Conductivity ($$K$$):It is the conductance of unit cube of material. S.I unit is S/m. Common unit is S/cm.The conductivity of an electrolytic solution always decreases with decrease in concentration that is on dilution. This is because with dilution, the degree of dissociation increases and the total number of current-carrying ions increases but the number of ions per unit volume decreases.Molar conductivity $$\\Lambda$$:It is the ratio of the electrolytic conductivity k to the molar concentration C of the dissolved electrolyte. $$\\displaystyle \\Lambda = \\dfrac {k}{C}$$It is also defined as the conductance of a volume of solution containing 1 mole of dissolved electrolyte when placed between parallel electrodes 1 cm apart and large enough to contain between them all the solution.The S.I unit of molar conductivity is $$\\displaystyle  S \\: m^2 \\: /mol$$The common unit of molar conductivity is $$\\displaystyle  S \\: cm^2 \\: /mol$$The molar conductivity of strong and weak electrolytes increases with dilution (i.e, decrease in the concentration). This is because with dilution, the degree of dissociation increases and the total number of current-carrying ions increases.