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Electrical resistance and conductance

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Electrical resistance is the ratio of the potential difference (i.e. voltage) across an electric component (such as a resistor) to the current passing through it:

R = V / I {\displaystyle R=V/I}

where R is the resistance, V the voltage and I the current.

Resistance is thus a measure of the component's opposition to the flow of electric charge. The SI unit of electrical resistance is the ohm. Its reciprocal quantity is electrical conductance measured in siemens.

Differential resistance or incremental resistance is defined as the slope of the V-I graph at a particular point, thus:

R = d V / d I {\displaystyle R=dV/dI}

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 V-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 V/I is still positive.

For a wide variety of materials and conditions, the electrical resistance does not depend on the amount of current flowing or the amount of applied voltage: the two are proportional and the proportionality constant is the electrical resistance. This case is described by Ohm's law.

Specific electrical resistance, a measure of a material's ability to oppose the flow of electric current, is also known as electrical resistivity.

The resistance R of a wire can be computed as

R = L ρ A , {\displaystyle R={L\rho \over A}\;,}

where L is the length of the wire, A is the cross-sectional area and ρ is the electrical resistivity of the material.

See electrical conduction for the more information about the physical mechanisms for conduction in materials.

See also