? 發問於 科學及數學其他 - 科學 · 1 十年前

physics

The wiring in a house must be thick enough so it does not become so hot as to start a fire. What diameter must a copper wire be if it is to carry a maximum current of 30 A and produce no more than 1.5 W of heat per meter of length?

2 個解答

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  • 1 十年前
    最愛解答

    Let x be the cross sectional area of the copper wire first.

    Then by using the data: Resistivity of copper = 16.78 nΩ·m, we have the resistance of one metre of the copper wire = [(16.78 × 10-9 × 1) / x] Ω.

    So to speak, power developed in one metre of the wire when carrying a current of 30A = 302 × [(16.78 × 10-9 × 1) / x] Watt

    ∴ From the given, 900 × [(16.78 × 10-9 × 1) / x] = 1.5

    x = 1.0068 × 10-5 m2

    Suppose the cross-section of the copper wire is circular in shape, we have:

    2πr2 = 1.0068 × 10-5 where r is the redius of the cross-section.

    r = 1.266 × 10-3 m

    Hence, the diameter of the copper wire should be at least 2.532 × 10-3 m or 2.532 mm.

    資料來源: My Physics knowledge
  • 1 十年前

    Mr,

    It definitely have code book for this kind of application.

    A copper wire of diameter=4mm should be enough.

    The relationship is described in this page, you can input voltage,

    amp, etc ...

    http://www.powerstream.com/Wire_Size.htm

    yifeng

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