Question

A potentiometer circuit has been set up for finding the internal resistance of a given cell. The main battery, used across the potentiometer wire, has an emf of $2\text{V}$ and a negligible internal resistance. The potentiometer wire itself is $4\text{m}$ long. When the resistance $R$ is connected across the given cell has value of $\left(i\right)$ infinity, $\left(ii\right)9.5\Omega$ the balancing length on the potentiometer wire are found to be $3\text{m}$ and $2.85\text{m}$ respectively. The value of internal resistance of the cell is

• A. $0.25\Omega$
• B. $0.95\Omega$
• C. $0.5\Omega$
• D. $0.75\Omega$

Answer 1

The correct option is C $0.5\Omega$

Given,
$l_1=3\text{m},$
$l_2=2.85\text{m}$,
$R=9.5\Omega$

Using, $r=(\frac{l_1}{l_2}-1)\times R$
$r=(\frac{3}{2.85}-1)\times 9.5$
$\therefore r=\frac{0.15}{2.85}\times 9.5=0.5\Omega$