Question

In a potentiometer experiment, a cell in the secondary circuit gives null point at $\text{2.5} \, m$ when the length of the potentiometer wire is $10 \, m.$ If the length of the potentiometer wire is increased by $1 \, m$ without changing the cell in the primary circuit, then the position of the null point will be

• A. $3.5m$
• B. $3m$
• C. $2.75 \, m$
• D. $2m$

Answer 1

Answer: (C)

The resistance of a potentiometer wire is given as,
$R=\rho \times \frac{l}{A}$
$R^{'}=\frac{2 .5 \rho }{A \times 10}$
Potential $V'=I\times R'$ ,
$=I \left\{\frac{\text{2.5} \rho }{A ⁡ \times 10}\right\}$
Now, again the length of potentiometer wire is increased by $1 \, m$ , then the resistance of null position wire.
$\mathrm{R}^{\prime \prime}=\frac{\rho \times 1}{11 \times \mathrm{A}}$
$V"=IR"$
and, $V'=V"$
$\frac{I \times 2 .5 \rho }{A \times 10}=\frac{I \times \rho \times l}{11 \times A}$
$\frac{2 .5 \times 11}{10}=l=\text{2.75} \, m$