Inductance vs frequency
Suppose we have a sine signal applied to a inductive load. Is the inductance of the load changed if the frequency of the signal is changed?
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If your question is theoretical (you are dealing with ideal components), then the answer of Olin is just fine. If it is concrete, that's the answer of Andy.
In the concrete case furthermore, I would add that what interest the engineer in general is not only the inductance, but the whole picture, which involve parasitic capacitances, resistances and inductances: you usually want to know how your load react at a given frequency, or in a certain range of frequencies. I wrote much more details about that in my answer to this question, so, I will not repeat myself.
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Inductance is defined by the shape of the coil, the area of the coil, the number of turns in the coil, the distance between turns, the ferromagnetic permeability of material within (and surrounding) the coil and induction to other not-so-obvious conducting parts.
Frequency lowering (with a fixed AC voltage) will produce more current and this can saturate magnetic permeable materials and this can lower inductance (sometimes quite considerably). Raising frequency beyond a point will cause some ferromagnetic materials to reduce their permeability and this will effectively lower inductance.
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No. An inductance is an inductance.
One way to look at an inductance is as an impedance that is a function of frequency:
Zind = ωL = 2πfL
Where Zind is the impedance magnitude of an inductance, ω and f the applied frequencies, and L the inductance. When ω is in radians/second, f in Hz, and L in Henrys, then Zind is in Ohms.
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