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What are they and what are they used for ?

Often one speaks of Reactance, Impedance and Inductance, but in the end they are all the same subject.
When we speak or write, we usually refer to a coil with or without a magnetic nucleus, which effects the electric line in AC.
A coil, usually wound on an isolated support, features an Inductance which represents the value of it’s inherent characteristics.
This coil, with a preset Inductance value, when followed by an AC currency, features a braking effect to the electric current circulation and this occurs thanks to the Reactance, which is only causing resistance against the AC.
The effect it produces in a circuit, is to limit the moving AC and to change it respectively to the voltage of abt. 90° .
To speak generally of a Reactance is incorrect, as it is more precise to speak of an Inductive Reactance against a Capacitive Reactance.

L = Inductance in HenryXr = 2 * p * f * L

Xr = Reactance in Ohm

Z = R + jXr

Z = Impedance in Ohm

Often we speak of a Filtered Impedance, but an Impedance is only a total Inductance, a coil with or without a nucleus, and has both a Reactance value and a ohm Resistance value.  The two values put together determine the Impedance value at the moment of the presence of current
The Reactance value is proportional to the used frequency (see the formula) and brakes the higher frequencies, when not wanted, which is the same effect given by a filter.
In magnetic start-up motor systems, the AC resistances used cause a voltage drop and feature a lower voltage than the actual nominal one, thus needing resistance groups with high dissipating powers.
If a circuit features high waveform deformations, there are surely multiple frequency harmonics, which can be blocked at the input with a series of Inductances.
Frequently, one can find rebuilt waveforms, as in inverters for three-phase motors, there are both a base AC component and many kHz frequencies, generated from the actual system.  In these cases is better to use an iron nucleus free Inductance and substitute it with one that has a magnetic circuit that is completely air bound.
Magnetic nucleus used for the frequency feature losses, which continue to increase when working.  The result will be, for the frequency at the kHz level, the inductive value of the coil is almost null and the magnetic nucleus increases it’s losses and overheats in an uncontrollable way.
We could discuss further about Inductance or Reactance or Impedance, but it is better to see them directly in their forms and most interesting uses.