 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've 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. Now 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.