Explain why the current through a metallic conductor is directly proportional to the potential difference applied across it, using a microscopic model of charge carriers.

A greater potential difference across a metallic conductor creates a larger electric field inside the conductor. The electric field exerts a force on the conduction electrons, increasing their mean drift velocity. Current is given by I = nAvq, where n is the number of charge carriers per unit volume, A the cross‑sectional area, v the mean drift velocity and q the charge of an electron. Thus, if the drift velocity increases in proportion to the applied potential difference, the current increases proportionally. At a constant temperature the collision frequency of the electrons – and therefore the resistance – remains unchanged, so the linear (Ohmic) relationship between current and potential difference is preserved.