resistivity

Meaning: Resistivity is a property of a material at a given temperature, not of a particular wire. Resistance depends on the material and on the geometry. Good conductors such as copper have low ρ, and insulators have very high ρ. In metals, ρ generally rises as temperature rises, because electrons collide more often with the vibrating lattice. In semiconductors, ρ generally falls as temperature rises, because more charge carriers become available. Conductivity is the reciprocal, σ = 1/ρ.

Equation: R = ρL/A, where R is resistance (Ω), ρ is resistivity (Ω·m), L is the length of the conductor (m), and A is its cross-sectional area (m²).

On the MCAT: A passage gives wires or solutions with different lengths, diameters or materials, and asks how resistance, current or power changes. Doubling L doubles R. Doubling the diameter multiplies A by 4, so R falls to one-quarter. Wires of the same material share the same ρ. The result is then carried into V = IR or P = I²R.

Common confusion: Students treat resistivity and resistance as the same thing. Stretching or cutting a wire changes L and A, so it changes R, but ρ stays the same because the material and temperature are unchanged. Also remember that A depends on the radius squared (A = πr²), not on the radius alone.