# What is Electrical Conductivity?

Electrical conductivity is a measurement of how easily a material allows electric current to flow through it. Inversely, electrical resistivity measures how strongly a material resists the flow of electric current. The two properties are exact inverses of each other. Electrical conductivity is denoted by the Greek letter σ and electrical resistivity is denoted by the Greek letter ρ.

Materials are often selected or discarded for applications due to their electrical conductivity when the passage of electrical current is crucial to the functionality of their application. Metals are generally the best conductors of electricity while polymers are the least conductors of electricity. Silver is the best conductor of electricity but it is rarely used for this function due to its scarcity and resultant prohibitive cost.

• What electrical conductivity is
• The measurement of electrical conductivity
• Applications of electrical conductivity
• Future materials and application

A cross-section of an underground electric cable.

## What is electrical conductivity?

Good conductors of electricity are also often good conductors of heat as evident in most metals. The temperature of a material can affect its conductivity in a not so straightforward manner. For materials known as conductors, an increase in temperature generally decreases their conductivity and vice versa. But for insulators, the reverse is the case as an increase in temperature actually increases their conductivity. This relationship between temperature and electrical conductivity is useful in the creation of superconductors. A superconductor is a material that conducts electricity almost perfectly, with virtually no resistance whatsoever. So far, all known superconductors require extremely low temperatures (up to -234oC) to exhibit this property.

The electrical conductivity of a material is given by the formula

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

Where ρ is the resistivity of the material.

Resistivity is measured in ohm·metres (Ω·m), while conductivity is measured in Siemens per metre (S/m), which is the reciprocal of the resistivity unit. The electrical conductivity or resistivity of a material is an immutable property that does not change with respect to the size or shape of the material.

The conductivity of a material varies with temperature, but it can also vary based on an applied magnetic field. So far, we’ve assumed that all materials are homogenous and isotropic; homogenous meaning that the properties of a material are the same regardless of where a sample is taken from, and isotropic meaning that these properties are of the same value regardless of which direction they are measured from. However, this is not always the case, especially for semiconductors, which are special materials that exhibit different conductivities in different directions. Furthermore, conductance and resistance should not be mistaken for conductivity or resistivity, respectively. Although they are related, they are not the same thing and are not interchangeable. Conductance and resistance vary corresponding to the size of the material in question, while conductivity and resistivity do not.

Table 1. Resistivity and Conductivity of common materials at 20°C [1]

 Material Resistivity ρ (Ω.m) at 20 °C Conductivity σ (S/m) at 20 °C Silver 1.59×10−8 6.30×107 Copper 1.68×10−8 5.96×107 Gold 2.44×10−8 4.10×107 Aluminium 2.82×10−8 3.5×107 Calcium 3.36×10−8 2.98×107 Tungsten 5.60×10−8 1.79×107 Zinc 5.90×10−8 1.69×107 Nickel 6.99×10−8 1.43×107 Lithium 9.28×10−8 1.08×107 Iron 1.0×10−7 1.00×107 Platinum 1.06×10−7 9.43×106 Tin 1.09×10−7 9.17×106 Carbon steel -1010 1.43×10−7 Lead 2.2×10−7 4.55×106 Titanium 4.20×10−7 2.38×106 Constantan 4.9×10−7 2.04×106 Stainless steel 6.9×10−7 1.45×106 Mercury 9.8×10−7 1.02×106 Carbon (amorphous) 5×10−4 - 8×10−4 1.25 - 2×103 Carbon (diamond) 1×1012 ~10−13 Silicon 6.40×102 1.56×10−3 Glass 10×1010 - 10×1014 10−11 - 10−15 Hard rubber 1×1013 10−14 Teflon 10×1022 - 10×1024 10−25 - 10−23

## Measurement of electrical conductivity

The two-point and four-point techniques are two of the most common techniques for measuring electrical conductivity [2].

