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 · 05 Apr 2024 · Shift 1 · Current Electricity

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of

\frac{1}{θ}

vs the resistance (R) of the resistance box is shown in the figure. The figure of merit of the galvanometer is ______

\times 1 0^{- 1} A

/division. [The source has emf 2V]

Answer: 5

In the half-deflection method

i = K θ

, and with the resistance box

R

in series,

\frac{1}{θ} = \frac{1}{K} \cdot \frac{R}{E} + const,

so that the slope of the

\frac{1}{θ}

R

line equals

\frac{K}{2}

for the given circuit. Reading the slope

= \frac{1}{4}

from the graph gives

K = 0.5 = 5 \times 1 0^{- 1}

A/division. Hence the figure of merit is

5

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Integer answer