Electrical resistance of a conductor of unit cross-sectional area and unit length. The resistivity of a conductor depends on its composition and its temperature. As a characteristic property of each material, resistivity is useful in comparing various materials on the basis of their ability to conduct electric current. As temperature increases, the resistivity of a metallic conductor usually increases and that of a semiconductor usually decreases.
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The electrical resistivity ρ (rho) of a material is given by
Electrical resistivity can also be defined as
|Material||Resistivity (Ω-m) at 20 °C||Coefficient*||Reference|
|Glass||1010 to 1014||?|
|Hard rubber||approx. 1013||?|
|Teflon||1022 to 1024||?|
*The numbers in this column increase or decrease the significand portion 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
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:
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:
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 , where n=2,3,4 depending on the dimensionality of the system.
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.
|Material||Resistivity (nΩ·m)||Density (g/cm^3)||Resistivity - density product (nΩ·m·g/cm^3)|
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