Q.i. What is a cell constant ?

By Ohm's law, resistance $R=V/I$; conductance $G=1/R$ (unit siemens, S). Since $R=\rho\dfrac{l}{a}$ for a conductor of length $l$ and cross-section $a$, conductance follows $G=k\dfrac{a}{l}$, where $k$ (conductivity, or specific conductance) is the conductance of a unit cube (1 cm³ or 1 m³) of the solution — the SI unit is $S\,m^{-1}$, the common unit $\Omega^{-1}cm^{-1}$. Because $k$ depends on how many current-carrying ions occupy each unit volume, it always DECREASES on dilution: although the total number of ions in the whole solution rises somewhat with dilution (more of the electrolyte dissociates), that rise is never proportional to the dilution itself, so the ion density (ions per cm³) actually falls. Conductivity is measured practically using a conductivity cell (two platinised-platinum plates) and a Wheatstone bridge: the cell is first calibrated against standard KCl solution to find its cell constant ($l/a$, in cm⁻¹), after which $k=\text{cell constant}/R$ for any unknown solution placed in it.