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 SIunit of electrical resistivity is the ohm meter.
The electrical resistivity ρ ("rho") of a material is given by
:"ρ" is the static resistivity (measured in ohm metres, Ω-m);:"R" is the
electrical resistanceof a uniform specimen of the material (measured in ohms, Ω);:"" 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, m²).
Electrical resistivity can also be defined as
:"E" is the magnitude of the
electric field(measured in volts per metre, V/m);:"J" is the magnitude of the current density(measured in amperes per square metre, A/m²).
Finally, electrical resistivity is also defined as the inverse of the conductivity "σ" ("sigma"), of the material, or
Table of resistivities
*The numbers in this column increase or decrease the significandportion of the resistivity. For example, at 30°C (303.15 K), the resistivity of silver is 1.65×10−8. This is calculated as Δρ = α ΔT ρo where ρo is the resistivity at 20°C and α is the temperature coefficient
In general, electrical resistivity of
metals increases with temperature, while the resistivity of semiconductors decreases with increasing temperature. In both cases, electron- phononinteractions can play a key role. At high temperatures, the resistance of a metal increases linearly with temperature. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature. Mathematically the temperature dependence of the resistivity ρ of a metal is given by the Bloch–Grüneisen formula:
where is the residual resistivity 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. 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:
#n=5 implies that the resistance is due to scattering of electrons by
phonons (as it is for simple metals)
#n=3 implies that the resistance is due to s-d electron scattering (as is the case for transition metals)
#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
An even better approximation of the temperature dependence of the resistivity of a semiconductor is given by the
where "A", "B" and "C" are the so-called Steinhart–Hart coefficients.
This equation is used to calibrate
In non-crystalline semi-conductors, conduction can occur by charges
quantum tunnellingfrom one localised site to another. This is known as variable range hoppingand has the characteristic form of , where n=2,3,4 depending on the dimensionality of the system.
When analyzing 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 impeditivity (in analogy to electrical impedance). Impeditivity is the sum of a real component, the resistivity, and an imaginary component, the reactivity (in analogy to reactance) [http://www.otto-schmitt.org/OttoPagesFinalForm/Sounds/Speeches/MutualImpedivity.htm] .
Resistivity density products
In some applications where the weight of an item is very important resistivity density products are more important than absolute low resistance- it is often possible to make the conductor thicker to make up for a higher resistivity; and then a low resistivity density product material (or equivalently a high conductance to density ratio) is desirable.
This fact is used for long distance overhead powerline transmission- aluminium is used rather than copper because it is lighter for the same conductance. Calcium, with a resistivity density product lower than aluminium, is rarely if ever used due to its highly reactive nature.
*cite book | author= Paul Tipler| title=Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.) | publisher=W. H. Freeman | year=2004 | id=ISBN 0-7167-0810-8
Electrical resistivity imaging
SI electromagnetism units
Electrical resistivities of the elements (data page)
* [http://www.reuters.com/article/environmentNews/idUSN2041399820080320?rpc=64&pageNumber=1&virtualBrandChannel=10150 New nanomaterial better efficient conductor]
* [http://www.ee.byu.edu/cleanroom/ResistivityCal.phtml/ Resistivity & Mobility Calculator/Graph from BYU cleanroom]
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