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An inductor is kinda like a funnel, or a strainer. When you pour water through it, it still flows through, but all of it doesn't go through, only some of it. Once it fills up, everything you put into the funnel goes "through" it (overflows out the edges) so you have 100% flow. Once you turn the faucet off, the funnel keeps draining because it has water stored up in it.
Inductors are just like this funnel that stores water (funny how electricity can be compared to water so well, but they don't go together at all -- except for pure water). The only difference is, inductors store energy rather than water. To further elaborate, they store energy as a magnetic field. When you put electricity through a piece of wire, it creates a magnetic field around the wire. When you take away the electricity, the magnetic field begins to dissipate. Now, electricity can be generated under a changing, or in this case, dissipating magnetic field. As the magnetic field dissipates and becomes weaker, it generates smaller amounts of electricity until it goes away completely. Of course, all this happens in fractions of a second.
The problem with the piece of wire is that it doesn't generate a strong enough magnetic field to be considered an inductor. Typically, an inductor is a piece of wire wrapped around something else, or in a coil, so that the magnetic field of the wire is compounded (combined) on itself. Remember how when you break a magnet in half, you get 2 weaker magnets each with 2 poles? Well, this is kinda the reverse, you are putting together 2 weaker magnets to form a stronger one.
Now, to connect my example to how PWM is applied to a motor. Okay, lets say we need to power a waterwheel with buckets of water. However, it takes too long to get the buckets of water. So, put a funnel above the waterwheel. Then, pour the water in, the funnel will drain and the waterwheel will spin, until the funnel is empty. However, it will keep spinning because of momentum (and inertia - an object in motion will stay in motion), kinda like how a bicycle wheel keeps spinning when it's not on the ground. The water wheel will keep spinning until friction in it's bearings stop it, or until you add another bucket of water to the funnel to keep it spinning longer.
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