Ride the thermometer from ambient to −190 °C and watch two archetypes diverge: a metal’s resistance falls as phonons freeze out; a semiconductor’s climbs as carriers freeze onto their donors.
Schematic archetypes: metallic R ∝ a + bT (phonon term shrinking on cooling) and a semiconductor with carrier freeze-out R ∝ eE/2kT-like rise — teaching curves with illustrative parameters, not data for any real material. Real R(T) fine structure (transitions, plateaus, hopping curvature) is the science; the measurement craft lives in the electrical chapters.