Resistivity

Also called rho

Resistivity is the property of a material that quantifies how strongly it opposes the motion of electric charge, measured in ohm meters. Every sample of a substance shares the same resistivity whatever its shape, and in a real conductor it typically rises with temperature.

Resistivity is a fundamental property of a material, set by its atomic and molecular structure. A copper shaving and a copper block the size of a house have the same resistivity. They do not have the same resistance, and keeping those two apart is something the CED's own exam-preparation note for Unit 11 asks of students by name.

	Resistivity $\rho$	Resistance $R$
Belongs to	a material	one particular object
Unit	$\Omega \cdot \text{m}$	$\Omega$
Cut the object shorter	unchanged	falls
Draw it out thinner	unchanged	rises

The unit does not need memorizing either. Rearrange $R = \rho \ell / A$ into $\rho = RA/\ell$ and the units read $\Omega \cdot \text{m}^2 / \text{m}$ , which is $\Omega \cdot \text{m}$ .

Temperature is where the CED sets two statements against each other, on purpose. The resistivity of a conductor typically increases with temperature, because a hotter lattice vibrates harder and obstructs the carriers. But an ohmic material is idealized as one whose resistivity is constant regardless of temperature. Both sentences sit in Topic 11.3. A real filament is not ohmic; the resistor in an exam problem is, unless the question tells you something has heated up.

Back to the physics glossary