1. Conduction in metals

1.1 Ohm's law and resistivity

In a metal, in the absence of an external field, electrons move in an unordered fashion. From time to time, they collide and their velocities are modified in direction and modulus. Thus, because of the random nature of the motion, the average velocity and mean displacement of an electron, evaluated over a sufficiently long time interval, must be zero.

When the conductor is subjected to an external electric field $\overrightarrow{E}$ , this exerts the force $\overrightarrow{F}=-e$