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 <math>\mathbf{J}</math> to the electric field strength <math>\mathbf{E}</math>:

<math>\mathbf{J} = \sigma \mathbf{E}</math>.

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). It is commonly represented by the Greek letter σ, but κ or γ are also occasionally used.

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Classification of materials by conductivity

Scientists often divide materials into three classes based upon their respective conductivities:

  • 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 certain frequencies of light.
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Some typical electrical conductivities

  • Silver: 63.01 · 106 S/m at 20 °C (630,100 S/cm; highest electrical conductivity of any metal)
  • Copper: 59.6 · 106 S/m (20 °C)
  • Aluminium: 37.8 · 106 S/m (20 °C)
  • Sea water: 5 S/m
  • Drinking water: 0.0005 – 0.05 S/m
  • Ultra pure water: 5.5 · 10-6 S/m
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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. [1]

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See also