Question

The resistivity of potentiometer wire is $40\times {10}^{-8}ohm$ - metre and its area of cross-section is $8\times {10}^{-6}{m}^2$. If $0.2$ ampere current is flowing through the wire, the potential gradient of the wire is:

• A. ${10}^{-1}V/m$
• B. ${10}^{-2}V/m$
• C. ${10}^{-3}V/m$
• D. ${10}^{-4}V/m$

Answer 1

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

Given : $\rho =40\times {10}^{-8}ohm-m$ $I=0.2$ A $A=8\times {10}^{-6}{m}^2$

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

Potential difference across the wire $V=IR=I\rho \frac{L}{A}$

Thus potential gradient of the wire $\frac{V}{L}=\frac{I\rho }{A}$

$\therefore$ $\frac{V}{L}=\frac{0.2\times 40\times {10}^{-8}}{8\times {10}^{-6}}$

$⟹$ $\frac{V}{L}={10}^{-2}V/m$