The resistance of a wire of 0.01 cm radius is 7 ohms. If the resistivity of the material of the wire is 44 × 10⁻⁶ ohm meter, calculate the length of the wire.
Generated by claude-sonnet-4-6 · 2026-06-15 06:45 · grounding rag
Model Answer
Given:
Radius of wire, r = 0.01 cm = 0.01 × 10⁻² m = 1 × 10⁻⁴ m
Resistance, R = 7 Ω
Resistivity, ρ = 44 × 10⁻⁶ Ω m
Formula: $R = \rho \dfrac{l}{A}$, where $A = \pi r^2$
Area of cross-section:
$$A = \pi r^2 = 3.14 × (1 × 10^{-4})^2 = 3.14 × 10^{-8} \text{ m}^2$$
Length of wire:
$$l = \frac{R \times A}{\rho} = \frac{7 × 3.14 × 10^{-8}}{44 × 10^{-6}}$$
$$l = \frac{21.98 × 10^{-8}}{44 × 10^{-6}} = \frac{21.98}{44} × 10^{-2}$$
$$\boxed{l \approx 0.005 \text{ m} = 0.5 \text{ cm}}$$
Source: Chapter 11, Section 11.5
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Explanation
- The key formula is $R = \rho \dfrac{l}{A}$, rearranged to $l = \dfrac{RA}{\rho}$.
- Always convert radius to metres before calculating area.
- Examiners award marks for: correct formula (1 mark), correct substitution with area calculation (1 mark), correct final answer with unit (1 mark).
- Note: the resistivity 44 × 10⁻⁶ Ω m matches Manganin from Table 11.2 — useful if the question asks to identify the material.