resistanceversustemperature

Resistance versus temperature refers to how the electrical resistance of a material changes as its temperature changes. The relationship is usually described by the resistivity ρ(T) or the resistance R(T) of a sample, and is summarized by the temperature coefficient of resistance (TCR), α, defined at a reference temperature T0 as α = (1/R0) dR/dT.

Metals typically have a positive TCR: resistance increases with temperature because lattice vibrations scatter conduction electrons more strongly. Over a limited range, the dependence is often approximated as R ≈ R0 [1 + α (T − T0)]. Typical α values are a few ×10^−3 per degree Celsius. Platinum, for example, has a well-characterized positive TCR around 0.00385 per degree Celsius and is used in many precision resistance thermometers.

Semiconductors often exhibit the opposite trend in ordinary temperature ranges: resistance decreases with increasing temperature. This occurs because increasing temperature raises the intrinsic carrier concentration, greatly enhancing conductivity, though mobility can decrease with temperature. The overall temperature dependence is nonlinear and strongly material- and temperature-range dependent. In intrinsic semiconductors, resistivity falls roughly as ρ ∝ exp(Eg/2kT). Doped semiconductors may show either behavior depending on temperature and doping level. Thermistors exploit these effects: NTC thermistors have negative TCR (resistance falls with temperature), while PTC thermistors have positive TCR.

Practical devices include resistance temperature detectors (RTDs), which use metals with stable positive TCR (e.g., Pt100), and thermistors, chosen for steep TCR in specific ranges. Measurement methods such as four-point resistance or Wheatstone bridge configurations improve accuracy by reducing contact and lead effects. In superconductors, resistance drops to zero below a critical temperature, representing a distinct temperature-dependent phenomenon.