Actually it is worse than that. There are many values for ohms/1000 feet for any gauge wire especially when it comes to stranded wire. I once measured a bunch and got these results: [Link: audiosciencereview.com]




As you see the DCR (in milliohm) changes a ton.  Here is the relative graph to Belden:



Your larger point is definitely correct.  We had a Savant thermostat which would reset once a day or two.  Turned out the AC run from the HVAC had too much voltage drop causing it to do that (Savant support instead sent our tech on a wild goose chase telling him the voltage was too high, needed new firmware, hardware, etc.).  Thicker wire solved that even though the run was not that long.

Amir,
thank you, thank you, thank you!

This whole thing reminds me of Ben Goldacre's GREAT website, badscience.net. We omit SO MUCH information and make SO MANY assumptions! I have been trying to wake people up to this. Unfortunately, getting accurate sometimes pisses people off because it requires being so, so picky about details. Like "how low a voltage can a camera actually run off of?" (And like, Amir, you did mean milliohms, not ohms, in the DC resistance column, right? NO UNITS are given.....)

I first ran across Goldacre's book, Bad Science, several years ago. ALL OF US here should read it! It helps to know how much we don't understand about what we're doing. Goldacre said at one point that if his column and books were to sponsor a T shirt, that shirt would say "I think you'll find it's a bit more complicated than that." Your post above shows in depth how much more complicated things can be. And he now sells that T shirt.

And Goldacre now has a book, "I think you'll find it's a bit more complicated than that," which I'll be ordering this week.

(At badscience.net you can order a T shirt that says "MMR IS SAFE. TELL YOUR FRIENDS.")

E.G.. My idea was based on not knowing acceptable voltage. Going off devices supplied power supply's output, there by letting the calculator determine a wire size that would get us close. That is without much loss. Besides you can do everything on cat wire and 16/2 these days. Heck I have seen guys use it to power subs. High voltage, not speaker level. Would I? No.

aye, aye, capn!

Here's an approach. Every wire gauge has a listed resistance, which may, as Amir shows, be totally unrealistic. But it's all we've got as a starting point.

Here's some arithmetic for you to do. I've listed below the supposed resistance per thousand feet of wire. You can use the values to figure out what you need.

Gauge followed by resistance per thousand feet in ohms.

26 40.81
24 25.67
22 16.14
20 10.15
18 6.385
16 4.016
14 2.525
12 1.588
10 0.9989

For instance, you've got a run of 16 ga that works. It's 89 feet long. You want to know, if you have to use 24 gauge, how long of a run will work just as well.

First, think. The skinnier wire will go a shorter distance, so the math will give an answer smaller than 89. Second, this is a matter or proportions, so something is going to be divided by something else.

We have two numbers, the resistance of 16 and the resistance of 24. The equation that will give the smaller number is 16ga/24ga = 4.016/25.67 = 0.156; multiply that times your working 16 ga length, 89 feet. A 13.92 foot length of 24 gauge will perform the same as an 89 foot length of 16 gauge.

This does NOT figure the maximum length that another gauge wire will work. It figures the length of the other wire with the equivalent resistance.

Ernie

How does 12/2 at 1.588 Ohms per 1000 feet equal .529 Ohms at 300 feet? Should be .4764 at 300 feet?

MISTAKE! MISTAKE! ERNIE MADE A MISTAKE! It was an arithmeticular mistake. You might not believe this, but the original post was longer with more numbers. I quoted the wrong number, I think.

For the record, then:

Be careful what your definition is. You're talking about 12/2. I was talking about a single conductor of 12 gauge wire. Is the resistance of 12/2 the same as the resistance of 12?

If you talk of 12/2, then the resistance, when the circuit supplies power, is twice as much per foot since the two wires would be seen as being in series. I suppose the resistance could be half that if you think of the two wires in parallel... but don't think of it that way for what we're doing here.

So, if 12 gauge measures 1.588 ohms per thousand feet, then it's 0.4764 ohms per three hundred feet. We're talking about two conductor wire, so the resistance would be double that, or 0.9528 ohms. THAT's the number to be used to figure the voltage drop.

(Did I get it right this time?)

Ernie

Semantics Ernie, it’s implicit in the calculation that one conductor is at hand.

I agree. It's implicit that one conductor is involved.

As soon as you say 12/2, however, you are being explicit that the subject at this point is two conductors. At that point you need to make explicit how you're dealing with two conductors.