Conductivity (k)

We have seen that $G = 1/R$ and that $R$ is directly proportional to length and inversely proportional to cross-sectional area. It therefore follows that $G$ is directly proportional to $a$ and inversely proportional to $l$:

The proportionality constant $k$ is called conductivity. $G = k$ if the length and cross-sectional area of the conductor are unity. Conductivity is thus the electrical conductance of a conductor of unit length and unit area of cross section — in other words, the electrical conductance of a unit cube ($\mathrm{1\ m^3}$ or $\mathrm{1\ cm^3}$) of material. The conductivity of a solution of an electrolyte is called electrolytic conductivity, which refers to the electrical conductance of unit volume of the solution.

From Eq. (5.2) and Eq. (5.4) we write

Combination of Eq. (5.3) and Eq. (5.5) shows that $k = 1/\rho$ — conductivity is the inverse of resistivity.

Units of electrolytic conductivity

| Quantity | SI unit | Common unit |

|---|---|---| …