Question

The length of a potentiometer wire is $l$. A cell of emf $E$ is balanced at a length $l/3$ from the positive end of the wire. If the length of the wire is increased by $l/2$. At what distance will the same cell give a balance point?

• A. $\frac{2l}{3}$
• B. $\frac{l}{2}$
• C. $\frac{l}{6}$
• D. $\frac{4l}{3}$

Answer 1

The correct option is B $\frac{l}{2}$

Potential gradient , $K=\frac{V}{L}$

Here, $K_1=\frac{V}{l},K_2=\frac{V}{\left(3/2\right)l}=\frac{2}{3}{K}_1$

Now, $\frac{E_1}{E_2}=\frac{K_1{l}_1}{K_2{l}_2}$

or $\frac{E}{E}=\frac{\left(K_1\right)\left(l/3\right)}{\left(2/3\right)K_1{l}_2}$

or $l_2=\frac{l}{2}$