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 evaluate each statement to identify the correct ones:

Statement Analysis:

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

• The torsional constant (\( k \)) represents the restoring torque per unit angular displacement. Its units are torque per radian. Torque has dimensions \([ML^2T^{-2}]\), confirming the correctness of this statement.

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

• Current sensitivity is defined as deflection per unit current (\( \theta/I \)). Voltage sensitivity is defined as deflection per unit voltage (\( \theta/V \)). According to Ohm's law, \( V = IR \). Therefore, voltage sensitivity is dependent on both current sensitivity and the galvanometer's resistance. Consequently, an increase in current sensitivity does not guarantee an increase in voltage sensitivity, as resistance can vary. This statement is correct.

C: If the number of turns \( (N) \) is doubled to \( (2N) \), then the voltage sensitivity doubles.

• Voltage sensitivity \( \left(\theta/V\right) = \left(\theta/I \right) \cdot \left(I/V\right) \) is directly proportional to the number of turns \( N \) (via \( \theta/I \)) but inversely proportional to the resistance \( R \). Doubling \( N \) doubles the current sensitivity. However, if the resistance \( R \) also doubles, the voltage sensitivity remains constant. Therefore, this statement is incorrect.

D: A moving coil galvanometer (MCG) can be converted into an ammeter by connecting a high-value shunt resistance in parallel with the galvanometer.

• To convert a galvanometer into an ammeter, a low-value shunt resistance is connected in parallel. This arrangement diverts most of the current through the shunt, allowing the ammeter to measure large currents accurately. Therefore, this statement is incorrect.

E: The current sensitivity of an MCG is inversely proportional to the number of turns of the coil.

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

Conclusion:

• Only statements A and B are correct. This aligns with the provided correct answer: A, B only.