Question

Three identical cells are connected across potentiometer as shown in figure. When switch S is open, null deflection length of potentiometer wire is 250 cm and when S is closed it is 200 cm. Then internal resistance of each cell is(up to two decimal places)

Answer 1

When S is open $\Rightarrow \left(\frac{V_{AB}}{L_{AB}}\right)\times 250=\in +\in -\in \frac{V_{AB}}{L_{AB}}=\frac{\in }{250}-\left(1\right)$
When S is closed $\Rightarrow \in -3ir=2i=\frac{V_{AB}}{L_{AB}}\times 200-\left(2\right)$
$\in -3ir=\frac{\in }{250}\times 200\Rightarrow \frac{\in }{5}=3ir$

$15ir=(2+3r)i\Rightarrow 12r=2\Rightarrow r=\frac{1}{6}=0.17\Omega$