Resistivity and What Sets a Wire's Resistance
A wire's resistance grows with its length and falls with its cross-section, and dividing out both leaves a number belonging to the material alone. That number is why copper is used for cables and why a strain gauge works at all.
What a learner can do afterwards
- Predicts how resistance changes when a wire is stretched, doubled in length or swapped for a thicker one
- Calculates a resistivity from measurements of resistance, length and diameter, with the diameter squared handled correctly
- Compares two materials by resistivity and says which suits a heating element and which a connecting lead
1 · Read
One wire owns its drag; its stuff owns a deeper mark. The tie is R as rho L by A. Twice the run means twice the drag; twice the cut means half.
Stretch a wire to twice its run at same cut and drag doubles. Fold it back to half run with twin cut and drag drops to a fourth. Small shifts in width swing wide since cut grows with width squared.
Heat turns use high-mark blends such as nichrome, which turn flow into glow. Links use low-mark copper that wastes scant power. Big rho fits fires; small rho fits links.
To weigh stuff, log drag, run, and width, then work rho as R A by L. Gauge width with fine jaws and square with care. Long, thin, hot, or high-mark lines all lift drag.
Long, thin, hot, or high-mark lines all lift drag, and rho alone tells which stuff fits which post.
More to read
9.3 Resistivity and Resistance
Resistance is a property of one particular wire; resistivity is a property of the material it is made from. The link is R = rho L / A: double the length and resistance doubles, double the cross area and it halves. Since area grows with diameter squared, a slightly thicker wire conducts far better than it looks. Heating elements exploit high resistivity alloys, while connecting leads use low resistivity copper. Measuring resistivity means measuring R, L and diameter, then solving for rho. The diameter enters squared, so measure it with calipers or a micrometer and handle the squaring with care. Compare materials by rho alone: bigger rho suits heaters, smaller rho suits leads.
20.3 Resistance and Resistivity
Stretch a wire longer and thinner and its resistance climbs twice over: more length plus less area. Fold it double and resistance quarters. Swap copper for nichrome and resistance leaps because the material itself resists more. Temperature joins in too, raising resistance for most metals as the lattice vibrates harder. Worked examples show the standard drill: convert millimetres to metres, square the radius for area, then divide rho L by A. Keep units consistent and the powers of ten behave. Predict before you compute: longer, thinner, hotter, or higher rho all push R up.
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2 · Watch
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Where it sits
Learn first
Optional connections
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.