## 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 length and has a voltage applied across its ends, the electric field is given by Multiplying both sides by the elementary unit of electric charge gives but will be the force experienced by the electron so Applying Newton's second law of motion gives where is the mass of the electron.

The electrons will collide with the atoms of the conductor. If we assume the average time between collisions is then the electrons will collide with a speed and the average speed of the electrons will be half of this – Substitute this into the electron drift equation to give (1)

Ohm's law gives the resistance so from (1) (2)

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

Equating (2) and (3) gives but the electron accelerates uniformly from rest so using to find the distance between collisions gives hence  