  This paper studies a possible connection between the way the time averaged
electromagnetic power dissipated into heat blows up and the anomalous localized
resonance in plasmonic structures. We show that there is a setting in which the
localized resonance takes place whenever the resonance does and moreover, the
power is always bounded and might go to $0$. We also provide another setting in
which the resonance is complete and the power goes to infinity whenever
resonance occurs; as a consequence of this fact there is no localized
resonance. This work is motivated from recent works on cloaking via anomalous
localized resonance.
