Misplaced Pages

Electrical resistance and conductance

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.

This is an old revision of this page, as edited by Icairns (talk | contribs) at 00:03, 29 October 2004 (remove bullets from parameters; remove unnecessary maths). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

Revision as of 00:03, 29 October 2004 by Icairns (talk | contribs) (remove bullets from parameters; remove unnecessary maths)(diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff)

Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. It 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 21 = ( V 2 − V 1 ) / I {\displaystyle R_{21}=(V_{2}-V_{1})/I\,}

where

R21 is the resistance between points 2 and 1 in the circuit, measured in ohms

V2 the voltage at point 2 in the circuit, measured in volts

V1 is the voltage at point 1 in the circuit, measured in volts

I is the current passing through the resistor R21, measured in amperes

The voltages are measured with respect to any fixed reference, such as ground.

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.

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 and such materials are known as ohmic devices.

Resistive loss

When a current, I {\displaystyle I} , flows through a object with resistance, R {\displaystyle R} , electrical energy in converted to heat at a rate (power) equal to

P = I 2 ⋅ R {\displaystyle P={I^{2}\cdot R}\,}

where

P is the power measured in watts

I is the current measured in amps

R is the resistance measured in ohms

This effect is useful in some applications like incandescent lighting and electric heating, but is undesirable in power transmission. Common ways to combat resistive loss include using thicker wire and higher voltages. Superconducting wire is used in special applications, but may become more common some day.

Resistance of a wire

The resistance R of a wire can be computed as

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

where

L is the length of the wire, measured in metres

A is the cross-sectional area, measured in square metres

ρ (Greek: rho) is the electrical resistivity (also called specific electrical resistance) of the material, measured in ohm · metre

Resistivity is a measure of the material's ability to oppose the flow of electric current.

Differential resistance

When resistance may depend on voltage and current, 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={\frac {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.

See also

Opposition to current

External links

Categories: