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)

$1.0\,\,\Omega$

Answer 2

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
$r=\left(\frac{\varepsilon}{V}-1\right)$
$R=\left(\frac{6}{5}-1\right)$
$5=1.0 \Omega$