Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimentions $$[ML^{2}T^{-2}]$$
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns (N) to its double (2N), 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:

Let us analyze each statement about the Moving Coil Galvanometer (MCG):

Statement A: The torsional constant has dimensions $$[ML^{2}T^{-2}]$$.

The restoring torque is $$\tau = k\theta$$, where $$k$$ is the torsional constant and $$\theta$$ is dimensionless (in radians).

So $$[k] = [\tau] = [ML^{2}T^{-2}]$$. Statement A is correct.

Statement B: Increasing the current sensitivity may not necessarily increase the voltage sensitivity.

Current sensitivity: $$I_s = \frac{NAB}{k}$$

Voltage sensitivity: $$V_s = \frac{I_s}{R} = \frac{NAB}{kR}$$

If we increase $$N$$ to increase current sensitivity, the resistance $$R$$ also increases (since $$R \propto N$$). So voltage sensitivity may not increase. Statement B is correct.

Statement C: If $$N$$ is doubled to $$2N$$, voltage sensitivity doubles.

When $$N$$ is doubled, $$R$$ also roughly doubles. So $$V_s = \frac{NAB}{kR}$$. Since both $$N$$ and $$R$$ double, $$V_s$$ remains approximately the same. Statement C is incorrect.

Statement D: MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel.

To convert a galvanometer into an ammeter, a small (low) resistance shunt is connected in parallel, not a large resistance. Statement D is incorrect.

Statement E: Current sensitivity depends inversely on number of turns.

Current sensitivity $$I_s = \frac{NAB}{k}$$, which is directly proportional to $$N$$, not inversely. Statement E is incorrect.

Therefore, only statements A and B are correct.

The correct answer is Option 4: A, B Only.