Question

A potentiometer having a wire of $4$ $m$ length is connected to the terminals of a battery with a steady voltage. A leclanche cell has a null point at $1$ $m$. If the length of the potentiometer wire is increased by $1$ $m$, the position of the null point is

• A. $1.5$ $m$
• B. $1.25$ $m$
• C. $10.05$ $m$
• D. $1.31$ $m$

Answer 1

Answer: (B)

$1.25$ $m$

Let the resistance per unit length of potentiometer wire be $r$ and EMF of battery connected across it's length is $E$.
the initially the resistance $=$ $4r$
let the balancing length initially, be $l_1=1m$
$E_1=I_{1}r\times l_1$

where$\left[I_1\right(4r)=E]$
final resistance $=$ 5r
let the balancing length $=l_2$
then $E_2=I_2\times r\times l_2$

where $\left[I_2\right(5r)=E]$
$\Rightarrow \frac{E_1}{E_2}=\frac{I_1{l}_1}{I_2{l}_2}$
as $[E_1=E_2]$
${\Rightarrow I}_2{l}_2=I_1{l}_1$
$l_2=\times 1$
$l_2=5/4=1.25m$