The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by `50%`.The percentage change in voltage sintivity of the galvanometer will be:

Options

A. `50%`
B. `75%`
C. `0%`
D. `100%`

Answer

To solve the problem, we need to understand the relationship between current sensitivity and voltage sensitivity in a moving coil galvanometer.

### Step-by-Step Solution:

1. **Understanding Current Sensitivity**:
- Current sensitivity (S_I) of a galvanometer is defined as the deflection per unit current. It is directly proportional to the number of turns (N) of the coil.
- Mathematically, we can express this as:
\[ S_I \propto N \]

2. **Increasing Current Sensitivity**:
- According to the problem, the number of turns of the coil is increased to increase the current sensitivity by 50%.
- If the initial current sensitivity is \( S_{I0} \), then the new current sensitivity \( S_{I1} \) can be expressed as:
\[ S_{I1} = S_{I0} + 0.5 S_{I0} = 1.5 S_{I0} \]

3. **Relating Voltage Sensitivity**:
- Voltage sensitivity (S_V) is defined as the deflection per unit voltage. It is related to current sensitivity by the formula:
\[ S_V = S_I \cdot R \]
- Where R is the resistance of the galvanometer. Assuming R remains constant, any change in current sensitivity will directly affect voltage sensitivity.

4. **Calculating the Change in Voltage Sensitivity**:
- The initial voltage sensitivity \( S_{V0} \) can be expressed as:
\[ S_{V0} = S_{I0} \cdot R \]
- The new voltage sensitivity \( S_{V1} \) becomes:
\[ S_{V1} = S_{I1} \cdot R = (1.5 S_{I0}) \cdot R = 1.5 S_{V0} \]

5. **Finding the Percentage Change**:
- The percentage change in voltage sensitivity can be calculated as:
\[ \text{Percentage Change} = \left( \frac{S_{V1} - S_{V0}}{S_{V0}} \right) \times 100\% \]
- Substituting the values:
\[ \text{Percentage Change} = \left( \frac{1.5 S_{V0} - S_{V0}}{S_{V0}} \right) \times 100\% = \left( \frac{0.5 S_{V0}}{S_{V0}} \right) \times 100\% = 50\% \]

### Final Answer:
The percentage change in voltage sensitivity of the galvanometer is **50%**.