Drift Velocity is defined as the velocity of free electrons with which they get drifted towards the positive terminal under the influence of the external field.
Resistivity (specific resistance) (ρ): If the material of a conductor is defined as the resistance of unit length and unit area of cross-section of the conductor.
And ρ = \(\frac{m}{ne^2\tau }\)
Thus resistivity of the material of a conductor depends upon
(i) ρ ∝ \(\frac{1}{n}\) i.e. resisitivity is inversely proportional to the number density of electrons (number of electons per unit volume) inside the conductor.
(ii) ρ ∝ \(\frac{1}{\tau}\) i.e. resistivity is inversely proportional to the average relaxation time of the free electrons in the conductor.
The value of n depends upon the nature of conductor and τ depends upon the temperature of the conductor.
Ohm’s law from drift velocity of electrons.
Since drift velocity vd and current I flowing in a conductor are related by the relation:
vd = \(\frac{I}{ne A}\) .........................(1)
Also drift velocity in terms of average relaxation time r is given by
![Also drift velocity in terms of average relaxation time r is given by](https://www.sarthaks.com/?qa=blob&qa_blobid=12640873976692778548)
This is Ohm’s law.
But \(\frac{V}{I} \) = R, the resistance of the conductor
So Eq. (3) becomes
![the resistance of the conductor](https://www.sarthaks.com/?qa=blob&qa_blobid=11222150532459359143)