WAEC 2024 Physics · Question 28

Four pieces of constantan wire, marked E, F, G, and H, each of length 1.0m, are at the temperature. Their…

Question

Four pieces of constantan wire, marked E, F, G, and H, each of length 1.0m, are at the temperature. Their respective diameters are 1 mm, 2 mm, 6 mm, and 10 mm. Which wire has the highest resistance?

Answer: A. E

Explanation written with AI and checked against the answer key

Analyze the question: Four wires of the same material (constantan), same length (1.0 m) and same temperature differ only in diameter. We need the one with the highest resistance. Concept: Resistance of a wire is R = ρL / A where ρ is resistivity (same for all, since the material and temperature are the same), L is length (same for all), and A is cross-sectional area. So R ∝ 1/A. Since A = πd²/4, we get R ∝ 1/d². The thinner the wire, the higher the resistance. Solution: Compare the quantity 1/d² for each wire. | Wire | Diameter (mm) | 1/d² (relative) | |------|---------------|-----------------| | E | 1 | 1 | | F | 2 | 1/4 = 0.25 | | G | 6 | 1/36 ≈ 0.028 | | H | 10 | 1/100 = 0.01 | Wire E has the largest value of 1/d², so it has the highest resistance. Wire H has the lowest. Answer: A. E Tip: For wires of the same material, length and temperature, remember "thin wire, high resistance." Resistance is inversely proportional to the square of the diameter. Wire E is the thinnest, so it resists current flow the most, just as a narrow pipe resists water flow more than a wide one.

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