## Complex conductivity

To analyze 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.^{2}

An alternative description of the response to alternating currents uses a real (but frequency-dependent) conductivity, along with a real permittivity. The larger the conductivity is, the more quickly the alternating-current signal is absorbed by the material (i.e., the more opaque the material is). For details, see Mathematical descriptions of opacity.

## Temperature dependence

Electrical conductivity is 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:

where

*σ*is the electrical conductivity at a common temperature,

_{T'}*T'*

*σ*is the electrical conductivity at a measured temperature,

_{T}*T*

*α*is the temperature compensation slope of the material,

*T*is the measured absolute temperature,

*T'*is the common temperature.

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

At extremely low temperatures (not far from absolute zero K), a few materials have been found to exhibit very high electrical conductivity in a phenomenon called superconductivity.

## See also

## Notes

- ↑
^{1.0}^{1.1}See J. Phys. Chem. B 2005, 109, 1231-1238 In particular page 1235. Note that values in this paper are given in S/cm, not S/m, which differs by a factor of 100. Retrieved September 25, 2008. - ↑ Otto H. Schmitt, Mutual Impedivity Spectrometry and the Feasibility of its Incorporation into Tissue-Diagnostic Anatomical Reconstruction and Multivariate Time-Coherent Physiological Measurements University of Minnesota. Retrieved September 25, 2008.

## References

- Giancoli, Douglas. 2007.
*Physics for Scientists and Engineers, with Modern Physics*(Chapters 1-37), 4th ed. Mastering Physics Series. Upper Saddle River, NJ: Prentice Hall. ISBN 978-0136139263 - Maini, A.K. 1997.
*Electronics and Communications Simplified*, 9th ed. New Delhi: Khanna Publishers. - Plonus, Martin. 2001.
*Electronics and Communications for Scientists and Engineers.*San Diego: Harcourt/Academic Press. ISBN 0125330847 - Tipler, Paul Allen, and Gene Mosca. 2004.
*Physics for Scientists and Engineers, Volume 2: Electricity and Magnetism, Light, Modern Physics*, 5th ed. New York: W.H. Freeman. ISBN 0716708108

## External links

All links retrieved September 18, 2017.

- Measurement of the Electrical Conductivity of Glass Melts Measurement Techniques, Definitions, Electrical conductivity Calculation from the Glass Composition
- Periodic Table of Elements Sorted by Electrical Conductivity