electrical resistivity
/ ree-zis-TIV-it-ee /
Push electric charge through a material and it fights back a little, the way water fights its way through a narrow pipe or a crowded corridor. Electrical resistivity is a single number that says how hard a given MATERIAL fights, no matter what shape you cut it into. It is written with the Greek letter rho and measured in ohm-meter. A low rho (copper) lets charge flow easily; a high rho (glass) chokes it off almost completely.
Resistivity is the material's own property; resistance is the property of a particular wire or block. They are linked by geometry: R = rho times L / A, where L is the length the current travels and A is the cross-sectional area it flows through. So a long thin wire has high resistance even from a low-rho metal, while a short fat bar of the same metal has low resistance. Flip it around to get rho = R times A / L, which is how you actually measure it: pass a known current, read the voltage, and divide out the size. For copper rho is about 1.7 times 10^-8 ohm-meter; for window glass it is around 10^12 ohm-meter or more, a gap of twenty orders of magnitude between two everyday solids.
That enormous span is why resistivity is the first thing materials scientists use to sort solids into conductors, semiconductors, and insulators. It is set from the inside by how many charge carriers the material has free to move and how easily they move, which in turn comes from bonding and the energy-band structure. Honest caveat: rho is not a fixed constant of nature, it depends on temperature and on impurities. In a metal, heating or adding foreign atoms makes rho RISE, because both give the moving electrons more to bump into.
A copper wire 2 m long with a cross-section of 1 mm^2 (which is 1 times 10^-6 m^2). Its resistance is R = rho times L / A = (1.7 times 10^-8) times 2 / (1 times 10^-6) = about 0.034 ohm. Cut the same wire in half and the resistance halves; double its thickness (four times the area) and the resistance drops to a quarter, all with the SAME resistivity.
Resistance changes with size; resistivity does not — it belongs to the material.
Do not confuse resistivity (a material property, ohm-meter) with resistance (a component property, ohm). A thick copper bar and a thin copper hair have very different resistances but exactly the same resistivity.