[GKRM2727]

My textbook states that the conductivity of an electrolytic cell κ  depends upon the concentration of ions in the cell. However it doesn't state about the dependence . Does it increase linearly or what ?
I know the relation of molar conductivity with concentration for strong electrolytes.
κ.V= Λ⁰-A√C
The volume V contains 1 mole of electrolyte.
Or
κ= (Λ⁰-A√C) C

Does this relation help in any way?

I also thought about the relation from physic regarding metallic conductors and conductivity
σ=neμ
Where n represents the electron density of the conductors , e is the charge on electron and μ is the mobility of electrons. This suggest linear relationship between concentration and conductivity.

Here
 1. Λ°= Limiting Molar conductivity

 2. κ= Conductivity or specific conductance of electrolytic cell

 3. A is some constant dependent upon the nature of electrolyte

 4. C is the concentration of electrolyte

 Thanks in advance.

[Borek]

It is linear for diluted solutions, it gets complicated for concentrated ones. Unfortunately "concentrated" starts around 0.1 M.

[Enthalpy]

For very dilute aqueous electrolytes, the conductivity drops very linearly. From some Ω×m at common solutions, the resistivity climbs to ~10MΩ×m for very carefully deionized water at room temperature. Since pure water conducts little, resistivity is a means to characterise the purity of water, notably in the semiconductor industry.

Pure water can even serve as an insulator for a short time, and then its permittivity of 80 and good breakdown field store much energy in little volume. And now I have an excuse to link to nice pictures:
http://www.sandia.gov/z-machine/
(the older design with sparks at the surface)