Understanding Complex Power Calculations: Why is S = 1/2 * V * I?

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The formula for complex power can be expressed as S = Veff * Ieff(conjugate) or S = 1/2 * V * I, with Veff and Ieff representing the effective values of voltage and current, respectively. The 'eff' indicates that these values are the root mean square (RMS) values, which are crucial for AC circuit calculations. The relationship between Veff and V, as well as Ieff and I, is clarified through the equation Veff = V/sqrt(2) and Ieff = I/sqrt(2), leading to the simplification of S to VI/2. Understanding these definitions helps clarify the calculations of complex power in circuit theory. This foundational knowledge is essential for mastering power calculations in electrical engineering.
arkturus
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I don't have a question about a specific HW problem, just a general questions.

When calculating complex power, I understand it's S = Veff*Ieff(conjugate). However, S can also be calculate as S = 1/2 * V * I. Why is this? I feel I'm missing something simple, but I'm pretty lost because the current chapter in circuit theory has a bunch of definitions.
 
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When you say S = Veff*Ieff(conjugate), what does the 'eff' stand for, and what is the difference between Veff and V, or Ieff and I?

Veff * Ieff = V/<something> * I/<something> = VI / <something>^2 ...
 
Ah thanks, simple enough. VeffIeff = V/sqrt(2) * I/sqrt(2) which simplifies to VI/2. Much appreciated.
 

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