why am i able to wire one up to a 12vcar battery and magically get 120v ac?
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Modern inverters are kind of like electrical hammers (the physics looks pretty much identical). You can’t apply very much force to a nail just by pushing directly on the hammer, so you swing it, exerting a small force over a large distance, and storing energy in the motion of the hammer head. Then the hammer impacts the nail, and the small force over a long distance is converted into a large force over a small distance.
In electrical circuits we use a component called an inductor, which stores energy in a magnetic field. By apply a small voltage to the inductor, we increase the current in it (like swinging the hammer). Then we use some kind of switch, usually a MOSFET or IGBT, to “impact” the thing we want to power, converting a small voltage over lots of electrical charge to a high voltage of a small amount of charge.
There are different kinds of circuits that work similarly to this known as switched mode power supplies. They can convert between DC and AC and are very common today.
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