Question

If along a uniform rod of length $l$ carrying current $I$ , the voltage $V$ changes with position $x$ along the length of the rod such that $dV/dx=-k$ , where $k$ is a positive number, then the resistance of the rod is

• A. $kl/2I$
• B. $kl/I$
• C. $I/kl$
• D. $klI$

Answer 1

Answer: (B)

$dV=-IdR=-I\rho \frac{d x}{A}$
$\frac{d V}{d x}=-I\frac{\rho }{A}=-k$
$\Rightarrow R=kl/I$
II Method:
$V_{2}-V_{1}=\displaystyle \int \left(\frac{d V}{d \ell }\right)dl=kL=IR$