Electrical resistivity
Intrinsic property that quantifies how strongly a material opposes electric current; measured in ohm-metre, inverse of conductivity, depends on composition and temperature and has wide technical uses.
Overview
Electrical resistivity is an intrinsic material property that quantifies how much a substance opposes the flow of electric current. It expresses the material's tendency to convert electrical energy into heat or to block carrier motion. The concept is central to electrical engineering and to materials science, and it helps classify conductors, semiconductors, and insulators according to their ability to carry electric charge. For basic discussions of current flow see electric current.
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Definition and units
Resistivity (commonly represented by the Greek letter rho, ρ) relates the electrical resistance of a specimen to its geometry. For a uniform material ρ is given by the formula ρ = R·A / L where R is the measured resistance between two faces, A is the cross-sectional area and L is the length between those faces. This definition means that resistivity is the resistance of a cube of material one metre on a side measured between opposite faces. The SI unit of resistivity is the ohm metre, introduced to follow the practice of measuring resistance in ohms and length in metres. For basic background on resistance see electrical resistance and on the SI system see SI units.
Relation to conductivity and material categories
Resistivity is numerically the reciprocal of electrical conductivity: σ = 1/ρ. Materials with small ρ are good conductors, while large ρ indicates poor conduction. Metals typically have low resistivity, semiconductors have much higher, and insulators have extremely high resistivity. Superconductors are a special case: below a critical temperature their resistivity effectively drops to zero. For concise comparisons see sources on electrical conductivity, semiconductors, and insulators.
Physical causes and temperature dependence
Resistivity arises from the scattering and trapping of charge carriers (electrons or holes) by atoms, impurities and crystal defects. In metals the dominant scattering mechanism is thermal motion of atoms; as temperature increases, resistivity usually rises. In many semiconductors, raising temperature increases carrier concentration and can lower resistivity. The exact temperature dependence varies by material and may be approximately linear for metals over moderate ranges but exponential or more complex in semiconductors and insulators.
Measurement techniques
Laboratory and industrial measurements use several standard techniques depending on sample shape and required accuracy:
- Two-point and four-point probe methods: four-point reduces contact-resistance errors and is common for thin films and bulk samples.
- Van der Pauw method: ideal for arbitrary-shaped thin samples with uniform thickness.
- Bridge circuits and specialized fixtures: used for high-precision or high-resistance measurements.
Practical guides and instrument references can be found through specialized sources such as measurement technique references.
Applications and significance
Knowing a material's resistivity is essential for designing wires, heating elements, sensors and electronic components. It determines conductor cross-section for a specified current, influences signal loss in transmission lines, and affects device performance in semiconductor technology. In geophysics and material testing, resistivity surveys reveal subsurface features because different rocks and soils have characteristic resistivities.
Distinctions and notable facts
Resistivity is an intrinsic property independent of sample size or shape; resistance is the extrinsic consequence of both material resistivity and geometry. The concept links to Ohm's law, and the term is widely used in engineering and science to compare materials and to guide material selection. For further reading on practical examples and engineering tables see related resources in electrical engineering and measurements in SI units.
Keywords: resistivity, conductivity, resistance, ohm-metre, four-point probe, van der Pauw, conductor, semiconductor, insulator.
Cause and temperature dependence
Responsible for the specific electrical resistance in pure metals are two components which overlap according to Matthiessen's rule:
- collisions of charge carriers (here electrons) with lattice vibrations (phonons); this part depends on the temperature, and
- Collisions of the charge carriers (here electrons) with impurities, defects and lattice defects; this fraction does not depend on the temperature, but on the concentration of the lattice defects.
The temperature-dependent portion of the resistivity is approximately linear for all conductors in a respective limited temperature range:
where α is the temperature coefficient, T is the temperature, and T0 is any temperature, e.g., T0 = 293.15 K = 20 °C, at which the electrical resistivity ρ(T0) is known (see table below).
Depending on the sign of the linear temperature coefficient, a distinction is made between positive temperature coefficient of resistance (PTC) and negative temperature coefficient of resistance (NTC). The linear temperature dependence only applies within a limited temperature interval. This can be comparatively large for pure metals. Beyond this, corrections must be applied (see also: Kondo effect).
Pure metals have a positive temperature coefficient of the specific electrical resistance of about 0.36 %/K to over 0.6 %/K. In the case of platinum (0.385 %/K), this is used to build platinum resistance thermometers.
The specific electrical resistance of alloys is only slightly dependent on temperature; here the proportion of impurities is predominant. This is used, for example, with constantan or manganin to obtain a particularly low temperature coefficient or a temperature-stable resistance value.
Tensor resistivity
For most materials, the electrical resistance is independent of direction (isotropic). A simple scalar quantity, i.e. a number with a unit, is then sufficient for the resistivity.
Anisotropy in electrical resistivity is found in single crystals (or multicrystals with preferred direction) with less than cubic symmetry. Most metals have a cubic crystal structure and are therefore isotropic. In addition, one often has a many-crystalline form with no distinct preferred direction (texture). An example of anisotropic resistivity is graphite as a single crystal or with preferred direction. The resistivity is then a 2nd level tensor relating the electric field strength 
to the electric current density . 
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AlegsaOnline.com Electrical resistivity Leandro Alegsa
URL: https://en.alegsaonline.com/art/30703