If the current sensitivity of a galvanometer is doubled, then its voltage sensitivity will be

Options

A. doubled
B. halved
C. unchanged
D. four times

Explanation

To solve the problem, we need to understand the relationship between current sensitivity (Is) and voltage sensitivity (Vs) of a galvanometer.

### Step-by-Step Solution:

1. **Understand Current Sensitivity (Is)**:
- Current sensitivity (Is) of a galvanometer is defined as the deflection (φ) produced per unit current (I). Mathematically, it is given by:
\[ I_s = \frac{\phi}{I} \]

2. **Understand Voltage Sensitivity (Vs)**:
- Voltage sensitivity (Vs) is defined as the deflection produced per unit voltage (V). It can be expressed as:
\[ V_s = \frac{\phi}{V} \]
- Since voltage (V) is related to current (I) and resistance (R) by Ohm's Law (V = IR), we can express voltage sensitivity in terms of current sensitivity:
\[ V_s = \frac{\phi}{I \cdot R} = \frac{\phi}{I} \cdot \frac{1}{R} = I_s \cdot \frac{1}{R} \]

3. **Relationship Between Is and Vs**:
- From the above equations, we can see that:
\[ V_s = I_s \cdot \frac{1}{R} \]
- This indicates that voltage sensitivity is directly proportional to current sensitivity and inversely proportional to resistance.

4. **Doubling Current Sensitivity**:
- According to the problem, if the current sensitivity (Is) is doubled, we can express this as:
\[ I_s' = 2 I_s \]
- If the current sensitivity is doubled, we also need to consider the effect on resistance (R). Since the current sensitivity is inversely proportional to resistance, if Is is doubled, R must also double to maintain the relationship:
\[ R' = 2R \]

5. **Calculate New Voltage Sensitivity**:
- Now, substituting the new values into the voltage sensitivity equation:
\[ V_s' = I_s' \cdot \frac{1}{R'} = (2 I_s) \cdot \frac{1}{2R} = I_s \cdot \frac{1}{R} = V_s \]
- This shows that the new voltage sensitivity (Vs') remains unchanged.

6. **Conclusion**:
- Therefore, if the current sensitivity of a galvanometer is doubled, the voltage sensitivity will remain unchanged.

### Final Answer:
The voltage sensitivity will remain unchanged.