Question

The resistivity of potentiometer wire is ${10}^{-7}\Omega m$ and its area of cross-section is ${10}^{-6}{m}^2$. When a current $i=0.1A$ flows through the wire, its potential gradient is

• A. ${10}^{-2}V/m$
• B. ${10}^{-4}V/m$
• C. $0.1V/m$
• D. $10V/m$

Answer 1

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

Given, $\rho ={10}^{-7}\Omega m,A={10}^{-6}{m}^2$and $\frac{dV}{dx}=?$
$\frac{dV}{dx}=\frac{iR}{l}\Rightarrow \frac{i\rho l}{Al}$
$\frac{dV}{dx}=\frac{i\rho }{A}$
$=\frac{{10}^{-1}\times {10}^{-7}}{{10}^{-6}}={10}^{-2}V/m$