Question

The current in the primary circuit of a potentiometer is $0.2\, A$. The specific resistance and cross-section of the potentiometer wire are $4 ??10^{-7}$ ohm metre and $8 ??10^{-7} \, m^2$ respectively. The potential gradient will be equal to :

• A. 1 V/m
• B. 0.5 V/m
• C. 0.1 V/m
• D. 0.2 V/m

Answer 1

Answer: (C)

0.1 V/m

Answer 2

$x = \frac{V}{\ell} = \frac{IR}{\ell} = \frac{IR}{\ell}\left(\frac{\rho\ell}{A}\right) = \frac{I\rho}{A}$ $x = \frac{0.2\times4\times10^{-7}}{8\times10^{-7}} = \frac{0.8}{8} = 0.1\,V/m.$