electricalresistivity

Electrical resistivity, denoted by the symbol ρ, is a material property that quantifies how strongly a material opposes the flow of electric current. It relates the current density J to the electric field E through J = σE, where σ is the electrical conductivity and ρ = 1/σ. The SI unit of resistivity is the ohm-meter (Ω·m). Resistivity is an intrinsic property of a material and is independent of its shape or size.

In a uniform conductor of length L and cross-sectional area A, the resistance is R = ρL/A. Thus resistivity determines how resistance scales with geometry, while resistance itself depends on both material and dimensions.

Resistivity also varies with temperature and material type. For metals, ρ typically increases approximately linearly with temperature, described by ρ(T) ≈ ρ0[1 + α(T − T0)], where α is the temperature coefficient of resistivity. Semiconductors and insulators can exhibit much stronger or non-linear temperature dependence, often decreasing resistivity as temperature rises.

Factors such as impurities, alloying, crystal structure, defects, and microstructure influence resistivity. Some materials are anisotropic, possessing different resistivity along different crystallographic directions.

Measurement methods include the four-point probe technique, which minimizes contact resistance, and the Van der Pauw method for flat samples. For fluids, resistivity is related to conductivity by ρ = 1/κ, where κ is the conductivity of the liquid.

Applications of resistivity span material selection, electronics, energy transmission, sensors, and geophysics, where resistivity contrasts help infer subsurface composition. In alternating current conditions, resistivity becomes part of a complex impedance due to frequency-dependent effects such as the skin effect.