Two cylindrical wires are made of the same metal. If wire 2 has 8 times the length and 10 times the diameter of wire 1.?
2016-07-17 6:29 pm
Two cylindrical wires are made of the same metal. If wire 2 has 8 times the length and 10 times the diameter of wire 1. What are the ratios of the resistances R2/R1 .
回答 (2)
2016-07-17 6:41 pm
✔ 最佳答案
R = ρ (length/area)Let L and d be the length and diameter of wire 1.
Then, the length of wire 2 is 8L, and the diameter is 10d.
Then, R₁ = ρ {L/[π(d/2)²] = 4ρL/(πd²)
and R₂ = ρ {8L/[π(10d/2)²] = (8/25)ρL/(πd²)
R₂/R₁
= [(8/25)ρL/(πd²)] / [4ρL/(πd²)]
= (8/25) / 4
= (8/25) × (1/4)
= 2/25
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