Question

Consider a moving coil galvanometer (MCG):
A : The torsional constant in moving coil galvanometer has dimensions \( [ML^2 T^{-2}] \)
B : Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C : If we increase the 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 the galvanometer.
E : Current sensitivity of MCG depends inversely on the number of turns of the coil.
Choose the correct answer from the options given below:

• A. A, B only
• B. A, D, only
• C. B, D, E only
• D. A, B, E only

Hint:

To determine the behavior of an MCG, remember that voltage sensitivity and current sensitivity depend on factors like the number of turns, torsional constant, and the shunt resistance, which can modify its properties.

Answer 1

The Correct Option is A

Let's analyze each statement to determine which ones are correct:

Statement Analysis: 

A: The torsional constant in moving coil galvanometer has dimensions \( [ML^2 T^{-2}] \)

• The torsional constant (\( k \)) is the restoring force per unit angular displacement and is expressed in terms of torque per radian. Torque has dimensions \([ML^2T^{-2}]\), which confirms this statement is correct.

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

• Current sensitivity of a galvanometer is defined as the deflection per unit current (\( \theta/I \)). Voltage sensitivity is defined as the deflection per unit voltage (\( \theta/V \)). By Ohm's law, \( V = IR \), we get that voltage sensitivity depends on both current sensitivity and resistance of the galvanometer. Hence, increasing current sensitivity doesn't necessarily increase voltage sensitivity as resistance can vary, making this statement correct.

C: If we increase the number of turns \( (N) \) to its double \( (2N) \), then the voltage sensitivity doubles.

• Voltage sensitivity \( \left(\theta/V\right) = \left(\theta/I \right) \cdot \left(I/V\right) \) depends linearly on the number of turns \( N \) through \( \theta/I \) but inversely with the resistance \( R \). If \( N \) is doubled, while current sensitivity doubles, resistance \( R \) also doubles, keeping voltage sensitivity constant. Thus, this statement is incorrect.

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

• To convert a galvanometer into an ammeter, a low-value shunt resistance is added in parallel. This allows most of the current to bypass the galvanometer since ammeters measure large currents. Thus, this statement is incorrect.

E: Current sensitivity of MCG depends inversely on the number of turns of the coil.

• Current sensitivity is \( \theta/ I = \frac{NBA}{k} \), where \( N \) is the number of turns, \( B \) is magnetic field strength, \( A \) is the area of the coil, and \( k \) is torsional constant. Clearly, current sensitivity is directly proportional to \( N \), not inversely. Thus, this statement is incorrect.

Conclusion:

• Only statements A and B are correct, which matches the given correct answer: A, B only.

Answer 2

Explanation:

In the given question, we have to evaluate the statements related to the properties and functioning of a moving coil galvanometer (MCG):

• Statement A: The torsional constant in moving coil galvanometer has dimensions \([ML^2 T^{-2}]\). This is correct. The torsional constant is a measure of the coil's resistance to twisting, and the dimensions match those of energy per radian.
• Statement B: Increasing the current sensitivity may not necessarily increase the voltage sensitivity. This is true because current sensitivity depends on the number of turns and the magnetic field, whereas voltage sensitivity also depends on the coil resistance.
• Statement C: If we increase the number of turns (N) to its double (2N), then the voltage sensitivity doubles. This is not necessarily correct, as it assumes constant resistance, which might not hold if the number of turns increases.
• Statement D: MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with the galvanometer. This is incorrect; a small value shunt resistance is used to allow most of the current to bypass the galvanometer.
• Statement E: Current sensitivity of MCG depends inversely on the number of turns of the coil. This is incorrect; current sensitivity actually depends directly on the number of turns.

Conclusion: Based on the analysis, only statements A and B are correct.

Correct Answer: A, B only