Q 12-04-073JEE MainJEE Main 2024 (5 Apr, Shift 1)Hard
In the experiment to determine the galvanometer resistance by the half-deflection method, the plot of $1/\theta$ vs the resistance ($R$) of the resistance box is shown in the figure. The figure of merit of the galvanometer is ______ $\times10^{-1}\ \text{A/division}$. [The source has emf $2\ \text{V}$]
Numerical value type. Enter your answer.
Answer: 5
With the galvanometer (resistance $G$, figure of merit $k$) in series with $R$ across the source:
$$k\theta = \frac{E}{R + G} \Rightarrow \frac1\theta = \frac{k}{E}R + \frac{kG}{E}$$
From the graph, slope $= \dfrac{2 - 1}{6 - 2} = 0.25\ \Omega^{-1}\text{div}^{-1}$.
$$k = 0.25\times E = 0.25\times2 = 0.5\ \text{A/div} = 5\times10^{-1}\ \text{A/div}$$
Solution by Sreeraj P, M.Sc Physics