Which of the following operations will not increase the sensitivity of a potentiometer?

Options

A. Increase in the number of wires of the potentiometer.
B. Reducing the potential gradient .
C. Increasing the current through the potentiometer .
D. Increasing the sensitivity of the galvanometer.

Answer

To determine which operation will not increase the sensitivity of a potentiometer, we need to understand the relationship between sensitivity, potential gradient, and the factors affecting them.

### Step-by-Step Solution:

1. **Understanding Sensitivity**:
Sensitivity of a potentiometer refers to its ability to measure small potential differences accurately. Higher sensitivity means the device can detect smaller changes in voltage.

2. **Potential Gradient**:
The potential gradient (k) is defined as the potential drop per unit length of the potentiometer wire. It is given by the formula:
\[ k = \frac{V}{L} \]
where \( V \) is the potential difference across the wire and \( L \) is the length of the wire.

3. **Relationship Between Sensitivity and Potential Gradient**:
Sensitivity is inversely related to the potential gradient:
\[ \text{Sensitivity} \propto \frac{1}{k} \]
This means that if the potential gradient decreases, the sensitivity increases.

4. **Factors Affecting Potential Gradient**:
The potential gradient can be affected by:
- Increasing the length of the wire (L)
- Decreasing the potential difference (V)
- Changing the current (I) flowing through the wire

5. **Evaluating the Options**:
- **Increasing the number of wires**: This increases the cross-sectional area and decreases the potential gradient, thus increasing sensitivity.
- **Reducing the potential gradient**: This directly increases sensitivity.
- **Increasing the current through the potentiometer**: This increases the potential gradient (since \( k = \frac{IR}{L} \)), which decreases sensitivity.
- **Increasing the sensitivity of the galvanometer**: This is unrelated to the potentiometer's sensitivity.

6. **Conclusion**:
Among the options, the operation that will not increase the sensitivity of the potentiometer is **increasing the current through the potentiometer**. This operation actually decreases sensitivity.

### Final Answer:
The operation that will not increase the sensitivity of a potentiometer is **increasing the current through the potentiometer**.