# Electrical Resistivity; definition, formula & units

### Electrical resistivity is a key parameter for any material used in electrical circuits.

Resistivity is a measure of the resistance of a given size of a specific material to electrical conduction.

Although materials resist the flow of electrical current, some are better at conducting it than others.The resistivity is a figure that enables comparisons of the way in which different materials allow or resist current flow.

To enable resistivity figures to be meaningful, specific units are used for resistivity, and there are formulas for calculating it and relating it to the resistance in Ohms for a given size of material.

Materials that conduct electrical current easily are called conductors and have a low resistivity. Those that do not conduct electricity easily are called insulators and these materials have a high resistivity.

## Resistivity definition & units

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

#### Resistivity definition:

The resistivity of a substance is 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 electrical resistivity is the electrical resistance per unit length and per unit of cross-sectional area at a specified temperature.

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. It is possible to devise an electrical resistivity formula.

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

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 electrical resistivity formula or equation:

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

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, 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.

Electrical resistivity is a key parameter for material that are to be used with electrical and electronic systems. Those substances with a high electrical resistivity are termed insulators and can be used for this purpose. This with a low level of electrical resistivity are good conductors and can be used in a host of applications from wire, to electrical connections and much more.

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