Electrical conductivity

Electrical conductivity is a measure of a material's ability to conduct an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current. The conductivity σ is defined as the ratio of the current density $\mathbf{J}$ to the electric field strength $\mathbf{E}$ :

\mathbf{J} = \sigma \mathbf{E}

. It is also possible to have materials in which the conductivity is anisotropic, in which case σ is a 3×3 matrix (or more technically a rank-2 tensor) which is generally symmetric.

Conductivity is the reciprocal (inverse) of electrical resistivity, and has the SI units of siemens per metre (S·m^-1). It is commonly represented by the Greek letter σ, but κ or γ are also occasionally used.

Classification of materials by conductivity

A conductor such as a metal has high conductivity.
An insulator like glass or a vacuum has low conductivity.
The conductivity of a semiconductor is generally intermediate, but varies widely under different conditions, such as exposure of the material to electric fields or specific frequencies of light.

Some typical electrical conductivities

	Electrical Conductivity (S·m^-1)	Temperature(°C)	Notes
Silver	63.01 × 10⁶	20	Highest electrical conductivity of any metal
Copper	59.6 × 10⁶	20
Annealed Copper	58.0 × 10⁶	20	Referred to as 100 %IACS or International Annealed Copper Standard. The unit for expressing the conductivity of nonmagnetic materials by testing using the eddy-current method. Generally used for temper and alloy verification of Aluminum.
Aluminium	37.8 × 10⁶	20
Sea water	5
Drinking water	0.0005 to 0.05
Deionized water	5.5 × 10^-6		changes to 1.2 × 10^-4 in degassed water; see J. Phys. Chem. B 2005, 109, 1231-1238

Complex conductivity

To analyse the conductivity of materials exposed to alternating electric fields, it is necessary to treat conductivity as a complex number (or as a matrix of complex numbers, in the case of anisotropic materials mentioned above) called the admittivity. This method is used in applications such as electrical impedance tomography, a type of industrial and medical imaging. Admittivity is the sum of a real component called the conductivity and an imaginary component called the susceptivity. ^*

Temperature dependence

Electrical conductivity is more or less strongly dependent on temperature. In metals, electrical conductivity decreases with increasing temperature, whereas in semiconductors, electrical conductivity increases with increasing temperature. Over a limited temperature range, the electrical conductivity can be approximated as being directly proportional to temperature. In order to compare electrical conductivity measurements at different temperatures, they need to be standardized to a common temperature. This dependence is often expressed as a slope in the conductivity-vs-temperature graph, and can be used:

\sigma_{T'} = {\sigma_T \over 1 + \alpha (T - T')}

where

σ_T′ is the electrical conductivity at a common temperature, T′

σ_T is the electrical conductivity at a measured temperature, T

α is the temperature compensation slope of the material,

T is the measured temperature,

T′ is the common temperature.

The temperature compensation slope for most naturally occurring waters is about 2 %/°C, however it can range between (1 to 3) %/°C. This slope is influenced by the geochemistry, and can be easily determined in a laboratory.

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Classification of materials by conductivity

Some typical electrical conductivities

Complex conductivity

Temperature dependence

See also