Question

A potentiometer has uniform potential gradient. The specific resistance of the material of the potentiometer wire is ${10}^{-7}$ ohm-metre and the current passing through it is $0.1$ ampere, cross-section of the wire is ${10}^{-6}{m}^2$. The potential gradient along the potentiometer wire is:

• A. ${10}^{-6}V/m$
• B. ${10}^{-4}V/m$
• C. ${10}^{-8}V/m$
• D. ${10}^{-2}V/m$

Answer 1

The correct option is D ${10}^{-2}V/m$

Given : Resistivity $\rho ={10}^{-7}\Omega m$

Cross-section area $A={10}^{-6}{m}^2$

Current in the wire $i=0.1$ A

Resistance of the wire $R=\rho \frac{l}{A}$

Thus resistance gradient $R^{\prime }=\frac{R}{l}=\frac{\rho }{A}=\frac{{10}^{-7}}{{10}^{-6}}=0.1$

$\therefore$ Potential gradient $V^{\prime }=i{R}^{\prime }=0.1\times 0.1={10}^{-2}$ V/m