Sensitivity of a moving coil galvanometer increases as:

Options

A. number of turns decreases
B. number of turns increases
C. torsional rigidity increases
D. area of coil decreases

Explanation

To solve the question regarding the sensitivity of a moving coil galvanometer, we need to understand the relationship between sensitivity and the various factors involved in the operation of the galvanometer.

### Step-by-Step Solution:

1. **Understanding Sensitivity**:
Sensitivity (S) of a moving coil galvanometer is defined as the angular deflection (θ) produced per unit current (I) flowing through the coil. Mathematically, it can be expressed as:
\[ S = \frac{\theta}{I} \]

2. **Factors Affecting Sensitivity**:
The sensitivity of a moving coil galvanometer depends on several factors including:
- The number of turns (N) of the coil.
- The magnetic field strength (B).
- The area (A) of the coil.
- The torsional rigidity (C) of the suspension.

3. **Deriving the Formula**:
From the principles of electromagnetism, we know that:
\[ \theta = \frac{N B A I}{C} \]
Therefore, substituting this into the sensitivity formula gives:
\[ S = \frac{N B A}{C} \]

4. **Analyzing Each Factor**:
- **Number of Turns (N)**: Increasing the number of turns increases sensitivity (S) because it increases the torque produced for a given current.
- **Magnetic Field Strength (B)**: Increasing the magnetic field strength also increases sensitivity.
- **Area of the Coil (A)**: Increasing the area of the coil increases sensitivity.
- **Torsional Rigidity (C)**: Increasing torsional rigidity decreases sensitivity because it requires more torque to achieve the same angular deflection.

5. **Conclusion**:
From the analysis, we conclude that the sensitivity of a moving coil galvanometer increases with:
- An increase in the number of turns (N).
- An increase in the magnetic field strength (B).
- An increase in the area of the coil (A).
- A decrease in torsional rigidity (C).

### Final Answer:
The sensitivity of a moving coil galvanometer increases as the number of turns increases, the magnetic field strength increases, and the area of the coil increases, while it decreases with an increase in torsional rigidity.