#electrical engineering

We’ve been talking about mutual inductance and magnetically coupled circuits. If you have a couple of coils of wire adjacent to each other such that they can get caught up in each other’s magnetic fields when a current is run through one or both of them, one coil can induce a voltage in the other, even though the circuits are not physically connected.

This setup is the basic construction for a transformer, one of the most ubiquitous pieces of equipment in power transmission. Just as in the examples we’ve been looking at, a transformer consists of two coils of wire next to each other. In a transformer, they’re both usually wrapped around a magnetic core of some kind. The purpose of this is to channel the magnetic flux so that more of it is caught by the coils and increase the strength of the magnetic coupling between them.

Let’s assume for the moment that this core is perfectly ideal - that it channels ALL the magnetic flux perfectly efficiently, such that the same magnetic flux is experienced by both coils.

If this is the case, then the ratio of the coil voltages is equal to the ratio of coil turns. In other words, you can convert from one voltage to another by adjusting the number of coils in the transformer.

There’s a similar relationship going on with the currents.

If we manipulate these equations a little, we find that the total power of the transformer is zero. (For an ideal transformer, at least.)