Resistivity and conductivity

Resistance is a property of one specific object — this particular wire, this particular resistor. Resistivity is a property of the material it is made from, independent of shape or size, the way density is independent of how much of a substance you have. Copper has one resistivity wherever it appears; a copper wire's resistance depends on that resistivity together with its specific length and cross-section.

The relationship is R = ρL/A: resistance grows in direct proportion to length, and falls in inverse proportion to cross-sectional area. Both directions have an intuitive reading once stated. A longer wire gives charge carriers a longer obstacle course to push through, so resistance rises with length — the opposite of the common guess that more metal must mean less resistance. A wider wire gives more parallel lanes for current to flow through at once, so resistance falls as area grows; halving the area is like closing half the lanes on a road.

Conductivity is simply the reciprocal, σ = 1/ρ: a material that resists weakly conducts strongly, and vice versa. Metals have low resistivity and are excellent conductors; rubber and glass have enormous resistivity and are used as insulators for exactly that reason. Resistivity also depends on temperature — for most metals it rises as the metal heats, since the ions vibrate more and scatter the flowing electrons more often, which is part of why a light bulb's filament resistance is much higher glowing than cold.