Introduction

When a very large number of atoms of a metal come together to form a solid, the outermost (valence) electrons of each atom no longer stay bound to their own individual atom. Because the atoms are packed so closely and regularly, the wavefunctions of these outer electrons overlap and the electrons become de-localized -- free to wander through the entire body of the metal rather than orbiting one nucleus. This 'sea' of de-localized electrons is what we call the conduction electrons or free electrons of the metal.

With no potential difference applied across the conductor, these free electrons are in continuous, completely random thermal motion in every direction, so there is no preferred direction of flow and hence no net current. The moment a potential difference (and therefore an electric field) is applied across the two ends of the conductor, every free electron additionally experiences a force from the field. This superimposes a slow, organised drift on top of the electrons' random thermal motion, and it is this collective drift of the free-electron sea that constitutes the electric current in a metallic conductor. The rest of this chapter builds up, quantitatively, exactly how this current is defined, how it is related to the microscopic drift of electrons, how it behaves under Ohm's law, and how resistors, resistivity, and cells combine to control it in a circuit.