In the given circuit, the resistance of the galvanometer is \( G = 100\,\Omega \). Resistance box R contributes \( 4900\,\Omega \). When key K is closed, the needle of the galvanometer deflects to the 20th division. The figure of merit of the galvanometer is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 2 \times 10^{-5}\,\mathrm{A/div} \)
The figure of merit of a galvanometer is the current needed for a deflection of one division. The cell, the galvanometer and the resistance box are in series, so the current follows from Ohm's law.
\( E = 2\,\mathrm{V} \)
\( G + R = 100 + 4900 = 5000\,\Omega \)
\( \displaystyle I = \frac{E}{G + R} = \frac{2}{5000} = 4\times10^{-4}\,\mathrm{A} \)
\( \displaystyle \text{Figure of merit} = \frac{I}{\theta} = \frac{4\times10^{-4}\,\mathrm{A}}{20\,\mathrm{div}} = 2\times10^{-5}\,\mathrm{A/div} \)