Explain the measurement and calculation of the resistivity of an electrolytic solution.

(N/A) To measure the resistivity of an electrolytic solution,we first determine the conductivity cell constant $G^*$. By using this cell,we measure the resistance and ionic conductivity of the solution.
$(A)$ Measurement of resistance of solution: The setup for the measurement of the resistance is shown in the figure. It consists of two known resistances $R_3$ and $R_4$,a variable resistance $R_1$,and the conductivity cell having the unknown resistance $R_2$. The Wheatstone bridge is fed by an oscillator $O$ (a source of $a.c.$ power in the audio frequency range $550$ to $5000$ cycles per second). $P$ is a suitable detector (a headphone or other electronic device),and the bridge is balanced when no current passes through the detector.
$(B)$ Calculation for resistance of solution: In the balanced condition,the unknown resistance $R_2$ of the solution is obtained by the formula:
$R_2 = \frac{R_1 R_4}{R_3} = R$
These days,inexpensive conductivity meters are available. Electric resistance $R$ is measured in ohm $(\Omega)$. The relationship between resistance,resistivity,and cell constant is:
$R = \rho \left( \frac{l}{A} \right) = \frac{1}{\kappa} \left( \frac{l}{A} \right) = \frac{G^*}{\kappa}$
Where,
$R = \text{Resistance}$
$G^* = \text{Cell constant} = \frac{l}{A}$
$\rho = \text{Resistivity}$
$\kappa = \text{Conductivity of solution}$
Thus,resistivity $\rho$ can be calculated as $\rho = R \left( \frac{A}{l} \right) = \frac{R}{G^*}$.