# The length of the potentiometer wire is l. A cell of emf E is balanced at length $\large\frac{l}{3}$ from the positive end of the wire. If the length of the wire is increased by $\large\frac{l}{2}$, at what distance will the same cell give a balance point

$\begin {array} {1 1} (A)\;\large\frac{l}{3} & \quad (B)\;\large\frac{l}{2} \\ (C)\;\large\frac{2l}{3} & \quad (D)\;\large\frac{3l}{4} \end {array}$

The student is expected to have an understanding of the construction of a potentiometer.
Potential gradient in the first case = $\large\frac{E_0}{l}$
$E=\large\frac{l}{3}$ $\large\frac{E_0}{l}$ $\large\frac{E_0}{3}$
In the second case $= \large\frac{2E_0}{\Large\frac{3l}{2}}$
$E = (X) \large\frac{2E_0}{\Large\frac{3l}{2}}$
On solving these two equations, we get $x = \large\frac{l}{2}$
Ans : (B)
edited Mar 14, 2014