Question

A potentiometer wire has length $10\text{m}$ and resistance $10\Omega$. It is connected to a battery of emf $11\text{V}$ and internal resistance $1\Omega$, then the potential gradient in the wire is

• A. $10\text{V/m}$
• B. $1\text{V/m}$
• C. $0.1\text{V/m}$
• D. none

Answer 1

The correct option is B $1\text{V/m}$

Given,
$E=11\text{V};r=1\Omega ;R=10\Omega$


So, current $i$ passing through circuit will be
$i=\frac{E}{r+R}=\frac{11}{1+10}$

$\therefore i=1\text{A}$

So, potential drop across wire $\text{AB}$ will be

$V_{AB}=iR=1\times 10=10\text{V}$

Therefore, potential gradient $K$ is

$K=\frac{V_{AB}}{L}=\frac{10}{10}=1\text{V/m}$

Hence, option $\left(b\right)$ is correct.