When the number of turns of the coil is doubled, the current sensitivity of a moving coil galvanometer is doubled whereas the voltage sensitivity of the galvanometer

Options

A. Remains the same
B. Is halved
C. Is doubled
D. Is quadrupled

Explanation

To solve the problem, we need to analyze how the current sensitivity and voltage sensitivity of a moving coil galvanometer change when the number of turns in the coil is doubled.

### Step-by-Step Solution:

1. **Understanding Current Sensitivity**:
- Current sensitivity (S_I) is defined as the deflection (θ) per unit current (I).
- The formula for current sensitivity is given by:
\[ S_I = \frac{NAB}{C} \]
where:
- N = number of turns of the coil
- A = area of the coil
- B = magnetic field strength
- C = constant

2. **Effect of Doubling the Number of Turns on Current Sensitivity**:
- If the number of turns is doubled (N becomes 2N), the new current sensitivity (S'_I) becomes:
\[ S'_I = \frac{2NAB}{C} = 2 \cdot \frac{NAB}{C} = 2S_I \]
- Therefore, the current sensitivity doubles when the number of turns is doubled.

3. **Understanding Voltage Sensitivity**:
- Voltage sensitivity (S_V) is defined as the deflection (θ) per unit voltage (V).
- The formula for voltage sensitivity is given by:
\[ S_V = \frac{NAB}{CR} \]
where R = resistance of the coil.

4. **Effect of Doubling the Number of Turns on Voltage Sensitivity**:
- When the number of turns is doubled, the resistance R also doubles (since resistance is proportional to the number of turns).
- Thus, the new voltage sensitivity (S'_V) becomes:
\[ S'_V = \frac{2NAB}{C(2R)} = \frac{NAB}{CR} = S_V \]
- Therefore, the voltage sensitivity remains unchanged when the number of turns is doubled.

5. **Conclusion**:
- When the number of turns of the coil is doubled:
- Current sensitivity is doubled.
- Voltage sensitivity remains unchanged.