resistivity n : a material's opposition to the flow of electric current; measured in ohms [syn: electric resistance, electrical resistance, impedance, resistance, ohmic resistance]
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.
The electrical resistivity ρ (rho) of a material is given by
Electrical resistivity can also be defined as
Finally, electrical resistivity is also defined as the inverse of the conductivity σ (sigma), of the material, or
- \rho = .
Table of resistivitiesThis table shows the resistivity and temperature coefficient of various materials at 20 °C (68 °F)
Temperature dependenceIn general, electrical resistivity of metals increases with temperature, while the resistivity of semiconductors decreases with increasing temperature. In both cases, electron-phonon interactions 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 \rho(0) 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. \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:
- 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.
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 \ln(\rho) + C (\ln(\rho))^3 \,
where A, B and C are the so-called Steinhart–Hart coefficients.
This equation is used to calibrate thermistors.
In non-crystalline semi-conductors, conduction can occur by charges quantum tunnelling from one localised site to another. This is known as variable range hopping and has the characteristic form of \rho = Ae^, where n=2,3,4 depending on the dimensionality of the system.
Complex resistivityWhen 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 (reactance) http://www.otto-schmitt.org/OttoPagesFinalForm/Sounds/Speeches/MutualImpedivity.htm.
- Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.)
resistivity in Bulgarian: Специфично електрическо съпротивление
resistivity in Catalan: Resistivitat
resistivity in Danish: Elektrisk resistivitet
resistivity in German: Spezifischer Widerstand
resistivity in French: Résistivité
resistivity in Spanish: Resistividad
resistivity in Italian: Resistività elettrica
resistivity in Latvian: Īpatnējā pretestība
resistivity in Macedonian: Електрична отпорност
resistivity in Dutch: Soortelijke weerstand
resistivity in Japanese: 電気抵抗率
resistivity in Polish: Rezystywność
resistivity in Portuguese: Resistividade
resistivity in Romanian: Rezistivitate
resistivity in Slovenian: specifična upornost
resistivity in Finnish: Ominaisvastus
resistivity in Swedish: Resistivitet
resistivity in Ukrainian: Питомий опір