Question

In an experiment to measure the internal resistance of a cell by potentiometer, it is found that the balance point is at a length of $2 \, \text{m}$ when the cell is shunted by a $4 \, \Omega$ resistance and at $3 \, \text{m}$ when cell is shunted by a $8 \, \Omega$ resistance. The internal resistance of cell is -

• A. $12 \, \Omega$
• B. $8 \, \Omega$
• C. $16 \, \Omega$
• D. $1 \, \Omega$

Answer 1

Answer: (B)

$V_{A}-V_{B}=\phi\times l \, $
$E-\frac{E r}{r + 4}=\phi\times 2$ ....(i).
$E\left(\frac{4}{r + 4}\right)=\phi\times 2$ .... (i)
Similarly, $E\left(\frac{8}{r + 8}\right)=\phi\times 3$ ....(ii)
$\frac{e q_{1}}{e q_{2}}\Rightarrow \frac{r + 8}{2 \left(r + 4\right)}=\frac{2}{3}\Rightarrow 3r+24=4r+16\Rightarrow r=8\Omega$