Question

Resistivity of a potentiometer wire is $2\times {10}^{-4}ohm-m$.If 1mA current is flowing through it, what is the potential gradient?$(V/m)$ (take cross-sectional area =1)

• A. 0.2
• B. $2\times {10}^{-7}$
• C. $2\times {10}^7$
• D. 2

Answer 1

The correct option is B $2\times {10}^{-7}$

Given,

$\rho =2\times {10}^{-4}\Omega -m$

$I=1mA=1\times {10}^{-3}A$

$A=1m^2$

The potential gradient, $\frac{dV}{dx}=\frac{\rho I}{A}$

$\frac{dV}{dx}=\frac{2\times {10}^{-4}\times {10}^{-3}}{1}$

$\frac{dV}{dx}=2\times {10}^{-7}V/m$

The correct option is B.