# What is the formula for calculating resistance in a 1km copper wire?

• Enochfoul
In summary, the formula to calculate the resistance of a 1km length of 0.6mm diameter copper wire is: ##R = \rho \frac{(L/\pi D^2)}{4}##.
Enochfoul
Hi,

I am just starting out learning about DC curcuits and I have been presented with a formula in my learning materials to calculate the resistance of a 1km length of 0.6mm diameter copper wire.

The formula is attached as an image with the Answer 60Ω

My question is how would you enter this formula into a calculator as I can't seem to get the answer 60. Do I have to set the calulator to a specific setting? do we I have to break the calculation into different stages?

I don't know whether the format of my notes is messed up or its just me doing something wrong.

Thanks for the help

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ProfuselyQuarky
I believe that it's a matter of order of operation (you know, putting parentheses in the proper places). I punched in the values and got 60.1252--which is the correct answer rounded.

How did you do it? Could you post what you typed into the calculator?

ProfuselyQuarky said:
How did you do it? Could you post what you typed into the calculator?

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That's odd. I did the same thing. This is basic arithmetic, so calculator settings should not really matter. What answer did you get? I see that your calculator is in degrees, but radians vs. degrees doesn't matter here at all. What are you're other settings?

ProfuselyQuarky said:
That's odd. I did the same thing. This is basic arithmetic, so calculator settings should not really matter. What answer did you get? I see that your calculator is in degrees, but radians vs. degrees doesn't matter here at all. What are you're other settings?
Its set to Normal Mode in degrees

ProfuselyQuarky said:
3.757825045

Hold on, I'm thinking . . .

The only thing I could think of was that perhaps your calculator was on a different base system, but I don't think so . . . These are my all settings:

Display Digits: Float 6
Angle: Degree
Exponential Format: Normal
Real or Complex: Real
Calculation Mode: Auto
Vector Format: Rectangular
Base: Decimal

Compare this with your calculator. And here's mine, for the sake of it:

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ProfuselyQuarky said:
The only thing I could think of was that perhaps your calculator was on a different base system, but I don't think so . . . These are my all settings:

Display Digits: Float 6
Angle: Degree
Exponential Format: Normal
Real or Complex: Real
Calculation Mode: Auto
Vector Format: Rectangular
Base: Decimal

Compare this with your calculator. And here's mine, for the sake of it:
View attachment 98275
I am going to get a calculator app for my phone and give it another try. Thanks for your help at least I know I am not entering it in wrong

ProfuselyQuarky
You know, I'll try that too. I really want to know what's wrong now!

Enochfoul said:
Im going to get a calculator app for my phone and give it another try.
Ahh the youth of today. I would have thought it quite possible to put down the calculator and work out a simple sum like that on paper.
There's only a Pi (use three or four sig figs), a 60, a 1.7 and a 4 involved.

Merlin3189
sophiecentaur said:
Ahh the youth of today. I would have thought it quite possible to put down the calculator and work out a simple sum like that on paper.
There's only a Pi (use three or four sig figs), a 60, a 1.7 and a 4 involved.
Don't worry, I don't know about the OP, but I still love paper and No. 2 pencils as much as you do (and if I'm not youth, I don't know who is)

ProfuselyQuarky said:
and if I'm not youth, I don't know who is)
I get the impression that almost everyone is youth - relative to me (and a few other old PF gimmers)
So few people would even consider doing any arithmetic on paper, these days. It's refreshing to read that you would, though PQ.

ProfuselyQuarky
To the OP: In your calculator, you have entered ##R = \rho \frac{(L/\pi D^2)}{4}## instead of ##R = \rho \frac{L}{\pi D^2 / 4}##. Notice that the first one gives ##R = \rho \frac{L}{4 \pi D^2}## and the second one (the correct one) gives ##R = \rho \frac{4L}{\pi D^2}##

Although I'm in SophieCentaur's camp, I got as far as 1700/9π without anything. Then I did reach for a calculator. But when I got down to SC's comment, I tried that with pencil and back of envelope, just to see what happened, and with Pi at 22/7 it comes out at 60.1

But, since you are asking about calculator methods, I'd say your big mistake is to try to put it all into a single calculation. You CAN do that, but as far as I can see, even using a calculator, there is nothing to be gained in time nor accuracy, let alone mistakes, in combining the two calculations. Just work out A, then press reciprocal and enter the rest of your second formula, pausing only to note that 2.8x10-7 m2 for A is about right. If the second expression were more complex, just pop your first answer into a memory and use it wherever is convenient.

