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Is there a (preferably microscopic) explanation for why a resistor does not dissipate reactive power?

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First, the reactive power is not dissipated, but which corresponds to power delivered by the power stored in the reactive component (inductor or capacitor) during a semi-cycle; in the next half cycle, the component returns the stored energy to the source.
For this to occur, the component must have the ability to store energy. In the case of a capacitor, the energy is stored as electric field, whereas in the case of the inductor, the energy is stored as magnetic field.
For the resistor, by definition, this component does not have the ability to store energy, if not all of the energy that is given, is transformed (usually heat).

These concepts are in theory lumped circuit. For real resistors, you can always find reactive effects, but are negligible for normal applications; but may be noticeable at high frequencies.

If you deal with the theory of lumped circuits, the answer is that the resistor has no reactive effects due to their inability to store energy.

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perhaps because a resistor (at least an ideal resistor) is not a reactive component. and neither do reactive components (such as capacitors and ideal inductors) dissipate power.

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