Question

Deduce Ohm’s law from the concept of drift velocity.

Or

Show that the resistance of a conductor is given by 

R = \(\frac{ml}{ne^2A\tau}\)

or 

Show that the resistivity of a conductor is given by

ρ = \(\frac{mI}{ne^2\tau}\)

or

Explain how does the resistivity of a conductor depend upon (t) number density ‘n’ of free electrons, and (ii) relaxation time τ?

Or

Define the term resistivity and write its S.I. unit. Derive the expression for the resistivity in terms of number density of free electrons and relaxation time.

Answer 1

Since drift velocity v_d and current I flowing in a conductor are related by the relation:

v_d = \(\frac{I}{neA}\)  ...........(1)

Also drift velocity in terms of average relaxation time r is given by

This is Ohm’s law.

But \(\frac{V}{I}\)  = R, the resistance of the conductor

So Eq. (3) becomes