### Two-Point Technique

This method involves passing current (via a voltage source) through a sample (a rectangular bar) of a material. This current is delivered via two copper nodes which are attached to both ends of the bar (hence the name two-point technique). The amount of current that flows through the bar is measured and since the voltage is already known, the resistance is calculated with the formula below

R =\frac{V}{I}

Where R = Resistance in Ω, V = Voltage in volts, and I = Current in amperes.

The conductivity of the bar can be calculated as

\sigma =\frac{l}{Rwh}

Where σ is the conductivity in S/m, R is the measured resistance in Ω, and w, h, and l are the width, height and length of the sample bar, respectively.

### Four-Point Technique

The two-point technique is intrinsically error-prone because the measuring equipment effectively has properties that are also being measured at the same time as the test sample. This means that the measured conductivity of the material is usually lower than it really is. The four-point technique mitigates most of these errors by using a voltmeter connected across a certain length of the sample separately from the ammeter which is connected from the two ends. A current source passes current through the sample and the voltage and current are measured by the voltmeter and ammeter, respectively.

The conductivity of the bar can be calculated as

\sigma =\frac{Il^{1}}{Vwh}

Where σ is the conductivity measured in S/m, I is the current measured by the ammeter in amperes, V is the voltage measured by the voltmeter in volts, l1 is the length between the two points the voltage is measured, w and h are the width and height of the sample bar, respectively.

## Applications and materials

Electrical conductivity finds applications in various industries, ranging from power transmission to electronics. Here are a few examples of common applications of the principle of conductivity [3].

• The overhead power lines that are used to transmit electrical power are usually made of aluminium because it is a very good conductor of electricity. Similarly, most insulators are made of polymer with very low conductivity to protect humans from electrical shocks.
• To avoid ElectroStatic Discharge (ESD), electrically conductive plastics and composites are engineered to dissipate static electricity. This is important in electronics where plastics are used for casing and other applications where an electrostatic discharge may cause the ignition of flammable gas or liquid.
• Electrical conductivity can be used by a sensor to determine the interface between two liquids if they have a considerable difference in conductivity. This can be useful in chemical processing and the manufacture of food and beverages.
• Desalination of seawater use electrical conductivity to monitor how well dissolved ionic solids have been eliminated from the water and thus gives an insight to the completeness of the purification process.

## Future materials and applications

The rarity of certain materials, their costs of production and other factors mean that it is not often that the best material for a certain application, from an electrical conductivity point of view, is always selected. Silver, known as the best metal conductor, would have been perfect for integrated circuit applications as it is inert. Gold, although less conductive, would be better than silver when protection from radiation is important. Diamond, the least conductive material we’ve mentioned so far, may be the only option when high pressures are involved. Lastly, superconductors are near perfect materials but require temperatures close to absolute zero to function. Quantum supercomputers are being designed in a way that would require superconductors, since their calculations rely on precise numbers of electron discharge to operate at their speed and accuracy [4].

Power transmission lines require a combination of materials with both electrical conductivity and electrical resistivity properties.

## Sources

[1] A. Helmenstine, "Table of Electrical Resistivity and Conductivity", [Online] Available from: https://sciencenotes.org/table-of-electrical-resistivity-and-conductivity/, 2019.

[2] Heaney, Michael B. "Electrical Conductivity and Resistivity." Electrical Measurement, Signal Processing, and Displays. Ed. John G. Webster. CRC Press, 2003.

[3] "Theory and Application of Conductivity", Emerson Process Management [Online] Available from: https://www.emerson.com/documents/automation/application-data-sheet-theory-application-of-conductivity-rosemount-en-68442.pdf

[4] G. Maglione, "Exploring the Realm of Conductivity", [Online] Available from: https://ysjournal.com/exploring-the-realm-of-conductivity/

## Fun facts

• There are several factors that affect the electrical conductivity of a material, and these include temperature, impurities, electromagnetic fields, frequency, and crystal structure.
• Out of all insulators, organic molecules display low levels of conductivity as the covalent bonds that hold them together do not allow free electrons and many molecules are stabilised by hydrogen bonding.