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

Definitions

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The electrical resistivity ρ (rho) of a material is usually defined by the following:

$\backslash rho=\backslash frac\{x^n\}\{(e^x-1)(1-e^\{-x\})\}dx$

where $\backslash rho(0)$ is the residual resistance due to defect scattering, A is a constant that depends on the velocity of electrons at the fermi surface, the Debye radius and the number density of electrons in the metal. $\backslash Theta\_R$ is the Debye temperature as obtained from resistivity measurements and matches very closely with the values of Debye temperature obtained from specific heat measurements. n is an integer that depends upon the nature of interaction:

1. n=5 implies that the resistance is due to scattering of electrons by phonons (as it is for simple metals)
2. n=3 implies that the resistance is due to s-d electron scattering (as is the case for transition metals)
3. n=2 implies that the resistance is due to electron-electron interaction.

As the temperature of the metal is sufficiently reduced (so as to 'freeze' all the phonons), the resistivity usually 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. The value of the residual resistivity of a metal is decided by its impurity concentration. Some materials lose all electrical resistivity at sufficiently low temperatures, due to an effect known as superconductivity.

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

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

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

This equation is used to calibrate thermistors.

Complex resistivity

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When analysing the response of materials to alternating electric fields, as is done in certain types of tomography, it is necessary to replace resistivity with a complex quantity called impedivity, in analogy to impedance. Impedivity is the sum of a real component, the resistivity, and an imaginary component, the reactivity (reactance) ^*.

Sources

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See also

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• electrical conductivity
• SI electromagnetism units

External links

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• http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Sensors/TempR.html

Electronics | Physical quantity | Materials science

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