Electrical resistance
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:
- <math>
R_{21} = (V_2-V_1)/I \,
<math>
where <math>R_{21}<math> is the resistance between points 2 and 1 in the circuit, <math>V_2<math> the voltage at point 2 in the circuit, <math>V_1<math> the voltage at point 1 in the circuit, and <math>I<math> the current passing through the resistor <math>R_{21}<math>. The voltages are measured with respect to any fixed reference, such as ground.
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.
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.
Resistive loss
When a current, <math>I<math>, flows through a object with resistance, <math>R<math>, electrical energy in converted to heat at a rate (power) equal to
- <math>
P = {I^{2} \cdot R} \,
<math>
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
- <math>
R = {L \cdot \rho \over A} \,
<math>
where L is the length of the wire, A is the cross-sectional area and ρ (Greek: rho) is the electrical resistivity (also called specific electrical resistance) of the material. 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:
- <math>
R = dV/dI \,
<math>
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
