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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There are many good answers here, withthe math all worked out, but I’d like to add an analogy: in capacitors and inductors, the apparent resistance of the component depends on what it is actually doing at the moment, and what it’s doing depends on what happened to it earlier.
An empty capacitor can pass loads of current, because there’s no voltage in it pushing back, so it’ll start out acting as a wire, then act more as a resistor as it’s being charged, until it’s full and acts like an open circuit. When it’s being discharged, it’ll act like a tiny battery that quickly runs out, before returning to wire->resistor->open circuit.
An inductor does the exact opposite: as soon as power is applied, a magnetic field is created which induces an opposing voltage that tries to eliminate the current flowing. If it got eliminated completely the field would stop changing, and only changing fields can cause induction, so there’ll be a balance where the field is slowly changing and the current slowly increasing, just as if there was a resistor with gradually diminishing resistance.
But just like a capacitor, the inductor stores the energy being put in before reaching steady state, so if you try to diminish the current, the magnetic field will fight this as well, now by generating more current as it winds down.
Fun fact: you can create high currents by shorting out a fully charged capacitor, or high voltages by suddenly disconnecting a fully energized inductor. These are both very useful phenomena, as well as fun to play around with.
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