Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimensions [ML² T⁻²]
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns (N) to its double (2 N), then the voltage sensitivity doubles.
D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E. Current sensitivity of MCG depends inversely on number of turns of coil.
Choose the correct answer from the options given below:

Solution

Physics sir · 2 steps

Write both sensitivities side by side. More turns also means more coil resistance, and that cancels out.

1. The two sensitivities. In an MCG the coil settles where NIAB = kφ, with k the torsional constant. Current sensitivity is deflection per unit current. Voltage sensitivity is deflection per unit voltage, and V = IG, where G is the coil resistance.

   φ/I = NAB/k, φ/V = NAB/kG

   Statement	Check	Verdict
   A	k = τ/φ and the angle has no dimensions, so [k] = [τ] = [ML²T⁻²]	True
   B	Raising N raises φ/I, but the longer wire raises G too, so φ/V need not rise	True
   C	N → 2N doubles NAB/k and also doubles G, so φ/V stays the same	False
   D	An ammeter needs a small shunt in parallel, so that most of the current bypasses the coil	False
   E	φ/I = NAB/k is directly proportional to N, not inversely	False

2. So. Only A and B are correct, which is option (b).

The idea to keep. Current sensitivity is NAB/k. Voltage sensitivity divides that by the coil resistance G, and G grows with N, so adding turns does not help voltage sensitivity.

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