Term: Electrical resistivity and conductivity

– Definition:
– Electrical resistivity is a property measuring a material’s resistance to electric current.
– It is represented by the Greek letter ρ and measured in ohm-metres.
– Electrical conductivity is the reciprocal of resistivity.
– Conductivity is represented by the Greek letter σ and measured in siemens per metre.
– Resistivity and conductivity are intrinsic properties of materials.

– Ideal case:
– Resistance is directly proportional to length and inversely proportional to cross-sectional area.
– Resistivity is expressed in ohm-metres.
– Resistivity is intrinsic and unaffected by geometric properties.
– Resistance varies with length and cross-sectional area.
– Conductivity is the inverse of resistivity.

– General scalar quantities:
– Resistivity varies with position in the material.
– Resistivity is the ratio of electric field to current density.
– Conductivity is the reciprocal of resistivity.
– Rubber has high resistivity and low conductivity.
– Copper has low resistivity and high conductivity.

– Material properties:
– Resistivity is an intrinsic property of materials.
– Pure copper wires have the same resistivity regardless of shape.
– Different materials have different resistivities.
– Resistivity determines the ease of current flow in a material.
– Conductivity is influenced by resistivity.

– Mathematical expressions:
– Resistivity is defined as the ratio of electric field to current density.
– Conductivity is the reciprocal of resistivity.
– Rubber has high resistivity and low conductivity.
– Copper has low resistivity and high conductivity.
– Ideal case simplifies resistivity and conductivity calculations.

Electrical resistivity and conductivity (Wikipedia)

This article is about electrical conductivity in general. For other types of conductivity, see Conductivity. For specific applications in electrical elements, see Electrical resistance and conductance.

Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the Greek letter ρ (rho). The SI unit of electrical resistivity is the ohm-metre (Ω⋅m). For example, if a 1 m³ solid cube of material has sheet contacts on two opposite faces, and the resistance between these contacts is 1 Ω, then the resistivity of the material is 1 Ω⋅m.

Resistivity
Common symbols	ρ
SI unit	ohm metre (Ω⋅m)
Other units	s (Gaussian/ESU)
In SI base units	kg⋅m3⋅s−3⋅A−2
Derivations from other quantities	${\displaystyle \rho =R{\frac {A}{\ell }}}$
Dimension	${\displaystyle {\mathsf {M}}{\mathsf {L}}^{3}{\mathsf {T}}^{-3}{\mathsf {I}}^{-2}}$

Conductivity
Common symbols	σ, κ, γ
SI unit	siemens per metre (S/m)
Other units	${\displaystyle \mathrm {s} ^{-1}}$ (Gaussian/ESU)
Derivations from other quantities	${\displaystyle \kappa ={\frac {1}{\rho }}}$
Dimension	${\displaystyle {\mathsf {M}}^{-1}{\mathsf {L}}^{-3}{\mathsf {T}}^{3}{\mathsf {I}}^{2}}$

Electrical conductivity (or specific conductance) is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter σ (sigma), but κ (kappa) (especially in electrical engineering) and γ (gamma) are sometimes used. The SI unit of electrical conductivity is siemens per metre (S/m). Resistivity and conductivity are intensive properties of materials, giving the opposition of a standard cube of material to current. Electrical resistance and conductance are corresponding extensive properties that give the opposition of a specific object to electric current.

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