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The deflection of a galvanometer falls to (1/ 10) th when a resistance of 5Ω is connected in parallel with it. If an additional resistance of 2Ω is connected in parallel to the galvanometer, the deflection falls to $\frac{2}{n}$ times the original deflection, then $n$ is ____

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answer is 65.

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Detailed Solution

Case I

Case II

Given $\frac{I_{2 g}}{I_{1 g}} = \frac{1}{10}$

$I_{2 g} = \frac{I}{10}$

$I_{2 g} (G) = (I - I_{2 g}) (5)$

$\frac{I}{10} (G) = (I - \frac{I}{10}) (5)$

$G = 45 Ω$

Case III

$I_{3 g} (G) = (I - I_{3 g}) (\frac{10}{7})$

$I_{3 g} (G) = I \times \frac{10}{7} - I_{3 g} \times \frac{10}{7}$

$I_{3 g} (45 + \frac{10}{7}) = I \times \frac{10}{7}$

$I_{3 g} = \frac{I \times \frac{10}{7}}{(\frac{325}{7})} = \frac{2}{65} I$

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