Electrical resistivity and conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that quantifies how strongly it resists electric current. Its inverse, called electrical conductivity, quantifies how well a material conducts electricity. 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-meter (Ω⋅m).[1][2][3] For example, if a 1 m 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.
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).
In an ideal case, cross-section and physical composition of the examined material are uniform across the sample, and the electric field and current density are both parallel and constant everywhere. Many resistors and conductors do in fact have a uniform cross section with a uniform flow of electric current, and are made of a single material, so that this is a good model. (See the adjacent diagram.)
Both resistance and resistivity describe how difficult it is to make electrical current flow through a material, but unlike resistance, resistivity is an intrinsic property. This means that all pure copper wires (which have not been subjected to distortion of their crystalline structure etc.), irrespective of their shape and size, have the same resistivity, but a long, thin copper wire has a much larger resistance than a thick, short copper wire. Every material has its own characteristic resistivity. For example, rubber has a far larger resistivity than copper.
In a hydraulic analogy, passing current through a high-resistivity material is like pushing water through a pipe full of sand — while passing current through a low-resistivity material is like pushing water through an empty pipe. If the pipes are the same size and shape, the pipe full of sand has higher resistance to flow. Resistance, however, is not solely determined by the presence or absence of sand. It also depends on the length and width of the pipe: short or wide pipes have lower resistance than narrow or long pipes.
