Question

A potentiometer wire, $4\text{m}$ long and resistance $12\Omega$ , is connected in series with a resistance of $1988\Omega$ and a cell of emf $2\text{V}$. What is the potential gradient along the wire ?

• A. $0.002\frac{\text{V}}{\text{m}}$
• B. $0.004\frac{\text{V}}{\text{m}}$
• C. $0.01\frac{\text{V}}{\text{m}}$
• D. $0.003\frac{\text{V}}{\text{m}}$

Answer 1

The correct option is D $0.003\frac{\text{V}}{\text{m}}$

Current in the circuit,
$i=\frac{2}{1988+12}$
$\Rightarrow i=\frac{1}{1000}A$
Voltage across, $AB$,
$V$ = $i\times R$ = $\frac{12}{1000}\text{V}$
Now, potential gradient = $\frac{V}{l}=\frac{\frac{12}{1000}}{4}=0.003\frac{\text{V}}{\text{m}}$