D sq x pi / 4 = recip x ρ x L = is one more keystroke than ρ x L / ( D sq x pi / 4 ) = but requires no thought nor planning and provides a small check along the way.

Even now Axmls has pointed out your possible error, I can't tell from your calculator display whether you did what he says or whether you put in something else. I can't read it as Axmls does. But he's probably correct, since your answer is a factor of 16 out.
If someone wrote that expression on paper as shown on your screen, I'd say it was wrong, but my reading of it does not give your answer.

ProfuselyQuarky
Merlin3189 said:
I tried that with pencil and back of envelope, just to see what happened, and with Pi at 22/7 it comes out at 60.1
Goooood boy. If I could reach, I'd give you a gold star in your book.

ProfuselyQuarky
sophiecentaur said:
I get the impression that almost everyone is youth - relative to me (and a few other old PF gimmers)
(when I said youth, I meant <18)
sophiecentaur said:
So few people would even consider doing any arithmetic on paper, these days. It's refreshing to read that you would, though PQ.
Thanks, I just get annoyed when I see 8-year-olds and 9-year-olds with TI-89 calculators doing math homework

I just want to peer over and say, "Umm, 321 plus 447 is called mental math for a reason!"

sophiecentaur
Merlin3189 said:
But, since you are asking about calculator methods, I'd say your big mistake is to try to put it all into a single calculation.
How did I do it, then? :(

I don't say it can't be done, just that it's asking for trouble with no great advantage.
But if you're really asking how I think you did it, maybe something like,
1 . 7 exp 8 ± x ( 1 0 0 0 / ( ( pi x 0 . 6 exp 3 ± ) x2 / 4 ) ) =
But I don't have one of these modern things and wouldn't be able to do anything with it if I had. I expect you have a cursor and move around entering the data in any order you like. Or maybe you pick the relevant equations from a list and it asks you questions?

ProfuselyQuarky
Merlin3189 said:
I don't say it can't be done, just that it's asking for trouble with no great advantage.
Agreed
Merlin3189 said:
But I don't have one of these modern things and wouldn't be able to do anything with it if I had. I expect you have a cursor and move around entering the data in any order you like.
Yes, I have a cursor on my calculator, but it is irrelevant for the purposes of the calculation discussed in this thread. It's more like a touch pad on a laptop--for navigating. I didn't do anything special at all to acquire the answer to the OP's problem, though. I just punched in the numbers the same way the OP did.
Merlin3189 said:
Or maybe you pick the relevant equations from a list and it asks you questions?
Yes, my calculator can do that, too, but I have to program it that way for each specific function. For example, I programmed a document where I could give the calculator variables ##a##, ##b##, and ##c## and then it would give me back an answer based on the quadratic formula (very handy for physics equations). It won't do it on its own, though.

It's a thing of beauty

I'm working on the idea of an abacus with reverse polish notation. Wadya think? Does it have potential?

Enochfoul said:
Hi,

I am just starting out learning about DC curcuits and I have been presented with a formula in my learning materials to calculate the resistance of a 1km length of 0.6mm diameter copper wire.

The formula is attached as an image with the Answer 60Ω

My question is how would you enter this formula into a calculator as I can't seem to get the answer 60. Do I have to set the calulator to a specific setting? do we I have to break the calculation into different stages?

I don't know whether the format of my notes is messed up or its just me doing something wrong.

Thanks for the help

When you have an expression with two fraction bars there can be ambiguity as to just what is meant. The order of entering the parts of the expression makes a difference in how it will be evaluated. For example, see this image:

The use of parentheses can remove the ambiguity.

Last edited:
sophiecentaur said:
I'm working on the idea of an abacus with reverse polish notation. Wadya think? Does it have potential?
Plenty o' potential!

I think I should try my hand at an abacus, too. An excellent skill in the 21 century, is it not?

sophiecentaur

## What is the formula for calculating resistance in a 1km copper wire?

The formula for calculating resistance in a 1km copper wire is R = (ρ * L) / A, where R is the resistance, ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area of the wire.

## What is the resistivity of copper?

The resistivity of copper is 1.68 x 10^-8 ohm-meters at room temperature.

## How do I calculate the resistivity of other materials?

The resistivity of other materials can be calculated by measuring the resistance of a known length and cross-sectional area of the material, then using the formula ρ = (R * A) / L.

## Why is the length and cross-sectional area of the wire important in calculating resistance?

The length and cross-sectional area of a wire determine the amount of space available for the electrons to flow through, which affects the amount of resistance in the circuit.

## What are some common units of measurement for resistance?

The most common units of measurement for resistance are ohms (Ω), kilohms (kΩ), and megohms (MΩ).

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