Determine the volume of a copper wire 25 km long, if its resistance is 1.7 kOhm?

| July 1, 2021 | education

1. Here are all the data from given in SI systems:
l = 25 km = 25000 m
R = 1.7 kΩ = 1700 Ω
2. Let’s write an expression to determine the volume of the wiring, as a cylinder:
V = Ssec * l
3. Let’s write down the expression to determine the resistivity of the wire:
ρsp = R * Ssech / l, where R is the resistance of the wire, l is the length of the wire, Ssech is the cross-sectional area.
4. Let us express the cross-sectional area of ​​the wire:
Ssection = ρsp * l / R
5. Substitute the formula for determining the cross-sectional area in the formula for the volume:
V = Ssection * l = ρsp * l² / R
Specific resistance of copper according to the reference book:
ρcopper = 1.7 * 10–8 Ohm * m
6. Substituting the numerical values, we have:
V = ρsp * l² / R = 1.7 * 10-8 * 25000² / 1700 = 0.00625 m³

Answer: the volume of wiring is 0.00625 m³.



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