For a certain value of torsional constant \( K \) and number of turns \( N \) current sensitivity of a moving coil galvanometer is \( 30' \) per \( \mu \)A. If number of turns are tripled and value of \( K \) is halved keeping other things constant, current sensitivity will become
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 3^{\circ} \) per \( \mu \)A
The current sensitivity of a moving coil galvanometer is the deflection per unit current:
\( \displaystyle \frac{\phi}{I} = \frac{NAB}{K} \)
With A and B unchanged, current sensitivity \( \propto N/K \).
\( \displaystyle \frac{S_2}{S_1} = \frac{N_2}{N_1}\times\frac{K_1}{K_2} = 3\times2 = 6 \)
\( S_2 = 6\times30' = 180' \)
\( 60' = 1^{\circ} \Rightarrow S_2 = 3^{\circ} \text{ per } \mu\mathrm{A} \)