Think back to when you’ve been stuck in a large group of people all trying to get to the same place, like down the corridor after assembly, or out of the exit at the tube station. You’ll find that in some situations, the people go s.o. s.l.o.w.l.y whereas in others, you might at least move enough to give you hope that you’ll be out of there one day! Every now and then, you might even spot a route that nobody is using.
And this is exactly the same with electrons, as they move through wires and work all your electronic gadgets. They are heading down a small corridor and around the electrical circuits, trying to find the easiest way of getting through. The factors that affect how much resistance there is for them, that is, how hard it is to get around, are very similar to us in the crowd.
The length of the narrow section that the crowd has to push through really affects the speed of the movement, the longer it is the slower you go. And with electrons, this is important too. Normal wire, which you may have used to connect up the bits in your electric circuit, has a resistance to it, and the longer it is, the more it has. So if you want your electrons to have an easy time, use a shorter wire.
The cross-sectional area too has a big effect, if you can only travel one person at a time, then that’s really going to cause a bottleneck. But if you can travel two or three at a time then it’s much faster. So the same is true for our doppelgangers, the electrons. A wire’s cross-sectional area is important, as the larger the area the lower the resistance.
Terrain (or the material) is an important factor as well. A crowd going through the tube station to the exit will have a much easier time of it than a crowd leaving a music festival when it’s rained a lot and there’s mud everywhere. Particularly if high heels are involved. The difficult terrain will slow everyone down. Someone might even fall over! Electrons are just the same, they hate mud. Wait, that’s not quite right. Electrons are just the same, some materials are harder to go through than others. But unlike with humans, where we fall down, cry or shout, the electrons will just soldier on, it’ll just be harder, so they get hot with all the effort. This can lead to the wire glowing red hot (like in your toaster) or white hot (like in a light bulb). So it can be a useful thing, but it’s also something to watch out for.
The last factor that influences resistance is temperature. This is where the crowds-electrons analogy falls down a little. So let’s say the crowd’s ‘temperature’ is their anger levels. As the anger levels rise, there will be more fights and the crowd will end up going more slowly as fighting people get in the way. With a wire, the electrons find that as the temperature rises. It’s harder to go through it, because all the molecules that make the wire start to vibrate a little more, and get in the way.
So we know that resistance increases with length, decreases with area, changes depending on the material, and increases with temperature. Thankfully for us, the materials wires are made of have all already been measured in the past so we can just look up the value of the resistivity, which is the measure of how hard it is for an electron to go down it. We can put all these together to make an equation from which we can work out the resistance of any wire. If only it was so simple with people.