Question

In the potentiometer circuit shown in the figure, the balance length $AJ = 58$ when switch $S$ is open. When switch S is closed and the value of $ R=5\,\Omega $ , balance length $AJ' = 50 \,cm$. The internal resistance of the cell $C'$ is

• A. $ 1.2\,\Omega $
• B. $ 1.0\,\,\Omega $
• C. $ 0.8\,\,\Omega $
• D. $ 0.6\,\,\Omega $

Answer 1

Answer: (B)

Here, $l_{1}=60\,cm$,
$l_{2}=50\,cm$,
$R=5\, \Omega$
$\varepsilon=kl_{1}$
where $k$ is the potential gradient across the wire $V=Kl_{2}$
$\therefore \frac{\varepsilon}{V}=\frac{l_{1}}{l_{2}}$
$=\frac{60}{50}=\frac{6}{5}$
Internal resistance of the cell is
$r=\left(\frac{\varepsilon}{V}-1\right)$
$R=\left(\frac{6}{5}-1\right)$
$5=1.0 \,\Omega$