Question

A battery is connected to a potentiometer and the balance point is obtained at $84\text{cm}$ along the wire. When its terminals are connected by a $5\Omega$ resistor, the balance point changes to $70\text{cm}$.

$\left(i\right)$ Calculate the internal resistance of the cell.

​​​​​​​$[$1 Mark$]$

• A. $4\Omega$
• B. $2\Omega$
• C. $5\Omega$
• D. $1\Omega$

Answer 1

The correct option is D $1\Omega$

The formula for internal resistance $r$ of cell using potentiometer is given by
$r=\left(\frac{l_1-l_2}{l_2}\right)R$
Where
$l_1$ - Balancing length when only the battery is connected.
$l_2$ - Balancing length when the battery is shunted by a resistance
$r=\left(\frac{84-70}{70}\right)\times 5=\frac{14}{70}\times 5$
$r=1\Omega$
$\therefore$ option $\left(d\right)$ is correct.