 Besides generators and motors, one other really handy device you can make with induction is the transformer. Essentially, transformers are just Faraday's original experiment in disguise. So you take one solenoid, which is just a coil of wire, and you pass the current through it. And that current is going to make a magnetic field running down there. And the advantage of having an alternating current is that that magnetic field is also going to be alternating up and down. And so you've got a changing magnetic field just going to give you a changing magnetic flux. And if you have a changing magnetic flux, then you're going to induce an electromagnetic force, a voltage in the second coil, because the second coil is sharing that magnetic field. That magnetic field is going to come out here and it's going to induce a voltage in that second coil. Now exactly how you place those coils doesn't matter too much. You could have them like that where they're basically in line with each other. You could help a little bit by putting a core of iron down the middle. So you can have a rod of iron that is shared by the two of them like that. And that way the first one will set up a magnetic field in the iron, and then that will be running right down through the second one, and that'll help set that changing magnetic field for the second one. You can also put them actually completely on top of each other, so you can wind them together. They have to be electrically separate of course, but you can have the coils around each other. Or you can even have them side by side up here like this, provided that you get a piece of ferromagnetic material. And join them together like that. And then even then the magnetic field generated by this coil will create a magnetic field that's changing inside that coil, and therefore you'll get a voltage. So one obvious question to ask is why do people build this? Because if I could create a potential difference between these two wires here, and I wanted to create a potential difference between these two wires, another obvious way of doing that is just to connect the wires directly. So I could connect this wire here, and that wire there, and ignore all that coil stuff. So why not do that? And the answer lies in here, in Faraday's law. The electromagnetic force, the voltage between those two wires, depends on the number of loops in the coil. And also when I make my solenoid, the strength of the magnetic field in this solenoid depends on the number of loops in the coil. And so if I have a large number of loops in say the first coil, and a small number of loops in the second coil, that I'm going to be creating a very large magnetic field, but I'm going to be producing a relatively small potential on the other one. So that allows me to take a very high voltage source, and turn it into a low voltage source. And that's a very, very handy thing. When we have 240 volts coming out of the power socket in our houses, we rarely want to plug that into a very delicate device that requires a low voltage without first stepping it through a transformer. And that's why most power packs and devices have transformers built in. Conversely, if you want to make a very large voltage, it turns out that it's much easier to transport electricity long distances efficiently at high voltage. And so what you want is a step up transformers. You want a large number of loops in the second coil. And that means that the voltage going out will be much greater than the voltage coming in. And the ratio of the voltages is just exactly given by the ratio of the number of windings of each coil. One of the possibly surprising things about transformers is just how efficient they can be. You can get nearly all the power coming out of a transformer that you put in. And that's really handy from an efficiency point of view, but it's also really handy because it means transformers tend not to get incredibly hot, for example, as they dump nearly all the power you're putting in. And they don't put out large amounts of radiation. So at 100% efficiency, the power in has to be equal to the power out. And we can remember the formula for the power in electrical circuits because it's just the energy per unit time, remember? And the voltage is the energy per unit charge and the current is the charge per unit time. And so the power is just the voltage times the current. And so the power in equaling the power out would be the voltage times the current for the first coil, would be the voltage times the current for the second coil. That's a little bit surprising because if you remember back to Ohm's law, you know that the current depends pretty much only on the voltage. Specifically, the current is just the voltage divided by the resistance. So we could write the power in terms of just the voltages and the resistance. And that should be a little bit concerning because it looks like the ratio of the voltages can be got from the ratio of the resistances. Whereas we know that the ratio of the voltages comes straight from the ratio of the number of turns on the coils. So how to resolve that? Remember this second one only applies at 100% efficiency. Whereas this one always applies. So actually that's telling us something very important about how to build a transformer so that it works efficiently. You have to carefully match the resistance of the power source and the first coil with the load and the second coil in order to satisfy this equation and this equation at the same time. That's the only way you can get 100% efficiency. And this is called impedance matching.