The resistance of a wire of 0.01 cm radius and 1.0 cm length is 7 Ω. Calculate its resistivity.
Generated by claude-sonnet-4-6 · 2026-06-15 06:41 · grounding rag
Model Answer
Given: radius $r = 0.01$ cm $= 1 \times 10^{-4}$ m, length $l = 1.0$ cm $= 1 \times 10^{-2}$ m, $R = 7$ Ω
Area of cross-section: $A = \pi r^2 = 3.14 \times (10^{-4})^2 = 3.14 \times 10^{-8}$ m²
Using $R = \rho \dfrac{l}{A}$:
$$\rho = \frac{R \times A}{l} = \frac{7 \times 3.14 \times 10^{-8}}{1 \times 10^{-2}}$$
$$\rho = 21.98 \times 10^{-6} \approx 2.2 \times 10^{-5} \text{ Ω m}$$
Source: Chapter 11, Section 11.5
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Explanation
- The key formula is $\rho = RA/l$ (rearranged from $R = \rho l/A$).
- Always convert all units to SI (metres) before substituting.
- Examiners award 1 mark for correct substitution and 1 mark for the final answer with correct unit (Ω m). Don't forget to write the unit.