In a meter bridge set up, which of the following should be the properties of the one meter long wire?

Options

A. High resistivity and low temperature coefficient
B. Low resistivity and low temperature coefficient
C. Low resistivity and high temperature coefficient
D. High resistivity and high temperature coefficient

Answer

To determine the properties of the one-meter-long wire used in a meter bridge setup, we can analyze the requirements based on the principles of resistance and sensitivity.

### Step-by-Step Solution:

1. **Understanding the Meter Bridge**:
- A meter bridge is based on the principle of the Wheatstone bridge and is used to measure unknown resistances. It consists of a one-meter-long wire that is uniform and has a constant cross-sectional area.

2. **Constant Length (L)**:
- The length of the wire (L) must remain constant at one meter. This is essential for accurate measurements because any change in length would affect the resistance calculation.

3. **Resistance Formula**:
- The resistance (R) of the wire is given by the formula:
\[ R = \frac{\rho L}{A} \]
where ρ (rho) is the resistivity of the material, L is the length, and A is the cross-sectional area. Since L is constant, the resistance will depend on the resistivity and the area of cross-section.

4. **Sensitivity Requirement**:
- The meter bridge should be sensitive to small changes in resistance. This sensitivity can be increased by using a wire with high resistivity (ρ). A higher resistivity means that for the same length and area, the resistance will be higher, making it easier to detect small changes.

5. **Temperature Coefficient**:
- The temperature coefficient of resistance indicates how much the resistance of a material changes with temperature. For the meter bridge to function accurately, the wire should have a low temperature coefficient. This ensures that the resistance remains stable and does not change significantly with temperature variations, helping to keep the length constant.

6. **Conclusion**:
- Therefore, the ideal properties of the one-meter-long wire in a meter bridge setup are:
- **High resistivity**: To enhance sensitivity.
- **Low temperature coefficient**: To maintain constant resistance and length.

### Final Answer:
The properties of the one-meter-long wire should be high resistivity and low temperature coefficient.

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