electrical conductivity – Too good to be true

Electrical conductivity or specific conductivity is a measure of a material’s ability to conduct an electric current. When an electrical potential difference is placed across a conductor, its movable charges flow, giving rise to an electric current. The conductivity σ is defined as the ratio of the current density $\mathbf{J}$ to the electric field strength $\mathbf{E}$ :

$\mathbf{J} = \sigma \mathbf{E}$ .

It is also possible to have materials in which the conductivity is anisotropic, in which case σ is a 3×3 matrix (or more technically a rank-2 tensor) which is generally symmetric.

Conductivity is the reciprocal (inverse) of electrical resistivity and has the SI units of siemens per metre (S·m^-1) i.e. if the electrical conductance between opposite faces of a 1-metre cube of material is 1 siemens then the material’s electrical conductivity is 1 siemens per metre. Electrical conductivity is commonly represented by the Greek letter σ, but κ or γ are also occasionally used.

Also:

For a device with electrical resistance R, the conductance G is defined as

$G = \frac1R = \frac{I}V,$

where

G is the conductance,
R is the resistance,
I is the current through the device and
V is the voltage (electrical potential difference) across the device.

The unit siemens for the conductance G is defined by 1 S = 1 A/V = 1 A²/W = 1 kg⁻¹·m⁻²·s³·A² =1 Ω^-1 = 1 kg⁻¹·m⁻²·s¹·C². So for a device with conductance 1 S, then the current through it with a 1 V voltage across it is 1 A, and for each extra V of voltage across it the current through it increases by 1 A.

Some tricks:

conductivity (S m⁻¹) = specific conductance (S)

resistance (Ω m⁻¹) = specific resistance (Ω)