Conductivity is defined as the conduction of ions when the distance between the electrodes is 1 cm and length is 1 cm.
Say for instance we have a solution where the distance between the electrodes is 2 cm and its height is also 2 cm, what will be the resulting conductivity of the solution?
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sigh... lifted out of Definitions section of wikipedia article on Conductivity (electrolytic)
Resistance, $R$, is proportional to the distance, $l$, between the electrodes and is inversely proportional to the cross-sectional area of the sample, $A$. Writing $\rho$ (rho) for the specific resistance (or resistivity),
$R={\frac {l}{A}}\rho$
In practice the conductivity cell is calibrated by using solutions of known specific resistance, $\rho^*$, so the quantities $l$ and $A$ need not be known precisely. If the resistance of the calibration solution is $R^*$, a cell-constant, $C$, is derived.
$ R^{*}=C\times \rho ^{*}$
The specific conductance (conductivity), $\kappa$ (kappa) is the reciprocal of the specific resistance.
$\kappa ={\frac {1}{\rho }}={\frac {C}{R}} $
So if $l_1 = 1 \text{ cm}$, $A_1 = 1 \text{ cm}^2$ but $l_2 = 2\text{ cm}$, $A_2 = 4 \text{ cm}^2$
$\kappa_1 ={\frac {C}{R}} $
$\kappa_2 ={\frac {2C}{R}} = 2\kappa_1 $
