Power and Superpositionality

Say $$v(t)=V_1\cos(\omega_1t+\phi_1)+V_2\cos(\omega_2t+\phi_2), \quad i(t)=I_1\cos(\omega_1t+\psi_1)+I_2\cos(\omega_2t+\psi_2).$$ then Now if ω1=ω2, those “cross-terms” become cosines at 0 hz or at 2w. The constant pieces from the cross-terms do not average out—they survive and alter the total DC power. In other words, the two sinusoids interfere (constructively or destructively), and you cannot separate the net power into a simple sum of “power of source A” plus “power of source B.”