Question

Conductivity of a cell $\left(\kappa \right)$ is equal to

where,
$R$ is resistance
$G$ is conductance
$G^{\ast }$ is cell constant
$l$ is length of the conducting cell
$A$ is cross section of cell

• A. $\frac{1}{R}\times \frac{l}{A}$
• B. $\frac{G}{G^{\ast }}$
• C. $\frac{G^{\ast }}{R}$
• D. $\frac{1}{G}\times \frac{A}{l}$

Answer 1

Answer: (A), (C)

$\frac{G^{\ast }}{R}$

The electrical resistance​ of a conductor(R) is directly proportional ​to its length (l)​ and inversely proportional to its area of cross section (A).
$R\propto \frac{l}{A}$
$R=\rho \times \frac{l}{A}$
Where,
$\rho$ is constant of proportionality
This constant of proportionality is called resistivity or specific resistance.
$\text{Specific resistance,}\rho =R\times \frac{A}{l}$
$\text{Conductance, G}=\frac{1}{\text{Resistance}}$
$\text{Resistance, R}=\rho \frac{l}{A}$

Thus,
$G=\frac{1}{\rho }\times \frac{A}{l}$

The inverse of​ resistivity is called conductivity / specific conductance $\left(\kappa \right)$.​

$G=\kappa \times \frac{A}{l}$

$\kappa =G\times \frac{l}{A}$

$\kappa =\frac{1}{R}\times \frac{l}{A}$

$\frac{l}{A}$ is the cell constant $\left(G^{\ast }\right)$ of the cell.
$\therefore$

$\kappa =G\times G^{\ast }$

$\kappa =\frac{1}{R}\times G^{\ast }$

$\kappa =\frac{G^{\ast }}{R}$