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)

$V_A-V_B=\varphi \times l$
$E-\frac{Er}{r+4}=\varphi \times 2$ ....(i).
$E\left(\frac{4}{r+4}\right)=\varphi \times 2$ .... (i)
Similarly, $E\left(\frac{8}{r+8}\right)=\varphi \times 3$ ....(ii)
$\frac{e{q}_1}{e{q}_2}\Rightarrow \frac{r+8}{2\left(r+4\right)}=\frac{2}{3}\Rightarrow 3r+24=4r+16\Rightarrow r=8\Omega$