The electrical system in those airplanes I once flew (someone suggest a nickname for it, eh?) underwent a few changes from version to version. I remember that the first one was the first airplane I flew equipped with generators, not alternators, the functional difference being that a generator will not charge the battery at low rpm, but it can be used to charge an absolutely flat battery (assuming the battery has the capability of holding a charge) while an alternator can charge at low rpm but needs there to be a bit of juice left in the battery to excite the field so it can work. You know what? I've recited that a hundred times, and can continue, but in order to ensure I really know what it means, I shall try to build an airplane electrical system from stone knives and bearskins. Let this be my apology for weeks of soul-searching, arts classes and lolcats.
Electricity is essentially the displacement of charges. Rub dissimilar materials and they may become oppositely charged and cling together. The differential may discharge in the form of a spark. It's as if every neutrally charged molecules were wearing a hat, but when you rub them together the hats all fly up in the air and the molecules with a greater millinery affinity grab more than their share. So when the dust settles you have the molecules of one substance wearing extra hats and the molecules of the other being hatless. This isn't a stable situation, and given the chance to correct it, the ones with extra hats will give up their headgear and the bareheaded ones will grab up stray hats. By this model, electric current would compare to a string of people with hats, all snatching the hat off the person to their left and putting it on, over and over again around in a circle.
A flow of electric current induces a magnetic field around a wire, and likewise movement of a wire through a magnetic field induces electric current in a wire. It's like passing hats creates a breeze, but a breeze itself lifts up people's hats. Can't have one without the other. The hat passing is driven by the power source, such as a battery. In a motor the magnetic field is used to create rotation--doing work with the breeze from the hats. In a generator, a breeze is used to make the hats move.
Rather than using just one wire for this effect, wire is wrapped in layers around a core, giving more electric-magnetic interaction in a more compact area, so making the whole thing neater and more efficient, like arranging your hat-wearing people on tiered benches so the same breeze can lift more hats or to increase the breeze in a small area. I think I'll stop talking about hats now, but if you like hats, then from here on read "movement of hats" for electric current and "breeze" for magnetic field.
In a generator an electromagnet creates a magnetic field around an armature (a spinny thing) wrapped with wire. The spinning movement induces an electric current along the wire. The force to spin the armature comes from the airplane's internal combustion engine, the thing that's driving the propeller. That's right, they use electricity to make a magnet, then they use the magnet to make more electricity. With this much information it seems as though the generator can't produce power unless it already has power, because otherwise what would power the electromagnet, but the trick is that having acted as the core of an electromagnet, the iron contains remanent magnetism. It's not a lot, just enough to induce a small current in the spinning armature, which is enough to increase the magnetic field so that it can generate a greater electric current and so on until it reaches a steady state. You can get more current by turning the engine faster, but you can't get more at low engine speeds. In fact you might not get enough at low engine speed, the weakness mentioned in the first paragraph of this entry. I've just learned from this site (which describes alternators and generators well, albeit without hats) that when you first connect a generator you need to polarize it before starting the engine. That also implies that if I disconnected a generator for some reason and then reconnected it, I could damage something by starting up without polarizing it. Another reason to keep screwdrivers out of the hands of your pilots.
The direction of the electrical current induced in a wire depends on the direction of its movement relative to the direction of the magnetic field. There are wacky things you can do with your fingers to figure out which way that is, but we're not reliving our grade eleven physics classes here, so you can put your fingers down. The point is, if you're spinning the armature, you can see that you'll get a relatively strong current as the wire cuts across the magnetic field, a current weakening to nothing as it moves to be parallel to the field, and then a strengthening current in the opposite direction. That is, it will produce an alternating current. An old airplane like this wants one-way direct current, so to prevent it from flipping back and forth, it's connected to the rest of the electrical system via a split ring device called a commutator, which reverses the connection every half turn. The end result of having both the connection reversed and the current reversed is steady current.
Generators are old-fashioned and more troublesome for maintenance, so the manufacturer allows you to replace the ones in this airplane with alternators. An alternator works on the same principle as the generator except that in the alternator, the wire windings in which the current will be induced are on the outside, and hold still, while the electromagnet that creates the magnetic field spins on the inside, connected to electrical power via a slip ring, which is simpler than a commutator. AC is converted to DC with a diode. A voltage regulator increases the current to electromagnet so that the alternator produces sufficient power for the aircraft electrical services, even at low rpm. That requires the alternator to draw power from the battery in order to get going, but it's worth it, because the alternator can then charge the battery immediately after start. A generator may be still discharging during low power taxi.
The POH copy I have here claims the aircraft has a 12V 33 ampere-hour battery and two 12V 50 A generators, one on each engine, but who knows if the airplane it belonged to still has generators. If it does, each generator has a voltage regulator and a there is a paralleling circuit to divide the load between the generators. If only one engine is running, a reverse current relay cuts its generator out of the circuit. Also, typically an alternator produces a higher voltage than the battery, so that it can charge the battery. I'm winding down now, so I'll see if I can write about voltage regulators, RCRs and paralleling circuits later.
Hyperphysics is an excellent site for this kind of thing, but I'm not too impressed with their 3D field diagrams.