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

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SUMMARY

The discussion clarifies the calculation of complex power in electrical engineering, specifically the formula S = 1/2 * V * I. This formula is derived from the effective values of voltage and current, denoted as Veff and Ieff, which represent the root mean square (RMS) values. The relationship S = Veff * Ieff(conjugate) is established, where Veff = V/sqrt(2) and Ieff = I/sqrt(2), leading to the simplification of the complex power equation. Understanding these definitions is crucial for accurate power calculations in circuit theory.

PREREQUISITES
  • Understanding of complex power in electrical engineering
  • Familiarity with root mean square (RMS) values
  • Basic knowledge of circuit theory
  • Concept of conjugate values in electrical calculations
NEXT STEPS
  • Research the derivation of complex power formulas in electrical engineering
  • Learn about root mean square (RMS) calculations for voltage and current
  • Explore the concept of conjugate values in AC circuit analysis
  • Study the implications of effective values in power factor calculations
USEFUL FOR

Electrical engineers, students studying circuit theory, and professionals involved in power system analysis will benefit from this discussion.

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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