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Phasor Circuit Analysis: Understanding Effective Value, Power, and Power Factor in R-C Circuits

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This lecture covers the fundamental concepts of phasor circuit analysis, focusing on effective value (RMS), average power, and the relationships between real, reactive, and apparent power in R-C circuits. Topics include capacitive reactance, power factor (leading and lagging), and the power triangle. Examples illustrate the use of RMS phasors for voltage sources and calculations of complex power. Visual tools like phasor diagrams will enhance understanding of voltage and current relationships among R-C circuits.

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Phasor Circuit Analysis: Understanding Effective Value, Power, and Power Factor in R-C Circuits

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  1. E E 2315 Lecture 15 Phasor Circuit Analysis, Effective Value and Complex Power: Watts, VAR’s and Volt-Amperes

  2. Effective Value of a Sinusoid (1/2) Average Power:

  3. Effective Value of a Sinusoid (2/2) In our example: Also: The effective value is also called the Root Mean Square value or rms value.

  4. R-C Circuit Example (1/6) Capacitive Reactance

  5. R-C Circuit Example (2/6) Using rms phasor for voltage source.

  6. R-C Circuit Example (3/6) Calculate Real Power: And Reactive Power: Apparent power is the product of voltage and current of the source. Also:

  7. R-C Circuit Example (4/6) Power Factor is the ratio of real power to apparent power: Power Factor is also the Cosine of the angle between the load voltage and the load current: If the load current leads the load voltage, the power factor is leading; if it lags the load voltage, the power factor is lagging.

  8. R-C Circuit Example (5/6) Phasor Diagram of Voltage and Current Current leads voltage.

  9. R-C Circuit Example (6/6) The Power Triangle showing leading power factor.

  10. Calculating Complex Power (1/2)

  11. Calculating Complex Power (2/2) From now on, we use the above method to calculate complex power.

  12. Lagging Power Factor Example (1/4)

  13. Lagging Power Factor Example (2/4) Calculate complex power directly:

  14. Lagging Power Factor Example (3/4) Power Factor: Power Factor is Lagging Phasor Diagram of Voltage and Current

  15. Lagging Power Factor Example (4/4) Power Triangle for lagging Power Factor

  16. Phasor Power Example (1/4)

  17. Phasor Power Example (2/4)

  18. Phasor Power Example (3/4) Capacitor VAR’s:

  19. Phasor Power Example (4/4)

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