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Encyclopedia > Electrical resistance
Electromagnetism
Electricity · Magnetism
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A 750-kΩ resistor, as identified by its electronic color code. An ohmmeter could be used to verify this value.

$R = {l cdot rho over A} ,$

where

"l" is the length
"A" is the cross sectional area, and
"ρ" is the resistivity of the material

Electrical resistance shares some conceptual parallels with the mechanical notion of friction. The SI unit of electrical resistance is the ohm, symbol Ω. The resistance of an object determines the amount of current through the object for a given potential difference across the object. // Headline text POOP!! Danny Hornsby (also known as Gnome) is a measure indicating how strongly a Gnome can opposes the flow of electric current. ... For other uses, see Friction (disambiguation). ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The ohm (symbol: Î©) is the SI unit of electric resistance. ... Omega (Î© Ï‰) is the 24th and last letter of the Greek alphabet. ... Potential difference is a quantity in physics related to the amount of energy that would be required to move an object from one place to another against various types of force. ...

$R = frac{V}{I}$

where

R is the resistance of the object, measured in ohms, equivalent to J·s/C2
V is the potential difference across the object, measured in volts
I is the current through the object, measured in amperes

For a wide variety of materials and conditions, the electrical resistance does not depend on the amount of current through or the amount of voltage across the object, meaning that the resistance R is constant. The ohm (symbol: Î©) is the SI unit of electric resistance. ... Josephson junction array chip developed by NIST as a standard volt. ... For other uses, see Ampere (disambiguation). ... In mathematics and the mathematical sciences, a constant is a fixed, but possibly unspecified, value. ...

## Resistance of a conductor GA_googleFillSlot("encyclopedia_square");

### DC resistance

As long as the current density is totally uniform in the insulator, the DC resistance R of a conductor of regular cross section can be computed as In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ...

$R = {l cdot rho over A} ,$

where

l is the length of the conductor, measured in meters
A is the cross-sectional area, measured in square meters
ρ (Greek: rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm · meter. Resistivity is a measure of the material's ability to oppose the flow of electric current.

For practical reasons, almost any connections to a real conductor will almost certainly mean the current density is not totally uniform. However, this formula still provides a good approximation for long thin conductors such as wires. The metre, or meter (symbol: m) is the SI base unit of length. ... A square metre (US spelling: square meter) is by definition the area enclosed by a square with sides each 1 metre long. ... // Headline text POOP!! Danny Hornsby (also known as Gnome) is a measure indicating how strongly a Gnome can opposes the flow of electric current. ...

### AC resistance

If a wire conducts high-frequency alternating current then the effective cross sectional area of the wire is reduced because of the skin effect. This causes the wire resistance to increase at a rate of 10dB/decade for wire radius much greater than skin depth. The skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core. ... When an electromagnetic wave interacts with a conductive material, mobile charges within the material are made to oscillate back and forth with the same frequency as the impinging fields. ...

In a conductor close to others, the actual resistance is higher than that predicted by the skin effect because of the proximity effect. A changing magnetic field will influence the distribution of an electric current flowing within an electrical conductor. ...

## Causes of resistance

### In metals

A metal consists of a lattice of atoms, each with a shell of electrons. This can also be known as a positive ionic lattice. The outer electrons are free to dissociate from their parent atoms and travel through the lattice, creating a 'sea' of electrons, making the metal a conductor. When an electrical potential difference (a voltage) is applied across the metal, the electrons drift from one end of the conductor to the other under the influence of the electric field. This article is about metallic materials. ... For other uses, see Atom (disambiguation). ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... 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. ...

Near room temperatures, the thermal motion of ions is the primary source of scattering of electrons (due to destructive interference of free electron wave on non-correlating potentials of ions) - thus the prime cause of metal resistance. Imperfections of lattice also contribute into resistance, although their contribution in pure metals is negligible.

The larger the cross-sectional area of the conductor, the more electrons are available to carry the current, so the lower the resistance. The longer the conductor, the more scattering events occur in each electron's path through the material, so the higher the resistance. Different materials also affect the resistance.[1]

### In semiconductors and insulators

In metals, the fermi level lies in the conduction band (see Band Theory, below) giving rise to free conduction electrons. However, in semiconductors the position of the fermi level is within the band gap, exactly half way between the conduction band minimum and valence band maximum for intrinsic (undoped) semiconductors. This means that at 0 Kelvin, there are no free conduction electrons and the resistance is infinite. However, the resistance will continue to decrease as the charge carrier density in the conduction band increases. In extrinsic (doped) semiconductors, dopant atoms increase the majority charge carrier by donating electrons to the conduction band or accepting holes in the valence band. For both types of donor or acceptor atoms, increasing the dopant density leads to a reduction in the resistance. Highly doped semiconductors hence behave metallic. At very high temperatures, the contribution of thermally generated carriers will dominate over the contribution from dopant atoms and the resistance will decrease exponentially with temperature.

