Question:
If the conductivity of mercury at $0^{\circ} \mathrm{C}$ is $1.07 \times 10^{6}$ $\mathrm{S} \mathrm{m}^{-1}$ and the resistance of a cell containing mercury is $0.243 \Omega$, then the cell constant of the cell is $\mathrm{x} \times 10^{4} \mathrm{~m}^{-1}$. The value of $\mathrm{x}$ is .(Nearest integer)
Solution:
$\mathrm{k}=1.07 \times 10^{6} \mathrm{Sm}^{-1}, \quad \mathrm{R}=0.243 \Omega$
$\mathrm{G}=\frac{1}{\mathrm{R}}=\frac{1}{0.243} \Omega^{-1}$
$\mathrm{k}=\mathrm{G} \times \mathrm{G}^{*}$
$\mathrm{G}^{*}=\frac{\mathrm{k}}{\mathrm{G}}=\frac{1.07 \times 10^{6}}{\frac{1}{0.243}} \simeq 26 \times 10^{4} \mathrm{~m}^{-1}$