The Power Superposition Principle

Consider a circuit with two sinusoidal voltage sources. Each one influences the circuit independently, and the superposition principle helps us understand the combined effect by adding up the responses from each source.

According to the superposition principle, the total current due to both sources is the sum of currents due to each source independently. When both sources work together, their individual currents (i₁ and i₂) add up to give the total current. Also, the instantaneous power is the square of the instantaneous current times the resistance.

This concept also applies to power, the rate at which energy is used. At any given moment, instantaneous power in the circuit is the current squared times the resistance. Integrating this over one period yields the average power, which equals the sum of average powers due to each source, and a third term becomes zero for sources having different frequencies.

The simplified equation signifies the power superposition principle, stating that the average power delivered by sources having different frequencies equals the sum of the average power delivered by each source. This principle is crucial in telecommunications, like radio broadcasting. Multiple radio stations broadcast their signals simultaneously, each acting as an independent source of electromagnetic waves. According to the power superposition principle, the total power received by radio is the sum of power transmitted by each station. Tuning the radio to a specific frequency allows the user to listen to one station at a time, despite receiving signals from multiple stations.