What is the resistivity of a copper wire with given dimensions and length?

In summary, the resistivity of a copper wire with given dimensions and length can be calculated using the formula R = (ρ * L)/A, where R is the resistance, ρ is the resistivity of copper (1.68 x 10^-8 Ωm), L is the length of the wire, and A is the cross-sectional area. The resistivity of a copper wire is dependent on its temperature, but for most practical purposes, it remains constant. Therefore, the resistivity of a copper wire can be easily determined by knowing its dimensions and length.
  • #1
freddy13
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0

Homework Statement



A number 12 copper wire has a diameter of 2.053mm. Calculate the resistance of a 31m long piece of such wire. Use rho=1.72x10-8 Ohm-m for the resistivity of copper.

Homework Equations



This is the part that I am unsure of, all of my equations for resistivity do not really have anything along the lines of the given constants, nor can I see where one is derived. If it needs to be derived from something else, please post where you get it from so I can figure it out!
 
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  • #2
freddy13 said:

Homework Statement



A number 12 copper wire has a diameter of 2.053mm. Calculate the resistance of a 31m long piece of such wire. Use rho=1.72x10-8 Ohm-m for the resistivity of copper.

Homework Equations



This is the part that I am unsure of, all of my equations for resistivity do not really have anything along the lines of the given constants, nor can I see where one is derived. If it needs to be derived from something else, please post where you get it from so I can figure it out!

You have a uniform cross section. Look here. http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity
 

1. What is resistivity?

Resistivity is a measure of a material's ability to resist the flow of electric current. It is represented by the symbol ρ (rho) and is measured in ohm-meters (Ω⋅m).

2. How is resistivity related to the resistance of a copper wire?

Resistivity is directly proportional to the resistance of a copper wire. This means that as the resistivity of the wire increases, so does its resistance. The relationship between resistivity (ρ), resistance (R), and length (l) and cross-sectional area (A) of the wire can be expressed as: R = ρ(l/A).

3. What factors affect the resistivity of a copper wire?

The resistivity of a copper wire is influenced by its length, cross-sectional area, and temperature. The longer the wire, the higher its resistivity. Similarly, a larger cross-sectional area results in lower resistivity. Additionally, the resistivity of copper increases as its temperature increases.

4. How does temperature affect the resistivity of a copper wire?

The resistivity of copper increases with temperature. This is because as the temperature of the wire increases, the atoms in the wire vibrate more, making it more difficult for electrons to flow through the wire. This increase in resistance leads to an increase in resistivity.

5. What is the resistivity of a typical copper wire?

The resistivity of a copper wire varies depending on its purity and temperature. However, at room temperature, the resistivity of a typical copper wire is around 1.68 x 10^-8 Ω⋅m. This value is often used as a reference point in electrical calculations.

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