# Electrical Conductivity: mho, siemens

### Electrical conductivity and its formulas are often used in electrical and electronic engineering with the units of siemens or mhos.

Unlike resistance that measures the opposition to a flow of electrical current, electrical conductivity or electrical conductance is a measure of how an electrical current moves within a substance.

The higher the electrical conductivity within a material, the greater the current density for a given applied potential difference.

In this way it can be seen that the electrical conductivity or electrical conductance of a substance is a measure of the its ability to conduct electricity.

The electrical conductivity or electrical conductance of a material is important because some substances are required to conduct electricity as well as possible. Wire conductors need to enable the current to flow as easily as possible. Other materials may be required to restrict the flow of current, as in the case of a resistor, and other materials are required not to conduct electricity, as in the case of insulators.

## Electrical conductivity basics

Electrical conductivity is a ratio of the current density to the electric field strength. The higher the value of the conductivity, the lower the resistance it provides to the flow of electric current.

The value of the electrical conductivity depends on the ability for electrons or other charge carriers such as holes to move within the lattice of the material.

Highly conductive materials such as copper allow the free movement of electrons within their molecular lattice. There are free electrons within the lattice.

Materials with a low level of conductivity or conductance have very few free electrons within their structure. Electrons are tightly held within the molecular structure and require a significant level of energy to pull them free.

## Electrical conductivity units: siemens and mho

The electrical conductivity units are siemens per metre, S⋅m-1.

The siemens also used to be referred to as a mho - this is the reciprocal of a an ohm, and this is inferred by spelling ohm backwards.

Conductance is the reciprocal of resistance and one siemens is equal to the reciprocal of one ohm.

The name siemens for the unit of conductance was adopted by the 14th General Conference on Weights and Measures as an SI derived unit in 1971. It was named after Ernst Werner von Siemens.

As with every SI, International System of Units name that is derived from the proper name of a person, the first letter of its symbol is upper case, i.e. in this case the letter "S" denotes a value in siemens, 10S. When an SI unit full name is spelled out in English, it should always begin with a lower case letter, i.e. in this case siemens. The exception to this is where any word would be capitalised, as in the case of the beginning of a sentence, etc.

The symbol that is most commonly used is the lower case version of the Greek letter sigma, σ, although but kappa, &kappa, gamma, &gamma, are also used on occasions.

Although the SI units for conductivity are most widely used, conductivity values are often stated in terms of their IACS percentage value. The IACS, International Annealed Copper Standard, was established by the 1913 International Electrochemical Commission.

The conductivity of the annealed copper (5.8001 x 107S/m) is defined to be 100% IACS at 20°C.

All other conductivity values are related back to this conductivity value. This means that iron with a conductivity value of 1.04 x 107 S/m, has a conductivity of approximately 18% of that of annealed copper and this is given as 18% IACS.

As metallic processing methods have improved since the introduction of the standard, some modern copper products now often have IACS conductivity values greater than 100% IACS because more impurities can now be removed from the metal.

## Electrical conductivity formulas

Resistivity and conductivity are interrelated. Conductivity is the inverse of resistivity. Accordingly it is easy to express one in terms of the other.

$\sigma =\frac{1}{\rho }$

Where:
σ is the conductivity of the material in siemens per metre, S⋅m-1
ρ is the resistivity of the material in ohm metres, Ω⋅m

This can then be substituted into the formula for resistivity to give the following relationship.

$\sigma =\frac{J}{E}$

Where:
σ is the conductivity of the material in siemens per metre, S⋅m-1
E is the magnitude of the electric field in volts per metre, V⋅m-1
J is the magnitude of the current density in amperes per square metre, A⋅m-2

Often it is necessary to relate the conductivity to a specific length of material with a constant cross sectional area..

Using this diagram, it is possible to relate the conductivity to the resistance, length and cross sectional area of the specimen in the conductivity formula below.

$\sigma =\frac{Rl}{A}$

$R=\frac{\sigma A}{l}$

Where:
R is the electrical resistance of a uniform specimen of the material measured in ohms
l is the length of the piece of material measured in metres, m
A is the cross-sectional area of the specimen measured in square metres, m2

Using these electrical conductivity formulas it is possible to calculate the conductivity from a knowledge of the resistance, length and cross sectional area of a block of a material.

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