Question

On the basis of electron drift, derive an expression for resistivity of a conductor in terms of no. of free electron and relaxation time

Answer 1

ρ = m/ ne^2τ

Resistivity of the materiel of a conductor depends on the relaxation time.

Explanation:

We have:

E = - V / l

Where V is the potential across the length l of the conductor.

Vd = eVτ / ml

Current flowing = neAVd

I =  neAVd eVr/ml = ne^2AVτ /ml

I/V = ne^2Aτ /ml = 1/R ---- (1)

R = ρ l/A

Comparing (1) and (2)

ρ = m/ ne^2τ

Resistivity of the materiel of a conductor depends on the relaxation time.