Which brings up an interesting point.
It's all too easy to consider a length of wire as an ideal conductor by ideal we mean:
That there is no power loss in the wire.
That the wire doesn't heat up.
That there is no voltage drop in the wire.
In short that there is no resistance in the wire.
current
An electric current is the movement of electrons through a substance. the harder it is for those electrons to move, the more resistivity that substance has.
Resistance is a real true opposition to the movement of electrons, hence a real opposition to the flow of current.
So what causes Resistance?
Basically, as the electrons travel through the material that is a conductor they bump and jostle with the atoms inside the conductor.
So why does Wire matter.
I suppose the easiest way to explain this is to go back to considering the electricity supply as water contained in a large bucket of header tank.
Think of a piece of wire as like a tube attached to the bottom of that bucket.
The longer the tube is the harder it is for water to rush out of the bucket, so the really long tube is providing resistance to the water flowing, now if you make the tube a lot shorter the water will run out the bottom of the bucket a lot faster.
Now consider making the tube a much larger diameter, again it's much easier for the water to flow through the tube.
The same is true of electricity and wire.
The thinner a piece of wire the less paths there are for electrons to flow through that piece of wire. the more chance that they'll be bumping into the atoms in the wire. The thicker the piece of wire, the more atoms there are, and therefore the more ways round those atoms.
It's like you've added another lane to a road and thus the electron traffic flows more freely.
The Calculations
In order to calculate the resistivity of a piece of wire. You need to know three things.
The cross sectional area of the wire, (it's thickness, if it's a round piece of wire, the are will be (Pi * d/2)^2
you need to know the length, from end to end.
And last but not least you need to know the p value of the wire, (it's conductivity).
R = pL/A
You can find a table of P values (expressed as Ohms per centimetre) here
That table also lets you see the kind of conductivity of the wires... this can lets you make some intelligent design choices.
Skin Effect
Skin effect is a bit of a strange phenomenon, and probably doesn't really fit into beginner lessons, but I can't really see that this will be covered in a second more advanced lesson about wire selection. So I figured it's be best to cover it here.
Skin effect starts to come into play when you're transmitting electrical signals at a high frequency.
Basically, rather than using the whole cross sectional area of the wire, the electrons only travel near the surface of the wire, not moving at the core of the conductor very much, or even at all.
Because the electrons are only flowing down a part of the wire, this has the effect of removing lanes in a road, there is more congestion, more resistance to the traffic of electrons.
Below is a diagram, it shows a particular gauge/thickness of wire.
next to this is the path that the electrons are using, you can see that at high frequency, the inside core of the wire isn't used any more.
Rearranging all the black pixels in the picture (so the same area of wire in use if this was a low frequency signal) shows you just how significantly smaller the effective gauge can be when the skin effect comes into play. -which can have knock on effects to the resistance of the wire, and the way it heats up, hence it's current carrying limits.
If can halve the diameter of your wire (depending on the gauge to begin with), so if you're planning on transmitting high power at high frequencies (for example if you're building a switch mode power supply) remember to include this into consideration when choosing your materials.
Conductor types
Perhaps one of the most important things that you're going to have to decide each time you buy wire is the type of wire you buy, that's multi strand/multi core vs. single strand/single core. Multi core has lots of smaller wires all bunched together, whilst single strange, well, only has a single strange.
There is a common misconception that using multi core wire will lessen the effects of skin effect (described above), however this is not true, all the conductors in the wire are connectted and act as a single solid core connector so the skin effect still happens in multi core wires.
So why have different types of wire?
Well single stand wire is a single piece of metal, if you move a single piece of metal enough is will flex a few times, but eventually it'll break. (suffers from fatigue) so this wire is not useful for applications where the wire will be constantly flexed e.g. a network patch cable, a musical instrument cable (guitar lead) computer cables.
Solid core wire is easier to manufacture, and thus is a little cheaper than multi core wires. So in applications where the wire won't be flexing, e.g. computer network structured cabling, Telecom structured cabling etc, you'd use solid core wire.
Solid core wiring also has less exposed surface area than lots of small conductors so corrodes far less slowly than multi core wiring.
The picture below shows a multi core wire next to a solid core wire, both are insulated (green) the black area shows the conductors, here you can see that, because there will always be small spaces when packing round objects next to each other, that for the same diameter outer cable a multi core wire will have a higher resistance, because the total conductor area is smaller.
Beneath the two conductors of equal diameter is a representation of how much conductor area is actually in the multi core wire, the red is again the space between the wires, just all pushed to the outside and the conductor all pushed to the middle.
Designing products: A Case study
A good example of the kind of design choices that you can make can be seen in the Telecom industry. Traditionally copper wire has always been used for wiring carrying the signals to the pole outside your house and from the pole to the inside of your house, however, during the 80's the price of copper soared in price, making it incredibly expensive to put copper wires in, so during this time the Telecom companies switched to using aluminium wires rather than copper, at a much reduced cost.
Aluminium is not as good of a conductor as copper, it also has a higher resistance (and hence greater transmission losses), but it did the job and was much cheaper.
Being an engineer isn't always about creating the fanciest design, it's about creating the best design, making the right decisions rather that the best decisions.
In this case for voice calls aluminium is a perfectly valid design choice.
There is of course a drawback, people with aluminium cabling living over a certain distance from the exchange, often find that they are unable to receive broadband, but in the 80's long distance broadband was just a pipe dream.
Considerations
The point of including the information above is basically to say: Chose all your components carefully. Different wire gauges constructions and materials all have different electrical properties characteristics and costs. There is no one tool to fit all jobs, and no one material to fit all jobs either.
Wire has resistance, so if you've got a really long wire with a thermistor on the end as a remote temperature sensor, don't expect to get the same values as in your test board where your thermistor was sat right onto the circuit analysing the readings.
With wire you have resistance, with resistance you have voltage drop, and heating inside the wire. no wire is a perfect conductor. get your wire sizes wrong on your mains wired project and you could end up burning down the house.
A basic chart for copper wire vs resistance at different gauges is shown on this page:
http://www.cirris.com/testing/resistance/wire.html
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