Conductivity (unit $S$) is directly proportional to the area of the vessel $(A)$ and the concentration of the solution $(C)$ in it,and is inversely proportional to the length of the vessel $(l)$. The unit of the constant of proportionality is:

What is the relation between cell constant,conductivity and electrical resistance?

The unit of equivalent conductivity is

Resistance and conductivity of a cell containing $0.1 \ M \ KCl$ solution at $298 \ K$ are $115 \ \Omega$ and $1.90 \times 10^{-6} \ S \ cm^{-1}$ respectively. What is the value of cell constant (in $cm^{-1}$)?

Resistance of a conductivity cell (cell constant $129 \; m^{-1}$) filled with $74.5 \; ppm$ solution of $KCl$ is $100 \; \Omega$ (labelled as solution $1$). When the same cell is filled with $KCl$ solution of $149 \; ppm$,the resistance is $50 \; \Omega$ (labelled as solution $2$). The ratio of molar conductivity of solution $1$ and solution $2$ is i.e.,$\frac{\wedge_{1}}{\wedge_{2}} = x \times 10^{-3}$. The value of $x$ is (Nearest integer). Given,molar mass of $KCl$ is $74.5 \; g \; mol^{-1}$.

Calculate the molar conductivity of $NH_4OH$ at infinite dilution if the molar conductivities of $Ba(OH)_2$,$BaCl_2$,and $NH_4Cl$ at infinite dilution are $520$,$280$,and $129 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ respectively.