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(D) The potential gradient $k$ is defined as the potential difference per unit length of the wire.$k = \frac{V}{L}$According to Ohm's law,the potentia

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$\frac{I \rho}{A}$

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(D) The potential gradient $k$ is defined as the potential difference per unit length of the wire.$k = \frac{V}{L}$According to Ohm's law,the potential difference $V$ across a wire of resistance $R$ is $V = I R$.Substituting the expression for resistance $R = \frac{\rho L}{A}$,we get:$V = I \left( \frac{\rho L}{A} \right)$Now,substituting this into the potential gradient formula:$k = \frac{I (\rho L / A)}{L}$$k = \frac{I \rho}{A}$Thus,the potential gradient is $\frac{I \rho}{A}$.

Let $A$ be the cross-sectional area and $\rho$ be the specific resistance (resistivity) of a potentiometer wire. If $I$ is the current passing through the wire,then the potential gradient along the length of the wire is

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