The product of conductivity and resistivity of a conductor

The electrical conductivity (σ) and resistivity (ρ) of a material are defined as reciprocal properties of each other [1]. Mathematically, this relationship is expressed as σ = 1/ρ or ρ = 1/σ. Consequently, the product of conductivity and resistivity (σ × ρ) is always equal to 1 (unity). Since this product is a mathematical identity derived from their definitions as inverses, it remains constant regardless of the specific material, its dimensions, or external conditions like pressure and current [1]. While individual values of resistivity and conductivity vary significantly between different conductors—such as copper having high conductivity and glass having high resistivity—their product remains identically the same for all conductors. Therefore, the product does not depend on applied pressure or current flow, but is a universal constant for any conducting medium.

Sources

1. [1] https://www.epa.gov/environmental-geophysics/electrical-conductivity-and-resistivity