physics

Question

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?

Answer 1

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.

Answer 2

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