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(A) The internal resistance $r$ of a cell using a potentiometer is given by the formula:$r = \left( \frac{l_1}{l_2} - 1 \right) R$where $l_1$ is the b

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$0.5$

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(A) The internal resistance $r$ of a cell using a potentiometer is given by the formula:$r = \left( \frac{l_1}{l_2} - 1 ight) R$where $l_1$ is the balancing length when the cell is in an open circuit (i.e.,$R = \infty$) and $l_2$ is the balancing length when an external resistance $R$ is connected across the cell.Given:$l_1 = 3\,m$$l_2 = 2.85\,m$$R = 9.5\,\Omega$Substituting the values into the formula:$r = \left( \frac{3}{2.85} - 1 ight) 	imes 9.5\,\Omega$$r = \left( \frac{3 - 2.85}{2.85} ight) 	imes 9.5\,\Omega$$r = \left( \frac{0.15}{2.85} ight) 	imes 9.5\,\Omega$$r = \frac{15}{285} 	imes 9.5\,\Omega$$r = \frac{1}{19} 	imes 9.5\,\Omega = 0.5\,\Omega$Thus,the internal resistance of the cell is $0.5\,\Omega$.

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