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I tore open an AC adapter to find out what I was doing wrong in my own power supply attempts. Before any other components, and connected directly to the outlet prongs, was a transformer. I know that it drops voltage and (by ohm's law) the amperage as well. But how does its survive the process? Why doesn't it have huge amounts of waste heat the way a current limiting resistor does?

Why doesn't the primary coil of the transformer--effectively a tiny wire short circuiting an AC outlet--burn up? I'm certain this has something to do with the impedance of an inductor, but I just can't figure out what!

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Physics magic!

Inductance is a function of magnetic flux. For a short time during the AC cycle, the magnetic core stores energy. As verence wrote, it's a very different, but a process with some parallels with capacitance.

A property of inductance is the ability of the changing flux to induce a voltage in a coil. So the process is symmetrical--change a magnetic field with current, and that changing flux can induce current flow elsewhere. All very predicable, and coincidentally very useful, electrically. In a well-designed transformer, This interplay is fairly efficient, and losses are minimal.

As verence also wrote, the impedance of an inductor rises with frequency. In a transformer, the load impedance of the secondary is reflected back to the primary coil. Which is why the primary coil of a transformer doesn't draw much current if there isn't a load on the secondary.

Light, electricity, magnetism--all very interconnected, magical things.

Reflected? So when there is no load(AC adapter plugged in, but nothing attached.) the secondary coil's impedance comes into play?

Actually, now that I think about it, the transformer is two inductors on the same core. The impedance of the whole would be a sum of the two.

Magical indeed!

Oh yeah! One way to think about it:

"Inductance" is the resistance to current flow, caused by the magnetic flux lines building and collapsing. [Lenz's Law:If an induced current flows, its direction is always such that it will oppose the change which produced it.]

If the secondary of a transformer is open (unconnected), there's nothing effecting the flux, so the transformer operation is mostly "self-induction" -- that property that resists flow.

When the secondary is drawing current from the core (mutual inductance), it also changes how the magnetic flux interacts with the primary (that resistance to flow) -- which in effect reduces the impedance of the primary coil. The more current draw in the secondary, the more current draw in the primary (it gets hotter, etc.).

So the load impedance of the secondary is reflected backwards to the primary. Pretty cool how that works.

It's not perfect, of course. There's flux leakage, etc.

Why does it work? Magic!

Well, no, not really. You are right, a transformer has a very low resistance - it is only a piece of wire (most of the times wrapped wrapped around a core). And that is the reason why transformers don't work for DC. For DC, only the resistance is important.

For AC on the other hand another property of the transformer is important:

Impedance. It's like a frequency dependant resistance (kind of). For a coil the impedance gets bigger the higher the frequency gets. For a capacitor it's just the other way round.

And there is another effect: Saturation. When a current flows through a wire it creates a magnetic field around it. The multiple loops multiply the field's strength. The core of the transformer can only handle that much of field before it is saturated (can't take any more). So the already existing field kind of pushes back against any new field a current would create - thus limiting the current.

The 'not getting warm' thing is another special feature of impedance: While it limits the current, it does not do it by converting any energy to heat.

Thanks Verence!

So, an inductor has a certain value of impedance based on it's number of coils, core material, etc. This is how much it resists changes in current, and is effectively resistance. This limits the amount of power the primary coil of my transformer will draw from the power outlet. Right?

And eventually, at a high enough amperage the core will become saturated. At this point the primary coil simply can't put more magnetism into the core. And the secondary coil can't draw more energy than is available, so this creates a limit on current draw on the secondary coil. Yes?

Granted, these are simplified.