Lesson 3 of 12 · 11 min
Electron drift and where resistivity comes from
NCERT § "Drift of Electrons and the Origin of Resistivity"
The heater glows within a second of the switch. Yet the electrons in its wire move slower than an ant. Both are true.
The lesson in notes
In short
Free electrons collide frequently with the ions of the lattice. The average time between successive collisions is the relaxation time τ.
An applied field E gives each electron an acceleration −eE/m between collisions, producing a small average velocity opposite to E, the drift velocity v_d = −eEτ/m.
The current through a conductor of area A with n free electrons per unit volume is I = neAv_d.
Drift speeds are very small, typically a fraction of a millimetre to a few millimetres per second, while the random thermal speeds of electrons are very large.
A lamp lights almost at once when switched on because the electric field is set up along the whole wire nearly instantly, starting all the electrons drifting together; it is not because electrons rush from the switch.
Combining the two results gives the resistivity in terms of microscopic quantities: ρ = m/(ne²τ).
For a wire of non-uniform cross-section carrying a steady current, the current is the same at every section, so the drift speed is larger where the wire is thinner.