The reciprocal of resistivity is known as specific conductance orsimply conductivity. It is denoted by k (kappa). Thus, if k is the specificconductance and G is the conductance of the solution, then
=R=

1

G

and ρ=

1

κ

∴‌

1

G

=

1

κ

×

l

A

,
κ=G×

l

A

Now, if l=1cm and A=1sq.cm, then κ = G.
Hence, conductivity of a solution is defined as the conductance of asolution of 1 cm length and having 1 sq. cm as the area of cross-section.Alternatively,it may be defined as conductance of one centimetre cube ofthe solution of the electrolyte.
Molar conductivity of a solution at a dilution V is the conductance of allthe ions produced from 1 mole of the electrolyte dissolved in V cm‌3ofthe solutionwhen the electrodes are one cm apart and the area of theelectrodes is so large that the whole of the solution is contained betweenthem. It is represented by Δm.
λm=

κA

l

Since l=1 cm and A=V (volume containing 1 mole ofelectrolyte)
λm=κVVariation of conductivityand molar conductivity withconcentration : Conductivityalways decreases withdecrease in concentration,for both weak and strongelectrolytes. This is becausethe number of ionsper unitvolume that carry the currentin a solution decreases ondilution.
Molar conductivity increases with decrease in concentration. This isbecause that total volume, V, of solution containing one mole of electrolytealso increases. It has been foundthat decrease in k on dilution of a solutionis more than compensated by increase in its volume.