What is the relation between cell constant, conductivity and electrical resistance?
What is the relation between cell constant, conductivity and electrical resistance?
$\mathrm{k}=\frac{\mathrm{R}}{\mathrm{b}}$
$\mathrm{k}=\frac{\mathrm{b}}{\mathrm{R}}$
$\mathrm{k}=\frac{1}{\mathrm{R} . \mathrm{b}}$
$\mathrm{k}=\mathrm{R} \cdot \mathrm{b}$
Solution
We know that cell constant G* \(=\frac{1}{A}\) where \(I\) is length and \(a\) is area of cross section and \(R=\rho \frac{1}{A}\)
\(\rho\) is specific resistance, \(R\) is resistance
The inverse of resistivity, called conductivity (specific conductance). Hence, \(\mathrm{k}\) - is specific conductance which is inverse of \(\rho\).
\(\therefore \mathrm{k}=\frac{1}{\rho}, \rho=\frac{1}{\mathrm{k}}\)
Substituting the value of \(\rho\) and \(\frac{1}{A}\) in equations \(R=\frac{\rho l}{A}\)
\(\mathrm{R}=\frac{1}{\mathrm{k}} \times \mathrm{G} * \text {. }\)
or \(\mathrm{k}=\frac{\mathrm{G}^*}{\mathrm{R}}\)