Electrical resistivity and conductivity

Electrical Resistivity and Conductivity
– Electrical resistivity measures the resistance of a material to electric current.
– It is represented by the Greek letter ρ (rho).
– The SI unit of electrical resistivity is ohm-metre (Ω⋅m).
– A low resistivity indicates a material that readily allows electric current.
– Resistivity is an intrinsic property and does not depend on the geometric properties of a material.
– Electrical conductivity is the reciprocal of electrical resistivity.
– It represents a material’s ability to conduct electric current.
– It is commonly represented by the Greek letter σ (sigma).
– The SI unit of electrical conductivity is siemens per metre (S/m).
– Conductivity and resistivity are intensive properties of materials.

Ideal Case
– In an ideal case, the cross-section and physical composition of the material are uniform.
– The electric field and current density are both parallel and constant everywhere.
– The resistance of the conductor is directly proportional to its length and inversely proportional to its cross-sectional area.
– The electrical resistivity (ρ) is the constant of proportionality.
– The resistivity can be expressed using the SI unit ohm-metre (Ω⋅m).

Resistance vs Resistivity
– Resistance depends on the geometric properties of a material, while resistivity is an intrinsic property.
– All pure copper wires have the same resistivity, regardless of their shape and size.
– A long, thin copper wire has a larger resistance than a thick, short copper wire.
– Every material has its own characteristic resistivity.
– Rubber has a far larger resistivity than copper.

Hydraulic Analogy
– Passing current through a high-resistivity material is like pushing water through a pipe full of sand.
– Passing current through a low-resistivity material is like pushing water through an empty pipe.
– The pipe full of sand has higher resistance to flow.
– Resistance is not solely determined by resistivity.
– Resistivity and resistance play important roles in determining the flow of electric current.

Additional Information
– The Greek letter ρ (rho) represents electrical resistivity.
– The SI unit of electrical resistivity is ohm-metre (Ω⋅m).
– The Greek letter σ (sigma) represents electrical conductivity.
– The SI unit of electrical conductivity is siemens per metre (S/m). Source:  https://en.wikipedia.org/wiki/Electrical_conduction

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)
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, γii
SI unit	siemens per metre (S/m)
Other units	z
Derivations from other quantities	${\displaystyle \sigma ={\frac {1}{\rho }}}$
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.