Statistical distributions are derived for power dissipation inside linear or nonlinear circuit elements driven by a circuit source and illuminated by an external random electromagnetic field. The probability density functions of the normalized power dissipated inside rectilinear, planar, and volumetric resistive elements are derived by splitting the total internal field in components with appropriate bias fields. These results are extended and generalized to several canonical configurations, for the combined internal and external deterministic or random excitation of single or multiple circuit elements. The results are fundamental to the analysis of the operation and malfunction of electronic circuits and their elements when placed inside complex electromagnetic environments, such as reverberation chambers, or on printed circuit board, as well as to their electromagnetic compatibility, emissions, and susceptibility.