Question

What is the relation between resistivity free electron concentration and relaxation time

Answer 1

Answer:

) Metals: As the temperature increases, the thermal speed of electrons increases. Free electrons collide more frequently with the positive metal ions. The relaxation time decreases. Consequently, the resistivity of the metal increases.

Answer 2

Required Answer ✋

• In Theoretical Terms :-

The average of velocities v_i of all electrons just after collisions is 0, as they get bounced in all random directions.

Hence the average velocity of an electron along the length of a resistor or conductor wire is equal to that gained due to electrostatic field E.

In Mathematical Terms :-

Force on an electron in this electric field = F = e E

Acceleration = F / m = a = e E /m = e V / (m L)

Current Density = J = I / A = V / (A R) = V A / ( r A L) = V /(r L)

J = σ E = E / ρ

Or, E = J ρ

Velocity gained in between collisions due to electric field E and force F = v

v = v_i + a τ = 0 + e E τ /m = e J ρ τ / m --- (1)

So drift velocity = v = e J ρ τ / m --- (2).

I = charge crossing a cross section in time t / time t

So, I = e (n A v t) / t = n e A v

J = n e v

Substituting in (2) we get,

J / (n e) = v = e J ρ τ / m

=> τ = m / ne² ρ

Or, ρ = m / (n e² τ)

Thanking You ✌