What an inductor is
A resistor decides how much current flows. An inductor decides how fast the current is allowed to change — which sounds like a footnote until you switch one off and it produces two hundred volts from a six-volt battery.
An inductor is a coil of wire. That is the entire part: no junction, no doping, nothing that a resistor does not also have. What makes it a component is the magnetic field the coil makes, and the fact that the field takes time to build.
Before the equation, here is the thing it describes. A turbine in a pipe with a heavy flywheel bolted to its shaft.
Pressure across that turbine does not set the flow. It sets how fast the flow is changing — and once the flow is going, it keeps going on its own. Both halves of that are true of a coil, and the second half is the one that costs people parts.
One equation, and it is not Ohm's law
VL = L · dI/dt
The voltage across a coil is its inductance times the rate of change of the current through it. Turned around, which is the way you will actually use it:
dI/dt = V ÷ L
Put a voltage across a coil and the current climbs at a fixed slope. Five volts across 100 µH climbs at 50 mA every microsecond, and it does not care what the current already is.
The destination is still Ohm's law — five volts and five ohms is one amp, whatever coil you put in the way. The inductor only decides how long the trip takes.
Two things fall out of that
The current through a coil cannot change instantly. To change it in zero time you would need infinite voltage, and the universe declines. So an inductor smooths current the way a capacitor smooths voltage — they are the same trick, turned ninety degrees.
To steady DC, an inductor is a piece of wire. Once the current has stopped changing, dI/dt is zero, so the voltage across it is zero, so all that is left is the resistance of the copper — usually a few tens of milliohms. A coil in a DC circuit that has settled is doing nothing at all.
Which means the interesting moments are the switching ones. Everything an inductor does that you can see happens in the microseconds after something turns on or off. That is why they live in switching supplies and radio filters and almost nowhere else.
Interrupt one and it fights you
The flywheel slams into the closed valve at the end of that figure, and the electrical version is the same event. A coil carrying current has energy stored in its field, and when you open the switch that energy has to leave in microseconds. The coil generates whatever voltage that takes.
A relay coil running on 6 V will happily produce 200 V in the reverse direction the instant its transistor turns off. That is not a fault or an edge case; it is V = L · dI/dt with a very small dt. Anything switching a coil needs a flyback diode across it, and that page is about nothing else.
Next: why winding the wire into a coil matters at all, and what the lump of grey ceramic in the middle is for.
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