For metals: R = (1 + alpha*), where alpha ~ 3-5 x 10^(-3) /K. Resistance increases with T because lattice vibrations increase, reducing relaxation time tau. For semiconductors and insulators: resistance decreases with T because more carriers are thermally excited across the band gap. Superconductors: R drops to exactly zero below the critical temperature . Carbon (graphite) has negative temperature coefficient (resistance decreases with T). Alloys like manganin and constantan have very small alpha — used in standard resistors. At absolute zero, pure metals have very low but non-zero resistance (due to impurities); superconductors have exactly zero.
Part of JES-03 — Current Electricity: Ohm's Law, Kirchhoff's & Circuits
Temperature Dependence of Resistance
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