# Electrical conductivity

the electrical conductivity (symbol [itex] \ sigma< /math>) is physical dimension, which indicates the ability of a material to lead electric current. It is defined as the proportionality constant between the current density [itex] \ vec j< /math> and the electrical field strength< math> \ vec E< /math> inthe general form of the Ohm's law

< math> \ vec j= \ sigma \ vec E< /math>.

Generally case is the electrical conductivity therefore a tensor 2. Stage, thus a square matrix. Since however in many cases the Stromleitung takes place parallel to the electrical field,been sufficient usually the indication as scalar size.

The electrical conductivity is with the specific electrical resistance [itex] \ rho< /math> over the formula

< math> \ sigma= \ frac {1} {\ rho}< /math>

linked. Following the fact that the conductance is the reciprocal value of the resistance, it becomesthe electrical conductivity often specific conductance mentioned.

## symbols and units

the symbol of the electricalConductivity is the Greek letter [itex] \ sigma< /math> (sigma). Further frequently used symbols for the electrical conductivity are [itex] \ kappa< /math> (kappa) and [itex] \ gamma< /math> (gamma).

The derived SI-UNIT of the electrical conductivity is S/m (Siemens per meter).Very common are besides S/cm and m/Ω*mm ², whereby the connections 1 S/cm = for 100 apply S/m and 1 m/Ω*mm ² = 10 6 S/m. A further particularly unit common in the USA is % IACS. Here the conductivity becomes as percentagethe conductivity of pure glowed copper expressed (so-called internationally Annealed copilot by standard). 100% IACS correspond to 58 MS/m.

## materials with different electrical conductivity

after the electrical conductivity one divides materials into

typical values(with 25°C):
• Silver: 62 · 10 6 S/m (highest electrical conductivity of all metals)
• sea waters: ~ 5 S/m
• tap water: ~ 0.05 S/m
• pure water: 5 · 10 -6 S/m (often also already nonconductor one calls)
typically < 10,-10 S/m.
with semiconductors depends the conductivity on factors, like temperature, pressure or exposure. The conductivity lies in the range between leadersand insulators.
below a material-dependent transition temperature is the conductivity quasi “infinitely”, the electrical resistance disappears completely.

## why is a material electrically conductive?

The conductivitya material or a material mixture depends on the availability on mobile charge carriers. Loosely bound electrons, as for example in metals, can do this in addition, in organic molecules with delokalisierten electrons (frequently by mesomere border structures to be described) or ions to be.

Aqueous solutions are characterised by a small conductivity. It rises, if the water ions, salts, acids or Basen are thus added. Accordingly sea water has a higher electrical conductivity than fresh water. Pure water (distilled or demineralized) hasan extremely small conductivity.

In semiconductors one uses purposeful impurities, in order to affect the conductivity (doping). They n-are endowed, p-endowed by electron donors by elements, which have less than four outer electrons. From the P doping electron defects , also holes resultcalled, those the conductivity likewise increase like surplus electrons in n-endowed semiconductors.

A model for the illustration and explanation of the conductivity of a crystal is given by the band model.

## examples

of metals specific conductivity (in 10 6 S/m)
silver 61,7
Copper 56.0
gold 47.6
aluminum 37.8
tungsten 18.2
platinum 10.2
iron 10.0
semiconductors specific conductivity (in S/m)
germanium 1.45
silicon 2,52 · 10 -4