Resistivity

Diagram of a uniform conductor of length, l, and area, A

The resistance R of a uniform conductor is proportional to the length l and inversely proportional to the cross-sectional area A. The resistivity ρ is a constant that depends upon the material the conductor is made from and other physical conditions such as the temperature.

R = ρl/A

S.I. Units
symbol	quantity	unit	unit symbol
R	resistance	ohm	Ω
ρ	resistivity	ohm metre	Ω m
l	length	metre	m
A	cross-sectional area	square metre	m²

ρ is the Greek letter rho.

Understanding resistivity.

ρ = RA/l

Diagram of a block 1 metre long and with a cross-sectional area of 1 square metre.

If you take a block with a length l of 1 m and with a cross-sectional area A of 1 m² the equation becomes:

ρ = R

That is, the resistivity is numerically equal to the resistance of a block one metre long and with a cross-sectional area of one square metre.

For a large block of metal such as copper the resistance is very small indeed. This is because in a large block there are a huge number of electrons available to carry a current. For copper the resistance is about 0.000000017 Ω and the resistivity about 0.000000017 Ω m.

Resistivity and temperature.

The resistance of a material changes with temperature. This means the resistivity of a material will also change with temperature. Hence it is normal to quote resistivity values at a specific temperature.

Resistivity and metals.

Adding impurities to a pure metal considerably increases its resistivity. Alloys (combinations of metals) have much higher resistivities than the metals they are made from.