Electrical resistivity

Resistivity (short for electrical resistivity or resistivity) is a temperature-dependent material constant with the formula sign ρ \rho (Greek rho). It is mainly used to calculate the electrical resistance of a (homogeneous) electrical conductor or a resistive geometry. Most often, resistivity is given in units of Ω {\displaystyle \mathrm {\tfrac {\Omega \cdot mm^{2}}{m}} }given. The SI coherent unit is Ω {\displaystyle \Omega \cdot \mathrm {m} }.

The reciprocal of the resistivity is the electrical conductivity.

Cause and temperature dependence

Responsible for the specific electrical resistance in pure metals are two components which overlap according to Matthiessen's rule:

  • collisions of charge carriers (here electrons) with lattice vibrations (phonons); this part depends on the temperature, and
  • Collisions of the charge carriers (here electrons) with impurities, defects and lattice defects; this fraction does not depend on the temperature, but on the concentration of the lattice defects.

The temperature-dependent portion of the resistivity is approximately linear for all conductors in a respective limited temperature range:

\rho (T)=\rho (T_{0})\cdot (1+\alpha \cdot (T-T_{0}))

where α is the temperature coefficient, T is the temperature, and T0 is any temperature, e.g., T0 = 293.15 K = 20 °C, at which the electrical resistivity ρ(T0) is known (see table below).

Depending on the sign of the linear temperature coefficient, a distinction is made between positive temperature coefficient of resistance (PTC) and negative temperature coefficient of resistance (NTC). The linear temperature dependence only applies within a limited temperature interval. This can be comparatively large for pure metals. Beyond this, corrections must be applied (see also: Kondo effect).

Pure metals have a positive temperature coefficient of the specific electrical resistance of about 0.36 %/K to over 0.6 %/K. In the case of platinum (0.385 %/K), this is used to build platinum resistance thermometers.

The specific electrical resistance of alloys is only slightly dependent on temperature; here the proportion of impurities is predominant. This is used, for example, with constantan or manganin to obtain a particularly low temperature coefficient or a temperature-stable resistance value.

Tensor resistivity

For most materials, the electrical resistance is independent of direction (isotropic). A simple scalar quantity, i.e. a number with a unit, is then sufficient for the resistivity.

Anisotropy in electrical resistivity is found in single crystals (or multicrystals with preferred direction) with less than cubic symmetry. Most metals have a cubic crystal structure and are therefore isotropic. In addition, one often has a many-crystalline form with no distinct preferred direction (texture). An example of anisotropic resistivity is graphite as a single crystal or with preferred direction. The resistivity is then a 2nd level tensor relating the electric field strength {\vec E}to the electric current density . {\vec j}

{\vec E}=\rho \cdot {\vec j}


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