Current in a vacuum and resistance of metals

In metals, when the temperature rises the lattice ions vibrate more, electrons collide with them more often, the drift speed and current fall – the resistance rises. Experiment: if an iron coil in series with a lamp is heated, the lamp glows more dimly. The relation is R = R₀(1 + αΔt), ρ = ρ₀(1 + αΔt), where R₀, ρ₀ are the values at 0 °C and α is the temperature coefficient of resistance (about 0.004 °C⁻¹ for pure metals; very small, ≈ 0.0002 °C⁻¹, for nichrome). This is used in resistance thermometers (platinum: high precision, very wide range). At very low temperatures the resistance of some substances drops abruptly to zero at a critical temperature – superconductivity (H. Kamerlingh Onnes, 1911, mercury ≈ 4.2 K). In such a conductor a current can flow for a long time without a source. The theory of the phenomenon was created in 1957 (Bardeen, Cooper, Schrieffer; N. Bogolyubov also contributed), and since 1986–1987 materials with much higher critical temperatures (≈ 90 K and above, i.e. above the temperature of liquid nitrogen) have been found. Uses: strong magnets (MRI scanners, accelerators) and low-loss power transmission.