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.

Basic concept of electrical resistivity

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.

Resistivity rho = ( E the magnitude of the electric field in volts per metre, V⋅m^-1) / (J the magnitude of the current density in amperes per square metre, A⋅m^-2)

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.


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