Electrical resistivity and conductivity

Electrical conductivity, also known as conductivity or EC value, is a physical quantity that indicates how strong the ability of a substance is to conduct the electric current.

The formula symbol of the electrical conductivity is σ (Greek sigma), also γ (gamma), in electrochemistry κ (kappa). The derived SI unit of electrical conductivity is S/m (Siemens per meter). The reciprocal of electrical conductivity is called resistivity.

The electric conductivity is defined as the constant of proportionality between the current density and the electric field strength :

In the special case of constant electrical conductivity, this definition equation corresponds to Ohm's law.

Conductivity as tensor

In the special case of an isotropic (direction-independent) and linear (field size-independent) medium, the electrical conductivity is a scalar (one-dimensional value). Only in this simple, but in application frequent case, therefore, the current conduction occurs proportionally and in the same direction as the electric field causing the current density.

In an anisotropic and linear material, the electrical conductivity is a 2nd level tensor (dyad), i.e. a multidimensional value. Examples of materials with such properties are materials with structures such as graphite, crystals and high-temperature superconductors.

Contexts and units

It should be noted that the above equation - which is one of the three fundamental material equations - cannot be derived from Maxwell's equations. Maxwell's equations with the continuity laws and the material equations represent the foundation of the non-relativistic electrodynamic field theory.

The conductance as the reciprocal of the resistivity is a property of a body. The conductivity σ as the reciprocal of the resistivity is a property of a material. and σ are related to each other by a factor resulting from the geometrical structure of the body.

Note: The basic standards such as DIN 1304, DIN EN 80000-6, IEC 60050 or IEV use the term "conductivity" or "electrical conductivity", but an addition "specific" does not occur there in connection with conductivity. The dependence on the respective material is already inherent in the definition of the term.

The derived SI unit of electrical conductivity is S/m (Siemens per meter). Also commonly used are S/cm, m/(Ω-mm2) and S-m/mm2, where the relationships 1 S/cm = 100 S/m and 1 m/(Ω-mm2) = 1 S-m/mm2 = ^{106 S/m} apply.

Another unit that is particularly common in the USA is IACS, which stands for International Annealed Copper Standard. Here, the conductivity is expressed in relation to the conductivity in pure annealed copper: 100 % IACS = 58 - ¹⁰⁶ S/m.