Electrical resistivity (also known as specific electrical resistance) is a measure of how strongly a material opposes the flow of electric current. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. A low resistivity indicates a material that readily allows the movement of electrical charge. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. The SI unit of electrical resistivity is the ohm metre. The ohm (symbol Ω) is the SI unit of Electrical impedance or in the Direct current case Electrical resistance, The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International

Definitions

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

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

where

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);

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). Rho (uppercase Ρ, lowercase ρ or ϱ) is the 17th letter of the Greek alphabet. Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is The ohm (symbol Ω) is the SI unit of Electrical impedance or in the Direct current case Electrical resistance, The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International

Electrical resistivity can also be defined as

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). 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 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 (that can The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International Current density is a measure of the Density of flow of a conserved charge. The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second M^2 redirects here For other uses see M². CM2 redirects here

Finally, electrical resistivity is also defined as the inverse of the conductivity σ (sigma), of the material, or

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. Uses PET can be semi-rigid to rigid depending on its thickness and is very lightweight In Chemistry, poly(tetrafluoroethene or poly(tetrafluoroethylene ( PTFE) is a synthetic Fluoropolymer which finds numerous applications The significand (also Coefficient or Mantissa) is the part of a floating-point number that contains its significant digits For example, at 30°C (303. 15 K), the resistivity of silver is 1. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic 65×10⁻⁸. This is calculated as Δρ = α ΔT ρ_o where ρ_o 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. The M acro E xpansion T emplate A ttribute L anguage complements TAL, providing macros which allow the reuse of code across Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that In both cases, electron-phonon interactions can play a key role. In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid 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 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. Θ_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:

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. In Physics, a phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the Atomic lattice of a Solid

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. Superconductivity is a phenomenon occurring in certain Materials generally at very low Temperatures characterized by exactly zero electrical resistance

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. The Steinhart–Hart equation is a model of the resistance of a Semiconductor at different Temperatures The equation is {1 \over

This equation is used to calibrate thermistors. A thermistor is a type of Resistor with resistance varying according to its Temperature.

In non-crystalline semi-conductors, conduction can occur by charges quantum tunnelling from one localised site to another. In Quantum mechanics, quantum tunnelling is a nanoscopic phenomenon in which a particle violates the principles of Classical mechanics by penetrating a 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. Introduction Variable range hopping or Mott variable range hopping is a model describing low temperature conduction in strongly disordered systems with localized

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. 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 (that can Tomography is imaging by sections or sectioning A device used in tomography is called a tomograph, while the image produced is a tomogram. Complex plane In Mathematics, the complex numbers are an extension of the Real numbers obtained by adjoining an Imaginary unit, denoted Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC Impeditivity is the sum of a real component, the resistivity, and an imaginary component, the reactivity (reactance) [1].

Sources

1. ^ ^{a b c d e f g h i j k l m n o} Serway, Raymond A. (1998). Principles of Physics, 2nd ed, Fort Worth, Texas; London: Saunders College Pub, p602. ISBN 0-03-020457-7.  
2. ^ ^{a b c d} Griffiths, David [1981] (1999). David J Griffiths (born 1942 is a US physicist and educator He has worked at Reed College since 1978 where he is currently the Howard Vollum "7. Electrodynamics", in Alison Reeves (ed. ): Introduction to Electrodynamics, 3rd edition, Upper Saddle River, New Jersey: Prentice Hall, 286. Prentice Hall is a leading educational publisher It is an Imprint of Pearson Education Inc ISBN 0-13-805326-x. OCLC 40251748. The OCLC Online Computer Library Center is according to its website a "nonprofit membership computer library service and research organization dedicated to the public purpose  
3. ^ ^{a b c} Giancoli, Douglas C. (1995). Physics: Principles with Applications, 4th ed, London: Prentice Hall. ISBN 0-13-102153-2.  
   (see also Table of Resistivity)
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. A semiconductor' is a Solid material that has Electrical conductivity in between a conductor and an insulator; it can vary over that Impurities are Substances inside a confined amount of Liquid, Gas, or Solid, which differ from the Chemical composition of 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.  

See also

• Electrical conductivity
• Electrical resistivity imaging
• SI electromagnetism units
• Sheet resistance
• Electrical resistivities of the elements (data page)

External links

• Resistivity & Mobility Calculator/Graph from BYU cleanroom
• http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Sensors/TempR.html
• http://www.trekinc.com/pdf/1005_Resistivity_Resistance.pdf