How do inductors and capacitors work????What do they do???

Answer 1

Electromagnetic energy can be stored in two ways: in the form of an electric field E, or in the form of a magnetic field B. The volume integral of the magnitude squared of each is proportional to the energy stored. Capacitors store energy by creating an internal E field by charging two plates or foils separated by a small distance with opposite charges. Inductors store energy by creating a magnetic field by current flowing in a looped or coiled conductor. The relationship between current and voltage in each is described by a simple equation you can look up yourself.

Answer 2

A good answer to "How do they work?" could be several chapters of a physics book. I can answer "What do they do?" fairly briefly.

A capacitor opposes sudden changes in voltage between its 2 contacts because it has stored a reservoir of charge at the current voltage. So the voltage can change but only after a significant current has flowed either into the cap or out of the cap, depending if the voltage is increasing or decreasing. This characteristic is often used to filter out high frequency noise or voltage transients.

An inductor opposes sudden changes in the current passing through it. It can do this because it has stored energy in its magnetic field.