# Resistance of a wire around the Earth

• Engineering
• godiswatching_
In summary: This is the same all the way around the Earth.In summary, the conversation discusses the calculation of a change in resistance using a formula and the assumption of a radius increase. The final answer was given, but the speaker expresses doubt and asks for confirmation. The other person encourages them to have faith in their work and explains the math behind the seemingly unbelievable result.
godiswatching_
Homework Statement
Homework statement in the image.
Relevant Equations
$$R=\rho\frac{l}{A}$$
$$l=2\pi r$$

I did (1) Using
$$R_{0}=\rho\frac{l}{A}$$

For (2) I assume the question means that the radius increases by a meter.
So I used $$\bigtriangleup L = 2\pi (r_{E}+1) - l$$
and then I used that L to find the new R. Then I said $$\bigtriangleup R = R-R_{0}$$

Does that seem right? This seems too simple to be right.

$$\bigtriangleup R = 3.4 \cdot 10^{-4} \Omega$$

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'Too simple' is not an argument ...
What could possible be wrong ?

##\ ##

BvU said:
'Too simple' is not an argument ...
What could possible be wrong ?

##\ ##
I don’t see anything wrong with my steps. I think they are all logically sound. It’s more so that I’m paranoid and don’t want to lose points on homework for no reason really.

PF isn't in the business of stamp-approving homework. It wouldn't help anyone. You do your calculation, get a result and check it. Twice if you want, three times if you are paranoid

Have some faith in your work ...

##\ ##

phinds
I find it pretty hard to believe that adding a mere 6.28 m of wire is enough to lift it by 1 meter off the ground all the way around the Earth, but it does indeed.

vela said:
I find it pretty hard to believe that adding a mere 6.28 m of wire is enough to lift it by 1 meter off the ground all the way around the Earth, but it does indeed.
It seemed unbelievable when I first heard this one, but the math bears it out.
##C = 2\pi r \Rightarrow \Delta C = 2\pi \Delta r## -- this is an equality due to the linearity of this function.
If ##\Delta r = 1 \text{ meter}##, then ##\Delta C = 2\pi \cdot 1 \approx 6.28 \text{ meters}##

## 1. What is the resistance of a wire around the Earth?

The resistance of a wire around the Earth depends on various factors such as the material of the wire, its thickness, and the temperature. However, in general, it can be calculated using the formula R = ρL/A, where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

## 2. How does the resistance of a wire around the Earth affect its conductivity?

The resistance of a wire around the Earth is inversely proportional to its conductivity. This means that as the resistance increases, the conductivity decreases. This is because materials with higher resistance have more obstacles for the flow of electrons, resulting in lower conductivity.

## 3. Can the resistance of a wire around the Earth be reduced?

Yes, the resistance of a wire around the Earth can be reduced by using materials with lower resistivity, increasing the thickness of the wire, or reducing the length of the wire. Additionally, keeping the wire at a lower temperature can also help reduce its resistance.

## 4. How does the resistance of a wire around the Earth affect the flow of electricity?

The resistance of a wire around the Earth can significantly affect the flow of electricity. As the resistance increases, the flow of electrons becomes more difficult, resulting in a decrease in the amount of current that can pass through the wire. This can also cause a decrease in the voltage across the wire.

## 5. What factors can cause the resistance of a wire around the Earth to change?

The resistance of a wire around the Earth can change due to various factors such as changes in temperature, changes in the material of the wire, and changes in the length or thickness of the wire. Additionally, the presence of impurities or defects in the wire can also affect its resistance.

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