it states that the voltage across an inductor is V = L(di/dt), why do we not use V = IR? Or what is the derivation of V = L(di/dt) or the conceptual explanation?
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Ohms law only applies to *Ohmic* devices.
That is devices where I increase proportionally to V across the whole range. Most resistors fall under this and we treat incandescent light bulbs and heating elements like they are because they’re close enough in the operating range, but a cold incandescent lightbulb has about 1/10th the resistance of a hot one so the current changes significantly as voltage increases
For non-Ohmic devices you have to use the right equation. For inductors its V=L di/dt, for capacitors its I=C dv/dt, for diodes and transistors its a lot more complicated
The important thing is knowing what equation to apply when. Just as you can’t solve projectile motion with just Distance=Velocity*Times you need to use all of the *proper* equations to get to the right result in electronics
For an inductor, the current flow induces a magnetic field and magnetizes the core. If you crank current up quickly you try to quickly change the magnetic field in the core and the existing magnetic field pushes back on that change causing the voltage required to get that change in current to go up. If you go slowly then everything has time to get into the right alignment and you can build up to the same magnetic field with much lower voltage, or once you’re fully charged up the push back from the inductor drops to zero and now its basically a short.
V=L di/dt is a fundamental relationship, it is a first principle and therefore cannot be derived from other lower level things
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