Resistivity
Electricity and Magnetism

# Resistivity, electrical

Glossary Definition for 16-19 ## Description

The electrical resistivity of a material is an intrinsic, bulk property that determines the electrical resistance of a sample of that material given the sample’s physical dimensions.

Resistivity is usually represented by the symbol ρ . Resistivity is defined by the equation

ρ = RAL

where R is the resistance of a piece of material of length L and cross-sectional area A, as shown in figure 1. Figure 1: A sample of material of length L and cross-sectional area A.

## Discussion

The resistance of a sample, such as a wire, depends on its physical dimensions and the resistivity of the material from which it is made. The resistivity depends in detail on the nature and crystal structure of the material and, in general, depends strongly on temperature; the resistivity of a metal, such as copper or silver, increases roughly linearly with temperature around room temperature. The resistivity at lower temperatures is strongly dependent on the purity of the metal. Resistors made from platinum and other easily purified metals are often used as thermometers. The resistivity of most non-metals decreases as temperature rises.

Resistivity has an enormous range of values. It is common to refer to materials with low values of ρ as conductors and those with high values as insulators. Semiconductor materials are insulators in their pure state but their electrical resistivity may be greatly reduced by the addition of a relatively small amount of impurity. Different amounts of different impurities can be used to produce semiconductors with particular electrical properties (for example, resistivity that changes in response to external conditions such as temperature or illumination); this is one of the main reasons why semiconductors are so important in the electronics industry.

Resistivity is the reciprocal of electrical conductivity.

ohm-metre, Ωm

m3 kg s-3 A-2

## Mathematical expressions

• ρ = RAL

where R is the resistance of a piece of material of length L and cross-sectional area A
• ρ = 1σ

where σ is the electrical conductivity of the material.

## Related entries

• Conductivity, electrical
• Resistance, electrical

## In context

Electrical resistivity has a huge range of values for everyday materials. The resistivity at room temperature for a good conductor such as silver is around 22 orders of magnitude lower than that of a good insulator such as rubber. The resistivity of silver at room temperature is about 1.6 × 10-8 Ωm, whereas that of rubber is of the order 1013–1015 Ωm.

###### Resistivity
appears in the relation R=ρL/A σ=1/ρ