why am i able to wire one up to a 12vcar battery and magically get 120v ac?
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There are many ways it can be done. The simplest way is likely by using a transformer.
You can change the AC voltage level with a transformer. The difference in input vest output voltage depends on the number of winding in the input relative to the output side. This is the main reason AC is used in the power grid. It is simple to change the voltage, a higher voltage is more efficient in transporting the same amount of power than a lower voltage. At the same voltage, DC is more efficient than AC in power distribution the problem is it is a lot harder to change the voltage.
Transformers require AC, they do not work with DC. So how do you use one with a battery? The simple way is to just change how the battery is connected to the coil. If you flip the position of the wires to the battery and do that over and over you create AC. It is simple to do with a switch with multiple poles and then to physically reconnect the wires you can then use a specially controlled switch ie a relay. That is how it works in the past today transistors are used as switches to create AC from DC.
A DC motor do exactly this with a commutator, which is a rotation mechanical part that changes the direction in the DC is connected to the could in the motor. Conductive brushes typically made of carbon are pushed agas a rotational commutator with multiple separate conductive areas. Inverter does not use rotational parts like that but is quite simple way to understand how you can make AC from DC mechanically https://www.cs.uaf.edu/2015/fall/cs480/lecture/09_11_motor_control.html
Just changing how the DC is connected produces an AC square wave, not a sine wave like we have in the power grid. It is good enough for some application but not for all and more complex designs exist that create sine waves
https://en.wikipedia.org/wiki/Power_inverter
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.
A transformer will convert amps for volts, so…the watts of power stays about the same (maybe 5% loss of power due to waste-heat and other inefficiencies).
The incoming 12V energy at maybe 20 amps = 240 Watts. The transformer converts that into a 240W magnetic field. Then the output half of the transformer converts that 240W magnetic field into 120V at 2 amps.
I could go into more detail, but that’s the simple version.
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