How long do inductors take to change voltage?

Question

I'm an EE designing a power converter, and this question has been nagging at me for years, so I wanna ask people who know more fundamental stuff than I do.

Also, I don't have a physics degree, so please forgive me if this question is dumb.

In circuit theory textbooks, inductors can change voltage instantaneously, just like capacitors can change current instantaneously. But the change cannot take 0 time, can it? I am aware that voltage arises from QM, so I can see how in a coherent quantum system, where many particles are sharing an entangled state, the information of voltage could travel instantly from one location to another, and perhaps a superconducting inductor in that scenario could change the voltage in 0 time.

But a normal inductor with resistance at room temperature cannot possibly behave like that, can it?

When I take my finger off the trigger of my drill, how long does it take for the voltage across the motor coils to jump from a few volts to the thousands of volts necessary to make a nice spark?

Answer 1

In AC circuit theory, "voltage on inductor" means difference of the Coulomb potential. This is instantaneous function of position of all charges in the world, but in practice, only the closest charges matter. Thus change of voltage on an inductor is directly determined by changes of electric charge distribution in the circuit (and nearby objects, which we usually neglect).

This Coulomb potential (instantaneous function of position of charges) has nothing to do with information. Also, information, as opposed to changes in Coulomb potential, does not travel instantly, since (we believe) information propagation obeys Lorentzian relativity (finite speed of propagation) as opposed to Galilean relativity (infinite speed of propagation).

Non-zero change of voltage requires non-zero displacement of a charged particle. Such displacement cannot happen instantaneously, it takes time for the charges to move. When inductor is being connected to a battery, this means there is movement of wires or inductor, and it takes some time. During this time, before the connection, there is no strong current, and only electric charges on surfaces of conductive objects rearrange themselves so that the whole inductor is at the same potential. Right after the inductor is connected to the battery and conductive circuit is established, this electric charge on surface of conductors quickly rearranges itself so that there is potential difference between the terminals of the inductor. This takes some short time.

So indeed, finite change of voltage between inductor terminals can't happen in zero time. It takes a little time for the charges to rearrange themselves to produce the given potential difference.

However, the time required is in practice so small, that in many practical cases of circuits (where the relevant frequencies are low enough), we can simplify and assume that charges rearrange themselves to produce the voltage instantaneously at the time of connection to voltage source.

This simplifying assumption may start to fail in some cases, such as when the time needed for rearrangement is comparable to period of waves we are interested in. This may be e.g. for radiating circuits, or when relevant frequencies we are interested are high enough.

Answer 2

Forget about coherent quantum systems and some such. You are an EE, you know that all real wires including coil wires have a natural Ohmic resistance so that the resulting voltage drop is proportional to the current along the wire. If you combine that resistance with a magnetic behavior modeled as an inductive phenomenon, ie., an inductance in series (in series because the current inducing the magnetism is also along the wire) you do not have anymore any instantaneous, hence, unphysical behavior.