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# Electrical resistivity

Electrical resistivity (also known as specific electrical resistance) is a measure indicating how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electrons. The SI unit for electrical resistivity is the ohm metre.

The electrical resistivity of a material is usually given by :

$\rho={{RA}\over l}$

where

ρ is the electrical resistivity (measured in ohm metres)
R is the resistance of a uniform specimen of the material (measured in ohms)
l is the length of the specimen (measured in metres)
A is the cross-sectional area of the specimen (measured in square metres)

Electrical resistivity can also be defined as:

$\rho={E \over J}$

where

E is the magnitude of the electric field (measured in volts per metre)
J is the magnitude of the current density (measured in amperes per square metre)

Finally, Electrical resistivity is also defined as the inverse of the conductivity of the metal, or:

$\rho = {1 \over \sigma}$

where σ is the conductivity of the substance

In general, electrical resistivity of metals increases with temperature, while the resistivity of semiconductors decreases with temperature. As the temperature of a metal is reduced, the resistance usually reduces until it reaches a constant value, known as the residual resistivity. This value depends not only on the type of metal, but on its purity and thermal history. Some materials lose all electrical resistivity at sufficiently low temperatures, due to an effect known as superconductivity.

The reciprocal quantity is electrical conductivity.

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## Typical values

Typical resistivities for various materials (at 20 °C; 10-6 Ωm equals Ω·mm²/m) are shown in the table below:

 Material Resistivity (ohm metres) Silver 0.0159 × 10-6 Copper 0.017 × 10-6 Gold 0.0244 × 10-6 Aluminium 0.0282 × 10-6 Tungsten 0.056 × 10-6 Iron 0.1 × 10-6 Steel, Stainless 0.72 × 10-6 Platinum 0.11 × 10-6 Lead 0.22 × 10-6 Nichrome (A nickel-chromium alloy commonly used in heating elements) 1.50 × 10-6 Carbon 35 × 10-6 Germanium 0.46 Silicon 640 Glass 1010 to 1014 Hard rubber approximately 1013 Sulfur 1015 Quartz (fused) 75 × 1016 Human skin approximately 5.0 × 105

## Temperature dependence

• The electric resistivity of a typical metal conductor increases linearly with the temperature.
• The electric resistivity of a typical semiconductor decreases exponentially with the temperature.

An even better approximation of the temperature dependence of the resistivity of a semiconductor is given by the Steinhardt-Hart equation:

$1/T = A + B \ln(R) + C (\ln(R))^3 \,$

where A, B and C are the so-called Steinhardt coefficients.

This equation is used to calibrate thermistors.