The sensitivity of the potentiometer can be increased by

Options

A. increasing the length of the wire
B. increasing the e.m.f. of the cell
C. decreasing the length of the wire
D. none of these

Answer

To solve the question regarding how to increase the sensitivity of a potentiometer, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Sensitivity**:
- Sensitivity of a potentiometer refers to its ability to detect small changes in voltage. It is defined as the potential difference (voltage) per unit length of the potentiometer wire.

2. **Defining Potential Gradient**:
- The potential gradient (k) is defined as the potential difference (V) across the potentiometer wire divided by its length (L). Mathematically, it can be expressed as:
\[ k = \frac{V}{L} \]
- Here, \( V \) is the voltage applied across the potentiometer wire and \( L \) is the length of the wire.

3. **Increasing Sensitivity**:
- To increase the sensitivity of the potentiometer, we need to increase the potential gradient (k). This can be achieved by:
- **Increasing the Voltage (V)**: By applying a higher voltage across the same length of wire, the potential gradient increases.
- **Decreasing the Length (L)**: By using a shorter length of wire while keeping the voltage constant, the potential gradient also increases.

4. **Practical Example**:
- For example, if we have a potentiometer wire of 1 meter with a potential difference of 100 volts, the potential gradient would be:
\[ k = \frac{100 \text{ volts}}{1 \text{ meter}} = 100 \text{ volts/meter} \]
- If we increase the voltage to 200 volts while keeping the length the same, the new potential gradient becomes:
\[ k = \frac{200 \text{ volts}}{1 \text{ meter}} = 200 \text{ volts/meter} \]
- Alternatively, if we keep the voltage at 100 volts but reduce the length to 0.5 meters, the potential gradient would be:
\[ k = \frac{100 \text{ volts}}{0.5 \text{ meters}} = 200 \text{ volts/meter} \]

5. **Conclusion**:
- Therefore, the sensitivity of the potentiometer can be increased by either increasing the voltage applied across it or decreasing the length of the potentiometer wire.