Question

The balancing length for a cell is $560cm$ in a potentiometer experiment. When an external resistance of $10\Omega$ is connected in parallel to the cell, the balancing length changes by $60cm$. If the internal resistance of the cell is $\frac{N}{10}\Omega$, where N is an integer then value of N is ______.

Answer 1

Let the emf of cell be E and internal resistance is r.

Let the potential gradient of potentiometer wire be x.

Case 1. When only the cell is connected

Ref. image I

$\because$ In balanced condition current through galvanometer $=0$

So, $V_{AB}=V_{DF}=500x$

$V_{DF}=560x$

$E=560x$

Case 2. When $10\Omega$ Resistor is connected in parallel

Ref. image II

$V_{A{B}^{\prime }}=V_{DF}=V_{MN}$

$i=\frac{E}{r+10}$

$V_{A{B}^{\prime }}=V_{MN}$

$500x=i10=\left(\frac{E}{r+10}\right)\times 10$

$500x=\left(\frac{560x}{r+10}\right)\times 10$

$r+10=11.2$

$r=1.2$

$\because r=\frac{N}{10}=1.2$

$\Rightarrow N=12$