Question

A potentiometer consists of a wire of length 4m and resistance 10$\Omega$. It is connected to a cell of e.m.f. 3V. The potential gradient of wire is

• A. 0.75 V/m
• B. 2 V/m
• C. 6 V/m
• D. 10 V/m

Answer 1

The correct option is A 0.75 V/m

$\text{Step 1: Potentiometer Figure}$

Using KVL in above simple circuit of 1 loop, we get current $I=\frac{V}{R}=\frac{3}{10}=0.3A$

AB is potentiometer wire

From figure we can say that potential difference across AB will be equal to e.m.f of cell.

$V_{AB}=E=3V$, Also $V_{AB}=IR$

$\Rightarrow V_{AB}=0.3\times 10=3V$

$\text{Step 2: Potential gradient calculation}$

Potential gradient $K=\frac{V_{AB}}{L}$

$=\frac{3}{4}=0.75V/m$

Hence, Option $A$ is correct.