### In ionic liquids/electrolytes

In electrolytes, electrical conduction happens not by band electrons or holes, but by full atomic species (ions) traveling, each carrying an electrical charge. The resistivity of ionic liquids varies tremendously by the salt concentration - while distilled water is almost an insulator, salt water is a very efficient electrical conductor. In biological membranes, currents are carried by ionic salts. Small holes in the membranes, called ion channels, are selective to specific ions and determine the membrane resistance. An electrolyte is any substance containing free ions that behaves as an electrically conductive medium. ... Conduction is the movement of electrically charged particles through a transmission medium (electrical conductor). ... This article is about the electrically charged particle. ... Look up cell membrane in Wiktionary, the free dictionary. ... Ion channels are pore-forming proteins that help to establish and control the small voltage gradient that exists across the plasma membrane of all living cells (see cell potential) by allowing the flow of ions down their electrochemical gradient. ...

### Resistance of various materials

 Material Resistivity, ρ ohm-meter Metals 10 - 8 Semiconductors variable Electrolytes variable Insulators 1016 Superconductors 0

This article is about metallic materials. ... A semiconductor is a solid material that has electrical conductivity in between that of a conductor and that of an insulator; it can vary over that wide range either permanently or dynamically. ... An electrolyte is any substance containing free ions that behaves as an electrically conductive medium. ... This article or section is in need of attention from an expert on the subject. ... Superconductivity is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of electrical resistance and the damping of the interior magnetic field (the Meissner effect. ...

### Band theory simplified

Electron energy levels in an insulator.

Quantum mechanics states that the energy of an electron in an atom cannot be any arbitrary value. Rather, there are fixed energy levels which the electrons can occupy, and values in between these levels are impossible. The energy levels are grouped into two bands: the valence band and the conduction band (the latter is generally above the former). Electrons in the conduction band may move freely throughout the substance in the presence of an electrical field. Image File history File links A rough diagram illustrating the forbidden electron energy levels in an insulator. ...

In insulators and semiconductors, the atoms in the substance influence each other so that between the valence band and the conduction band there exists a forbidden band of energy levels, which the electrons cannot occupy. In order for a current to flow, a relatively large amount of energy must be furnished to an electron for it to leap across this forbidden gap and into the conduction band. Thus, even large voltages can yield relatively small currents.

## Differential resistance

When resistance may depend on voltage and current, differential resistance, incremental resistance or slope resistance is defined as the slope of the U-I graph at a particular point, thus:

$R = frac {mathrm{d}U} {mathrm{d}I} ,$

This quantity is sometimes called simply resistance, although the two definitions are equivalent only for an ohmic component such as an ideal resistor. If the U-I graph is not monotonic (i.e. it has a peak or a trough), the differential resistance will be negative for some values of voltage and current. This property is often known as negative resistance, although it is more correctly called negative differential resistance, since the absolute resistance U/I is still positive. A VI curve with a negative differential resistance region Negative resistance or negative differential resistance (NDR) is a property of electrical circuit elements composed of certain materials in which, over certain voltage ranges, current is a decreasing function of voltage. ...

## Temperature-dependence

Near room temperature, the electric resistance of a typical metal varies linearly with the temperature. At lower temperatures (less than the Debye temperature), the resistance decreases as T5 due to the electrons scattering off of phonons. At even lower temperatures, the dominant scattering mechanism for electrons is other electrons, and the resistance decreases as . At some point, the impurities in the metal will dominate the behavior of the electrical resistance which causes it to saturate to a constant value. Matthiessen's Rule[1][2] says that all of these different behaviors can be summed up to get the total resistance as a function of temperature, // Headline text POOP!! Danny Hornsby (also known as Gnome) is a measure indicating how strongly a Gnome can opposes the flow of electric current. ... For other uses, see Temperature (disambiguation). ... In thermodynamics and solid state physics, the Debye model is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (heat capacity) in a solid. ... Normal modes of vibration progression through a crystal. ...

where Rimp is the temperature independent electrical resistivity due to impurities, and a, b, and c are coefficients which depend upon the metal's properties.

The electric resistance of a typical intrinsic (non doped) semiconductor decreases exponentially with the temperature: A semiconductor is a solid material that has electrical conductivity in between that of a conductor and that of an insulator; it can vary over that wide range either permanently or dynamically. ... A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...

Extrinsic (doped) semiconductors have a far more complicated temperature profile. As temperature increases starting from absolute zero they first decrease steeply in resistance as the carriers leave the donors or acceptors. After most of the donors or acceptors have lost their carriers the resistance starts to increase again slightly due to the reducing mobility of carriers (much as in a metal). At higher temperatures it will behave like intrinsic semiconductors as the carriers from the donors/acceptors become insignificant compared to the thermally generated carriers.

The electric resistance of electrolytes and insulators is highly nonlinear, and case by case dependent, therefore no generalized equations are given.

## Measuring resistance

An instrument for measuring resistance is called a resistance meter or ohmmeter. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use four-terminal sensing. An Ohmmeter is an electrical measuring instrument that measures electrical resistance, the opposition to the flow of an electric current. ... Four-terminal sensing (4T sensing) is an electrical impedance measuring technique that uses separate pairs of current-carrying and voltage sensing electrodes to make more accurate measurements than traditional two-terminal (2T) sensing. ...

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## References

1. ^ A. Matthiessen, Rep. Brit. Ass. 32, 144 (1862)
2. ^ A. Matthiessen, Progg. Anallen, 122, 47 (1864)

Results from FactBites:

 Electrical resistance - Wikipedia, the free encyclopedia (1185 words) Electrical resistance is a measure of the degree to which an object opposes the passage of an electric current. The SI unit of electrical resistance is the ohm. R is the resistance of the object, usually measured in ohms.
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