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First off, I understand that current into and out of a resistor has to be the same, and the huge volume of people who are confused about this has made it very difficult to find an answer to this very different question:

Why is the current through an inductor and a resistor in series the same? Or, for that matter, a capacitor and a resistor?

By my understanding, an inductor works because a current creates a magnetic field. A changing current therefore creates a changing magnetic field, and a changing magnetic field creates a electric field pushing the current back.

I have been led to believe that, when this happens, there is a negative charge built up at one end of the inductor, electrons that are being repelled by the electric field piling up. This is what creates the Voltage across the inductor, the buildup of negative charges on one side creates a potential difference.

As small amounts of current eek their way through, the inductors resistance to current decreases. At the same time the voltage across it is increasing as negative charges build up. The greater the voltage, the more 'force' their is to push electrons past the electric field, the more current their is, the less the inductor resists said current, etc. until their is effectively no electric field and no resistance.

This was a long intro, but it comes down to this: if the buildup of charge on one side is a fundamental part of how inductors work, then that must mean that there is an amount of charge between and inductor and, say, a resistor. The same argument goes for capacitors. The only reason they work is because they store charge. Now, if, in a series circuit, the current flow through the capacitor/inductor is the same as the current flow through the resistor which, in this example, precedes it, how is it possible that charge builds up? To show in a diagram:

 === 5 amps==>  negative == 5 amps ==>
                buildup
_____ Λ Λ Λ ________________| |______
       V V V                | |

We know there is a buildup of negative charge on the capacitor plate, so how can the current be the same through both components? That would violate conservation of charge.

I should add that I am asking this more in the context of AC circuits.

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I have been led to believe that, when this happens, there is a negative charge built up at one end of the inductor, electrons that are being repelled by the electric field piling up. This is what creates the Voltage across the inductor, the buildup of negative charges on one side creates a potential difference.

This is incorrect. No charge accumulates in an [ideal] inductor. If it accumulates in a non-ideal inductor, we'd model that with a parasitic capacitor.

if the buildup of charge on one side is a fundamental part of how inductors work, then that must mean that there is an amount of charge between and inductor and, say, a resistor.

Since the premise of this is wrong, there's no need to discuss the conclusion.

We know there is a buildup of negative charge on the capacitor plate, so how can the current be the same through both components? That would violate conservation of charge.

Because for every negative charge that builds up on one plate of a capacitor, an equal charge is repelled from the other plate (leaving a positive charge behind), so the current exiting one plate is equal to the current entering the other.

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