The Electron Theory of Resistance

Suppose we consider the electrons in a conductor to have a random motion, like gas molcules are assumed to have – one of the assumptions of the kinetic theory of gases. If the conductor is of lengthand has a voltageapplied across its ends, the electric field is given by

Multiplying both sides bythe elementary unit of electric charge givesbutwill be the forceexperienced by the electron so

Applying Newton's second law of motiongives whereis the mass of the electron.

The electrons will collide with the atoms of the conductor. If we assume the average time between collisions isthen the electrons will collide with a speedand the average speedof the electrons will be half of this –

Substitute this into the electron drift equationto give(1)

Ohm's lawgives the resistanceso from (1)(2)

The resistance R of a material is also given in terms of its resistivityby(3)

Equating (2) and (3) givesbut the electron accelerates uniformly from rest so usingto find the distance between collisionsgives hence