In the experiment to determine the galvanometer resistance by half-deflection method, the plot of 1 / θ vs the resistance (R) of the resistance box is shown in the figure. The figure of merit of the galvanometer is _________ × 10⁻¹ A / division. [The source has emf 2 V]

Solution

Physics sir · 4 steps

Write 1/θ as a straight line in R; the slope is the figure of merit divided by the emf.

1. Current and deflection. The resistance box R is in series with the galvanometer G, so I = E/(R+G). The figure of merit k is the current per division, so I = kθ.

   1/θ = k/I = k/E R + k/E G

2. Read the slope. The line rises from 1/2 at R = 0 to 2 at R = 6 Ω. So the slope is (2 - 0.5)/6 = 0.25 div⁻¹ Ω⁻¹.
3. Solve for k. Slope = k/E, so k = 0.25 × 2 = 0.5 A/div. As a check, the intercept gives G = 0.5/0.25 = 2 Ω.
4. So. The figure of merit is 0.5 A/div = 5 × 10⁻¹ A/div, so the answer is 5.

The common slip: 20. Treating the slope as 1/kE instead of k/E gives k = 2 A/div, which is 20 in these units, not 5.

The idea to keep. Figure of merit means current per division, I = kθ. Turn the circuit equation into a straight line and match its slope and intercept to the graph.

Answer from the NTA final answer key. Solution by PrepWiser.