2 Drift of Electrons Limitations of Ohm_s Law

Drift of Electrons Limitations of Ohm’s Law

• Free electrons are in continuous random motion. They undergo change in direction at each collision and the thermal velocities are randomly distributed in all directions.

∴ Average thermal velocity, is zero … (1)

The electric field E exerts an electrostatic force ‘−Ee’.

Acceleration of each electron is,

Where,

m → Mass of an electron

e → Charge on an electron

• Drift velocity − It is the velocity with which free electrons get drifted towards the positive terminal under the effect of the applied electric field.

Where,

Thermal velocities of the electrons

Velocity acquired by electrons

τ₁, τ₂ → Time elapsed after the collision

Since = =0,

∴ v_d = a τ

Where,  is the average time elapsed

Substituting for a from equation (2),

Electron drift to a small distance in a time Δt = V_dΔt

Amount of charge passing through the area A in time Δt , q = IΔt

IΔt = neAv_dΔt

Where,

n→ Number of free electrons per unit volume

From equation (4),

Current density (J)

We know,

J = σ E

Mobility (μ)

• It is defined as the magnitude of the drift velocity per unit electric field.

• Unit of mobility is m²/Vs.

Limitations of Ohm’s Law

There are several materials and devices for which the proportionality of V and I are as follows:

• V ceases to be proportional to I.

• Sign of V affects the relation between V and I.

• There is more than one value of V for the same current.