Electrical Resistivity: formula & units

- details of resistivity including resistivity formula / equation and resistivity units used.

Materials naturally have some resistance to the flow of an electric current.

Some materials resist the flow of current more than others, and therefore it is known as the electrical resistivity of the substance.

The term electrical resistivity may also be known as the specific electrical resistance, or volume resistivity in some circumstances.

In addition to this, specific units are used for resistivity, and there are formulae or equations for calculating resistivity.

Resistivity basics

The electrical resistivity of a material is also known as its specific electrical resistance. It is a measure of how strongly a material opposes the flow of electric current.

A definition of resistivity is the electrical resistance per unit length and per unit of cross-sectional area. This is for a particular material at a specified temperature.

It is also possible to define the resistivity of a substance as the resistance of a cube of that substance having edges of unit length, with the understanding that the current flows normal to opposite faces and is distributed uniformly over them. The SI unit for electrical resistivity is the ohm metre, although it is also sometimes specified in ohm centimetres.

This means that a low resistivity indicates a material that readily allows the movement of electrons. Conversely a high resistivity material will have a high electrical resistance and will impede the flow of electrons.

Elements such as copper and aluminium are known for their low levels of resistivity. Silver and in particular, gold have a very low resistivity, but for obvious cost reasons their use is restricted.

Electrical resistivity units

The SI unit of electrical resistivity is the ohm⋅metre (Ω⋅m). It is commonly represented by the Greek letter ρ, rho.

Although the SI resistivity unit, the ohms metre is generally used, sometimes figures will be seen described in terms of ohms centimetres, Ω⋅cm.

Resistivity formula / equation

The resistivity of a material is defined in terms of the magnitude of the electric field across it that gives a certain current density.

Where:
ρ is the resistivity of the material in ohm metres, Ω⋅m
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

Many resistors and conductors have a uniform cross section with a uniform flow of electric current. It is therefore possible to create the more specific, but more widely used equation:

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, m^2

Material resistivity levels

Materials are put into different categories according to their level or resistivity. A summary is given in the table below.

Resistivity Regions for Different Categories of Materials
Material type Resistivity region
Electrolytes
Variable*
Insulators
~10^16
Metals
~10^-8
Semiconductors
Variable*
Superconductors
0

*   The level of conductivity of semiconductors is dependent upon the level of doping. With no doping they appear almost like an insulator, but with doping charge carriers are available and the resistivity falls dramatically. Similarly for electrolytes, the level of resistivity varies widely.

. . . .   |   Next >

Mark Patrick | mouser Electronics
Next Generation Freight Transport
As road freight transport levels continue to grow, concerns about the impact on the environment and human health come sharply into focus. Fossil fuel dependency makes it a leading source of greenhouse gas (GHG) emissions, but shifting freight to other transportation modes will prove challenging. Solutions that will improve the efficiency and performance of road freight transport are therefore essential to achieve defined environmental goals. In this blog, we will explore a potential solution that has been pioneered by Siemens - called eHighway. This combines the efficiency of electrified railways with the flexibility of trucks in order to form an innovative, next generation freight traffic system that is efficient, economical and environmentally friendly.

Channels
Radio-Electronics.com is operated and owned by Adrio Communications Ltd and edited by Ian Poole. All information is © Adrio Communications Ltd and may not be copied except for individual personal use. This includes copying material in whatever form into website pages. While every effort is made to ensure the accuracy of the information on Radio-Electronics.com, no liability is accepted for any consequences of using it. This site uses cookies. By using this site, these terms including the use of cookies are accepted. More explanation can be found in our Privacy Policy