Electric Circuits and Networks

7.6 THE POWER SUPERPOSITION PRINCIPLE

Current variables and voltage variables in a linear electric circuit obey the Superposition Theorem. However, instantaneous power in a linear circuit does not follow superposition principle. Consider a circuit driven by two sources v_S1(t) and v_S2(t) and let the corresponding response components for the voltage across a particular element be v₁₁(t) and v₁₂(t). The corresponding response components of current through that element are i₁₁(t) and i₁₂(t) as per the passive sign convention. Then,

The instantaneous power delivered to the element when v_S1(t) is acting alone, P₁(t) = v₁₁(t) i_ll(t)

The instantaneous power delivered to the element when v_S2(t) is acting alone, P₂(t) = v₁₂(t) i₁₂(t)

The instantaneous ...