Question

How is the electrical conductance of a conductor relates with length and area of cross section of the conductor?
where,
$G$ is conductance
$l$ is length of the conductor
$A$ is area of cross section of the conductor
$\kappa$ is conductivity

• A. $G=l\times A\times {\kappa }^{-1}$
• B. $G=\kappa \times l\times A^{-1}$
• C. $G=\kappa \times A\times l^{-1}$
• D. $G=\kappa \times l^{-1}\times A^{-1}$

Answer 1

The correct option is C $G=\kappa \times A\times l^{-1}$

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.

The inverse of the resistance ​is known as conductance.​
It is represented by ${}^{\prime }{G}^{\prime }$.
$G=\frac{1}{R}$
Thus,
$G=\frac{1}{\rho }\times \frac{A}{l}$

The inverse of​ resistivity is called conductivity / specific conductance $\left(\kappa \right)$.​
$\kappa =\frac{1}{\rho }$

Thus,
$G=\kappa \times \frac{A}{l}$
$G=\kappa \times A\times l^{-1}$