Electrical resistivity and conductivity

The resistivity (short for electrical resistivity or resistivity ) is a temperature-dependent material constant with the formula sign (Greek rho). It is used to calculate the electrical resistance of a homogeneous electrical conductor in particular. The derived SI unit is [ ρ ] SI = Ω · m ( results from the dimensional reduction of related Ω · m2 / m). The reciprocal of resistivity is conductivity.

Cause and temperature dependence

Responsible for the electrical resistivity in pure metals are two components that are superimposed according to the Matt Hiess 's rule:

• Collisions of charge carriers ( here electrons) with lattice vibrations ( phonons); This proportion is dependent on the temperature, and
• Collisions of charge carriers ( here electrons) with impurities, defects and lattice defects; this proportion is not dependent on the temperature, but the concentration of lattice defects.

The temperature- dependent part of the resistivity is all ladders, each in a limited temperature range approximately linear:

Wherein α is the temperature coefficient, T is temperature and T0 any temperature, for example, T0 = 293.15 K = 20 ° C, at which the electrical resistivity ρ ( T 0 ) is known (see table below).

Depending on the sign of the linear temperature coefficient distinction is made between PTC (English: positive temperature coefficient of resistance, PTC) and thermistors (English: negative temperature coefficient of resistance, NTC ). The linear temperature dependence is valid only in a limited temperature interval. This can be relatively large for pure metals. In addition, you have to install fixes (see also: Kondo effect).

The electrical resistivity of alloys is only slightly dependent upon the temperature, in this case the predominant proportion of the impurities. This is Ausgenutzt example, in constantan or manganin.

Resistivity as a tensor

For most materials, the electric resistance -directional ( isotropic). Then suffices for the resistivity of a simple scalar variable, ie a number with unit.

Anisotropy in electrical resistance can be found in single crystals (or polycrystals with a preferred direction ) with less than cubic symmetry. Most metals have cubic crystal structure and are therefore already isotropic. In addition, one often has a much - crystalline form without a pronounced preferred orientation (texture). An example of anisotropic resistivity is graphite as a single crystal or with a preferred direction. The resistivity is then a second stage tensor which connects the electric field strength of the electrical current density.

Connected with the electrical resistance

The electrical resistance of a conductor having a constant cross-sectional area along its length ( section perpendicular to the longitudinal axis of a body ) is:

Where R is the electrical resistance, ρ the specific resistance, L is the length and A is the cross-sectional area of the conductor.

Consequently, one can determine, from the measurement of the resistance of a conductor piece of known geometry:

The cross-sectional area A of a round conductor (eg, a wire ) is calculated from the diameter d:

The conditions for the validity of the formula for the electrical resistance R is a constant current density distribution over the conductor cross-section A, that is, at every point of the conductor cross -section, the current density J is the same. Approximately given that if the length of the conductor is large in comparison to the dimensions of its cross section, and the current is a direct current or low frequency. At high frequencies, the skin effect and inhomogeneous high-frequency magnetic fields and geometries lead the proximity effect in an inhomogeneous current density distribution.

More from the resistivity parameters are derivable

• The sheet resistance ( sheet resistance of a resistive layer ); unit or
• The resistance per length of a wire or cable; Unit / m

Classification of materials

In practice, the specific resistance is seldom reported in the case of thin wires, but in most cases. The unit is used for samples of material with a large cross -section. The following applies:

The specific resistance of a material is often used for the classification as a conductor, semiconductor or insulator. The distinction is made on the basis of resistivity:

• Officers: ρ <100
• Semiconductor: ρ = 100-1012
• Insulators or dielectrics: ρ > 1012

It should be noted that this classification has no fixed boundaries and must therefore be regarded as a guide only. Therefore, can be found in the literature data, which may differ by up to two orders of magnitude. One reason for this is the temperature dependence of the electrical resistance, in particular for semiconductors. A classification based on the position of the Fermi level is more useful here.