In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $\frac{1}{\theta}$ vs the resistance $(R)$ of the resistance box is shown in the figure. The figure of merit of the galvanometer is .............. $\times 10^{-1} \mathrm{~A} /$ division. [The source has emf 2V]
JEE MAIN 2024, Diffcult
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$i=K \theta$
$\frac{2}{G+R}=K \theta$
$\Rightarrow \frac{1}{\theta}=\frac{(G+R) K}{2}=R\left(\frac{K}{2}\right)+\frac{K G}{2}$
$\text { Slope }=\frac{K}{2}=\frac{1}{4} \Rightarrow K=0.5=5 \times 10^{-1} A$
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