In an ammeter, \(0.25 \%\) of main current passes through the galvanometer. If the resistance of the galvanometer is ' \(G\) ', the resistance of ammeter will be

\(\begin{aligned}
& \mathrm{I}=\mathrm{I}_{\mathrm{g}}+\mathrm{I}_{\mathrm{s}} \\
& \mathrm{I}=\frac{0.25 \mathrm{I}}{100}+\mathrm{I}_{\mathrm{s}} \\
& \mathrm{I}_{\mathrm{s}}=\frac{399}{400} \mathrm{I} ...(i)\\
& \mathrm{I}_{\mathrm{g}} \mathrm{G}=\mathrm{I}_{\mathrm{s}} \mathrm{~S} \\
& \mathrm{~S}=\frac{0.25}{100} \times \frac{400}{399} \times \mathrm{G} \\
& \mathrm{~S}=\frac{1}{399} \mathrm{G}...(ii)
\end{aligned}\)
...[From (i)]
Total resistance of ammeter
\(\begin{aligned}
R & =\frac{G S}{G+S} \\
& =\frac{G\left(\frac{1}{399}\right)G}{\left(G+\frac{1}{399}\right) G} \\
& =\frac{\frac{1}{\left(\frac{399}{400}\right)}}{399} G \\
R & =\frac{1}{400} G
\end{aligned}\)
...[From (ii)]