Conductivity of a solution is defined as the conductance of a solution of 1 cm in length and area of cross-section 1 sq. cm. The inverse of resistivity is called conductivity or specific conductance. It is represented by the symbol κ. If ρ is resistivity, then we can write: 

$\mathrm{K}=\frac{1}{\mathrm{\rho }}$

Step 2:

The conductivity of a solution at any given concentration is the conductance (G) of one unit volume of solution kept between two platinum electrodes with the unit area of cross-section and at a distance of unit length.

i.e., $\mathrm{G}=\mathrm{k}\frac{\mathrm{a}}{\mathrm{l}}=\mathrm{k}.1=\mathrm{k}$

(Since a=1, l=1)

Step 3:

Conductivity always decreases with a decrease in concentration, both for weak and strong electrolytes. This is because the number of ions per unit volume that carry the current in a solution decreases with a decrease in concentration.

Molar conductivity:

Molar conductivity of a solution at a given concentration is the conductance of volume V of a solution containing 1 mole of the electrolyte kept between two electrodes with the area of cross-section A and distance of unit length.

${\mathrm{\Lambda }}_{\mathrm{m}}=\mathrm{k}\frac{\mathrm{A}}{\mathrm{l}}$

Now, l = 1 and A = V (volume containing 1 mole of the electrolyte).

$\therefore {\mathrm{\Lambda }}_{\mathrm{m}}=\mathrm{kV}$

Step 4:

Molar conductivity increases with a decrease in concentration. This is because the total volume V of the solution containing one mole of the electrolyte increases on dilution. The variation of ${\mathrm{\Lambda }}_{\mathrm{m}} \mathrm{with} \sqrt{\mathrm{c}}$ for strong and weak electrolytes is shown in the following plot: