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Encyclopedia > Resistivity

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. This box:      Electric current is the flow (movement) of electric charge. ... Electric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... A multimeter can be used to measure resistance in ohms. ... This article is about the unit of length. ...

## Contents

A piece of resistive material with electrical contacts on both ends.

The electrical resistivity ρ (rho) of a material is given by Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Look up Î¡, Ï in Wiktionary, the free dictionary. ...

$rho=Rfrac{A}{ell}$

where

ρ is the static resistivity (measured in ohm-metres, Ωm);
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 Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... A multimeter can be used to measure resistance in ohms. ... This article is about the unit of length. ...

$rho={E over J}$

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 The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... Josephson junction array chip developed by NIST as a standard volt. ... This article is about the unit of length. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... For other uses, see Ampere (disambiguation). ... A square metre (US spelling: square meter) is by definition the area enclosed by a square with sides each 1 metre long. ... Not to be confused with electrical conductance, a measure of an objects or circuits ability to conduct an electric current between two points, which is dependent on the electrical conductivity and the geometric dimensions of the conducting object. ... Sigma (upper case &#931;, lower case &#963;, alternative &#962;) is the 18th letter of the Greek alphabet. ...

$rho = {1oversigma}.$

## Table of resistivities

This table shows the resistivity and temperature coefficient of various materials. The values are correct at 20 °C (68 °F) The temperature coefficient is the relative change of a physical property when the temperature is changed by 1 K (kelvin). ... For other uses, see Celsius (disambiguation). ... For other uses, see Fahrenheit (disambiguation). ...

Material Resistivity (Ωm) Coefficient*
Silver[1] 1.59×10−8 .0038
Copper[1] 1.7×10−8 .0039
Gold[1] 2.44×10−8 .0034
Aluminium[1] 2.82×10−8 .0039
Tungsten[1] 5.6×10−8 .0045
Brass[2] 0.8×10−7 .0015
Iron[1] 1.0×10−7 .005
Platinum[1] 1.1×10−7 .00392
Manganin[3] 4.82×10−7 .000002
Constantan[3] 4.9×10−7
Mercury[3] 9.8×10−7 .0009
Nichrome[1][4] 1.10×10−6 .0004
Carbon[1][5] 3.5×10−5 -.0005
Germanium[1][5] 4.6×10−1 -.048
Silicon[1][5] 6.40×102 -.075
Glass[1] 1010 to 1014 ?
Hard rubber[1] approx. 1013 ?
Sulfur[1] 1015 ?
Paraffin 1017 ?
Quartz (fused)[1] 7.5×1017 ?
PET 1020 ?
Teflon 1022 to 1024 ?

## 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-Gruneissen formula : This article is about metallic materials. ... For other uses, see Temperature (disambiguation). ... A semiconductor is a solid whose electrical conductivity is in between that of a conductor and that of an insulator, and can be controlled over a wide range, either permanently or dynamically. ... Normal modes of vibration progression through a crystal. ...

$rho(T)=rho(0)+Aleft(frac{T}{Theta_R}right)^nint_0^{frac{Theta_R}{T}}frac{x^n}{(e^x-1)(1-e^{-x})}dx$

where ρ(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. ΘR 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. Normal modes of vibration progression through a crystal. ... A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. ...

An even better approximation of the temperature dependence of the resistivity of a semiconductor is given by the Steinhart-Hart equation: The Steinhart-Hart equation is a model of the resistivity of a semiconductor at different temperatures. ...

$1/T = A + B ln(rho) + C (ln(rho))^3 ,$

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

This equation is used to calibrate thermistors. NTC thermistor, bead type, insulated wires Thermistor symbol A thermistor is a type of resistor used to measure temperature changes, relying on the change in its resistance with changing temperature. ...

## Complex resistivity

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 impeditivity, in analogy to electrical impedance. Impeditivity is the sum of a real component, the resistivity, and an imaginary component, the reactivity (reactance) [1]. In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... Tomography is imaging by sections or sectioning. ... In mathematics, a complex number is a number which is often formally defined to consist of an ordered pair of real numbers , often written: In mathematics, the adjective complex means that the underlying number field is complex numbers, for example complex analysis, complex matrix, complex polynomial and complex Lie algebra. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... It has been suggested that Electric reactance be merged into this article or section. ...

## Sources

1. ^ a b c d e f g h i j k l m n o p Serway, Raymond A. (1998). Principles of Physics, 2nd ed, Fort Worth, Texas; London: Saunders College Pub, p602. ISBN 0-03-020457-7.
2. ^ Cite error 8; No text given.
3. ^ a b c Giancoli, Douglas C. (1995). Physics: principles with applications, 4th ed, London: Prentice Hall. ISBN 0-13-102153-2.
4. ^ Ni,Fe,Cr alloy commonly used in heating elements.
5. ^ a b c The resistivity of semiconductors depends strongly on the presence of impurities in the material.
• Paul Tipler (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.

A semiconductor is a material that is an insulator at very low temperature, but which has a sizable electrical conductivity at room temperature. ... Impurities are substances inside a confined amount of liquid, gas, or solid, which differ from the chemical composition of the material or compound. ...

Not to be confused with electrical conductance, a measure of an objects or circuits ability to conduct an electric current between two points, which is dependent on the electrical conductivity and the geometric dimensions of the conducting object. ... Electrical resistivity imaging is a geophysical method of subsurface investigation that uses multiple measurements of electrical resistivity, configured in an array. ... ... This article or section does not cite any references or sources. ...

Results from FactBites:

 The T.W.I.N.K.I.E.S. Resistivity Test (0 words) To test the resistivity of a Twinkie, a 110V standard AC household current was run across it. After verifying that power was being supplied to the Twinkie, we concluded that the resistivity of the Twinkie must be so high that not enough current was passing through to cause any noticeable change. A quick measurement with a Digital Multimeter (DMM) confirmed that the resistivity was beyond the DMM's range.
 Resistance (912 words) The resistance to the flow of charge in an electric circuit is analogous to the frictional effects between water and the pipe surfaces as well as the resistance offered by obstacles which are present in its path. A third variable which is known to effect the resistance to charge flow is the material that a wire is made of. Consistent with the discussion above, this equation shows that the resistance of a wire is directly proportional to the length of the wire and inversely proportional to the cross-sectional area of the wire.
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