Question

The length of a potentiometer wire is $l$. A cell of emf $E$ is balanced at length $l/3$ from the positive end of the wire. If the length of the wire is increased by $l/2$. Then, 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

Answer: (B)

$\frac{l}{2}$

Let $x$ be the desired length.
Potential gradient in the first case $=\frac{E_0}{l}$
$E=\left(\frac{l}{3}\right)\cdot \left(\frac{E_0}{l}\right)=\frac{E_0}{3}$ .....(i)
Potential gradient in the second case.
$=\frac{E_0}{3l/2}=\frac{2E_0}{3l}$
$\therefore E=\left(x\right)\frac{2E_0}{3l}$ .....(ii)
From equations (i) and (ii), we get
$\frac{E_0}{3}=\left(\frac{2E_0}{3l}\right)x$
$\Rightarrow x=\frac{l}{2}$