Let $A$ be the cross-sectional area and $\rho$ be the specific resistance of a potentiometer wire. If $I$ is…
Let $A$ be the cross-sectional area and $\rho$ be the specific resistance of a potentiometer wire. If $I$ is the current passing through the wire, then the potential gradient along the length of the wire is
$\frac{I}{\rho A}$
$\frac{I A}{\rho}$
$I A \rho$
$\frac{I \rho}{A}$
Solution
Potential gradient $=$ Potential difference per unit length . So,
$k=\frac{V}{L}=\frac{I R}{L}=\frac{I(\rho L / A)}{L}=\frac{I \rho}{A}$
.