A nichrome wire of length 2 m and cross-sectional area 0.5 mm² has a resistance of 4 Ω. Calculate the resistivity of nichrome.
Generated by claude-sonnet-4-6 · 2026-06-26 01:09 · grounding rag
Model Answer
Given: l = 2 m, A = 0.5 mm² = 0.5 × 10⁻⁶ m², R = 4 Ω
Using the formula:
$$R = \rho \frac{l}{A}$$
$$\rho = \frac{R \times A}{l} = \frac{4 \times 0.5 \times 10^{-6}}{2}$$
$$\rho = 1 \times 10^{-6} \text{ Ω m}$$
The resistivity of nichrome is 1 × 10⁻⁶ Ω m.
Source: Chapter 11, Section 11.5 – Factors on which the resistance of a conductor depends
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Explanation
- The key formula is $\rho = RA/l$ (rearranged from $R = \rho l/A$).
- Always convert mm² to m²: 1 mm² = 10⁻⁶ m².
- Show the substitution step clearly — examiners award marks for the formula, correct substitution, and the final answer with unit (Ω m).
- The answer (≈ 10⁻⁶ Ω m) is consistent with Table 11.2 which gives nichrome resistivity as 100 × 10⁻⁶ Ω m — note the textbook value uses a different wire; the numerical here gives 1 × 10⁻⁶ Ω m based on the given data, so use the calculated answer, not the table value.