The discovery was a slow process. It basically started as a strange effect with no applications. People noticed that rubbing certain materials over each other created static electricity wich then repels or attracts each other.
Then the first big breakthrough was a guy named Volta discovering the Voltaic cell where chemicals could create the same effect. Then slowly more people discovered more properties of electrical charges, that metals transmitted them so you could use wires to direct it, and then very importantly that you can use magnets to generate electricity by spinning them inside a wire coil.
How it works is that every atom is made of a positively charged core and negatively charged electrons. Under several conditions you can move electrons from one place to another to create an imbalance that wants to balance out again by moving electrons back to equilibrium. This difference causes a voltage (“electrical pressure”) and when electrons actually flow thats amps (“electrical flow”).
Since they want to return to balance with quite a lot of force you can basically let them do usefull things on the way. For example when they move through a thin wire it heats up from the “friction” and when the wire gets very hot it will produce light. Moving electrons also cause a magnetic field around them wich you can use to move things in electrical motors
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