Question

A potentiometer wire PQ of $1\text{m}$ length is connected to a standard cell $E_1$ . Another cell $E_2$ of emf $1.02\text{V}$ is connected with a resistance ${}^{\prime }{r}^{\prime }$ and switch $S$ (as shown in figure). With switch $S$ open, the null position is obtained at a distance of $49\text{cm}$ from $Q$. The potential gradient in the potentiometer wire is

• A. $0.02\text{V/cm}$
• B. $0.01\text{V/cm}$
• C. $0.03\text{V/cm}$
• D. $0.04\text{V/cm}$

Answer 1

The correct option is A $0.02\text{V/cm}$

Potential gradient, $x=\frac{\text{Potential drop}}{\text{length}}$
Here, Potential drop $=1.02\text{V}$
Balancing length from $P=100–49\text{cm}$
$\therefore x=\frac{1.02}{100-49}=0.02\text{V/cm}$