerated because of the external electric field. They move from one place to another and current is produced.

Answer 2

Given that,

On the basis of electron theory,

We know that,

Drift velocity is defined as,

$v_{d}=\dfrac{eE\tau}{m}$​

Where, m = mass of electron

e = charge of electron

E = electric field

$\tau$ = relaxation time

We know that,

$E=\dfrac{-V}{l}$

Where, Potential across the length of the conductor

Put the value of E in the formula of drift velocity

$v_{d}=\dfrac{eV\tau}{ml}$

We need to calculate the resistance

Using formula of current

$I=neAv_{d}$

Put the value of velocity

$I=\dfrac{ne^2AV\tau}{ml}$

$\dfrac{I}{V}=\dfrac{ne^2A\tau}{ml}$

$\dfrac{1}{R}=\dfrac{ne^2A\tau}{ml}$

$R=\dfrac{ml}{ne^2A\tau}$....(I)

We need to calculate the resistivity of the conductor

Using formula of resistance

$R=\rho\dfrac{l}{A}$.....(II)

On comparing equation (I) and (II)

$\rho=\dfrac{m}{ne^2\tau}$

Hence, The resistivity of the conductor is $\dfrac{m}{ne^2\tau}$