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Two tangent galvanometers, A and B, have coil radii of 8 cm and 16 cm respectively, and each has a resistance of 8 $\Omega$. They are joined in parallel. When the applied voltages are 4 V and 6 V respectively, the corresponding deflections in A and B are 30$^\circ$ and 60$^\circ$. If galvanometer A has 2 turns, the number of turns in B is

1. 18 turns
2. 12 turns
3. 6 turns
4. 2 turns

Correct answer: 18 turns

Solution

For a tangent galvanometer, $\tan\theta \propto NIA$ for the same horizontal magnetic field. Since both have the same resistance and are in parallel, the currents are proportional to the applied voltages. Using the given deflections and radii, the turn ratio comes out to 9:1, so if A has 2 turns, B has 18 turns.

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