# Dictionary Definition

resistivity n : a material's opposition to the
flow of electric current; measured in ohms [syn: electric
resistance, electrical
resistance, impedance, resistance, ohmic
resistance]

# User Contributed Dictionary

## English

### Noun

resistivity- The degree to which a material opposes the flow of electricity or heat.
- The reciprocal of conductivity.

# Extensive Definition

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

The electrical resistivity ρ (rho) of a
material is given by

- \rho=\frac

- ρ is the static resistivity (measured in ohm metres, Ω-m);
- R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω);
- \ell 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

- \rho=

where

- 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

- \rho = .

## Table of resistivities

This table shows the resistivity and temperature coefficient of various materials at 20 °C (68 °F)- 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

## Temperature dependence

In 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:- \rho(T)=\rho(0)+A\left(\frac\right)^n\int_0^\fracdx

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 resistivity

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 (reactance) http://www.otto-schmitt.org/OttoPagesFinalForm/Sounds/Speeches/MutualImpedivity.htm.## Sources

- Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.)

## See also

## External links

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