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Dissipation refers to loss; an ideal capacitor is a lossless device because under an AC applied voltage, an AC current flows but no power is lost. That is because the current and voltage are out of phase by 90o.
The dissipation takes place in the dielectric and therefore air core (for all practical purposes) capacitors are close to ideal. For real dielectrics (say a plastic film), the dipoles (that are responsible for the high dielectric constant) take time to orient with the external electric field and that process is mainly responsible for the dissipation (Debye effect). This results in a phase shift different from 90o and that is the main factor for loss in a capacitor.
There are other factors that can also cause losses. Series resistance is important for electrolytic capacitor (Warburg effect) and sometimes you must consider inductance too. But the major source of loss in a capacitor is the dielectric.
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