The deflection of a galvanometer falls to$\text{1/10th}$ when a resistance of$\text{5}\Omega$ is connected in parallel with it. If an additional resistance of id connected in parallel to the galvanometer, the deflection is

${\text{i}}_{\text{g}}=\frac{\text{i}}{\text{10}}$ $5=\frac{\text{G}}{10-1}$

$\therefore \text{n}=10$                                    $\text{G}=45\Omega$

(Additional Resistance$\text{=}\text{2Ω}$ ) (Missing in Q’s)

$\text{R}=\frac{5\times 2}{5+2}=\frac{45}{\text{n}-1}$

$\Rightarrow \text{n}-1=\frac{45\times \text{I}}{10}=\frac{63}{2}\Rightarrow \text{n}=\frac{65}{2}$

$\therefore \frac{\text{i}}{{\text{i}}_{\text{g}}}=\frac{65}{2}\Rightarrow \frac{{\text{i}}_{\text{g}}}{\text{i}}=\frac{2}{65}\text{th}$