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

What is the relation between cell constant, conductivity and electrical resistance?
  1. $\mathrm{k}=\frac{\mathrm{R}}{\mathrm{b}}$
  2. $\mathrm{k}=\frac{\mathrm{b}}{\mathrm{R}}$
  3. $\mathrm{k}=\frac{1}{\mathrm{R} . \mathrm{b}}$
  4. $\mathrm{k}=\mathrm{R} \cdot \mathrm{b}$

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 \(\mathrm{k}=\frac{\mathrm{G}^*}{\mathrm{R}}\)

Asked in: MHT CET 2020 (15 Oct Shift 1)

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