Question

If the conductivity of mercury at $0^{\circ} C$ is $1.07 \times 10^{6}$ $S m ^{-1}$ and the resistance of a cell containing mercury is $0.243 \,\Omega$, then the cell constant of the cell is $x \times 10^{4} \,m ^{-1}$. The value of $x$ is _____.(Nearest integer)

Answer 1

$ k =1.07 \times 10^{6} Sm ^{-1}, $
$ R =0.243\, \Omega $
$ G =\frac{1}{ R }=\frac{1}{0.243} \Omega^{-1} $
$ k = G \times G ^{*}$
$G^{*} =\frac{ k }{ G }=\frac{1.07 \times 10^{6}}{\frac{1}{0.243}} \simeq 26 \times 10^{4}\, m ^{-1}$