A galvanometer connected to a cell of negligible internal resistance shows a deflection of 25 divisions. When a resistor of \( 20\,\Omega \) is connected in series with it, the deflection falls to 5 divisions. The resistance of the galvanometer is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 5\,\Omega \)
The deflection of a galvanometer is proportional to the current through it. The cell has emf \( \varepsilon \) and negligible internal resistance. The current is \( \varepsilon/G \) through the galvanometer alone. With the resistor in series, it is \( \varepsilon/(G+20\,\Omega) \).
The ratio of the two deflections is the ratio of the currents:
\( \displaystyle \frac{25}{5}=\frac{\varepsilon/G}{\varepsilon/(G+20\,\Omega)} \)
\( \displaystyle 5=\frac{G+20\,\Omega}{G} \)
\( 5G=G+20\,\Omega \)
\( \Rightarrow\; G=5\,\Omega \)