Specific resistance:

Consider the electrolytic cell shown above, its two electrodes are having a cross- sectional area of A m² and separated by l m. The resistance (R) of the electrolyte solution present between the two electrodes is:

R  ∝ l

R  ∝  1/A

R  ∝   l/A

R =  ρ l/A

where ρ (rho) is proportionality constant is called resistivity (formerly called specific resistance). It is a characteristic property of the material and it is the resistance offered by a conductor of unit length and unit area of cross section.

ρ =   R (A/l)

In SI units, l and A are measured in meters and square meters respectively, and the resistance is expressed in ohm, ? (omega). Thus, the unit of ρ is ohm meters (? m).  Formerly, resistivity measurements were made in terms of a centimetre cube of a substance, giving ρ the unit's ? cm.

Substitute the value of R from Eq. (2) in Eq. (3). The given expression for the conductance, G is

G =   1/R = 1/ρ (A/l) = κ A/l

where K (kappa) is reciprocal of specific resistance called as specific conductance or conductivity. It is measured within ?^-1 m^-1. This quantity may be considered to be the conductance of a cubic material of edge length unity. However, in SI system, the unit for conductance is 'Siemens' and, given the symbol 'S'. Therefore, the unit for conductivity will be S m-1 (1S = 1?^-1) or S cm^-1. It may be remembered that S m^-1 = 1/100 S cm^-1. However conductivity is customarily reported in smaller units as milli Siemens per meter (mS m^-1) and micro Siemens per cm (µS cm^-1).