Question

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

Answer 1

The formula for the internal resistance of the battery using potentiometer is given by,

$r=\left(\frac{l_o-l_c}{l_c}\right)R$

Where,
$l_o\to \text{balancing length when battery is}\text{in open circuit}$
$l_c\to \text{balancing length when battery is}\text{shunted by an external resistance R}$

Here, $l_o=560\text{cm},l_c=560-60=500\text{cm}$

$\Rightarrow r=\frac{60}{500}\times 10$

$\Rightarrow r=\frac{6}{5}$

Given that, $r=\frac{N}{10}$

$\Rightarrow \frac{N}{10}=\frac{6}{5}$

$\Rightarrow N=12$

Hence, $12$ is the correct answer.