I know that back-EMF can be considered as a voltage source in series with the motor which is proportional to speed. This is the common understanding, and I totally get it. Before I understood this, I developed an alternate explanation on my own, and I wonder if it has any validity.
Think of this: an inductor resists change in current. A bigger inductor resists it more. A stalled motor resists change in current. A spinning motor resists it more.
A small inductor at a given current has some stored energy. A bigger inductor at the same current has more stored energy. A stalled motor at a given current has some stored energy. A spinning motor at the same current has more stored energy.
Hopefully you can see what a student might intuitively hypothesize: a motor's windings exhibit an inductance that increases with the motor's speed. Not because it's magically growing more turns of wire of course, but perhaps it's a sort of mechanical inductor, storing energy in the motor's momentum, rather than in a magnetic field. My intuitive understanding of an inductor is, after all, a flywheel. Maybe this is an inductor that actually is a flywheel.
Can this analogy be stretched further? In a resistive and inductive load, AC current lags behind AC voltage. Add more inductance, and current lags more. In a motor, current lags behind voltage. If the motor is spinning faster, does it lag more?
And if that much is true, can it be shown that back-EMF is equivalent to an inductance that increases with motor speed?
And if not, why? Intuitive examples would be appreciated first, then the math. I never seem to understand when presented in the opposite order.