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The question asks which measurement gives the largest uncertainty in the calculated value of the resistivity.

### Key Points:
- The resistivity \(\rho\) is calculated using the formula:
  \[
  \rho = R \cdot \frac{A}{L}
  \]
  where:
  - \(R\) is the resistance,
  - \(A\) is the cross-sectional area (which depends on the diameter \(d\) of the wire),
  - \(L\) is the length of the wire.

- The uncertainty for each measurement is 1%.

### Uncertainty Contributions:
- **Current** and **Potential Difference** are used to determine the resistance \(R = V/I\). Both have the same 1% uncertainty, so they contribute equally to \(R\)'s uncertainty.
- **Length** contributes directly to the uncertainty in the resistivity formula since \(\rho \propto \frac{1}{L}\).
- **Diameter** affects the cross-sectional area \(A = \pi (d/2)^2\), so the uncertainty in the diameter has a squared effect on the area, meaning the uncertainty contribution from the diameter is larger.

### Conclusion:
Since the uncertainty in diameter is squared in the calculation of the area, it contributes the largest uncertainty in the calculated value of the resistivity. Therefore, **the correct answer is B (diameter)**.

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Would you like further details or have any other questions?

Here are five related questions you might consider:
1. How does the uncertainty in each measurement affect the overall uncertainty in resistivity?
2. How can measurement tools, like a micrometer, improve accuracy in experiments like this?
3. What methods can be used to reduce uncertainty in such experiments?
4. How does squaring the diameter affect uncertainty propagation?
5. How do systematic and random errors differ in an experiment like this?

**Tip:** When dealing with quantities that are squared or have a higher order dependency (like the diameter in this case), always check how uncertainties propagate, as they often get amplified.

A student carries out an experiment to determine the resistivity of a metal wire. She determines the resistance from measurements of potential difference between the ends of the wire and the corresponding current. She measures the length of the wire with a ruler and the diameter of the wire using a micrometer. Each measurement is made with an uncertainty of 1%. Which measurement gives the largest uncertainty in the calculated value of the resistivity? (A) current, (B) diameter, (C) length, (D) potential difference.

Explore how different measurements like current, potential difference, length, and diameter affect uncertainty in calculating the resistivity of a metal wire. Understand the role of error propagation, especially when squaring values like diameter, which leads to greater uncertainty amplification.

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