Calculating Maximum Average Power of AC Circuit

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SUMMARY

The discussion centers on calculating the maximum average power in an AC circuit by correctly identifying the load impedance. The correct approach is to set the load resistance, \( R_L \), equal to the magnitude of the Thevenin impedance, \( |Z_{th}| \), which is \( 9.412 \, \Omega \). The confusion arose from the assumption that a reactive component could be added to the load resistance, which is incorrect. The conclusion is that the load impedance must be purely real to maximize power dissipation.

PREREQUISITES
  • Understanding of Thevenin's theorem and impedance in AC circuits
  • Familiarity with complex numbers and their representation in electrical engineering
  • Knowledge of maximum power transfer theorem
  • Basic concepts of AC circuit analysis
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  • Study the maximum power transfer theorem in detail
  • Learn about Thevenin and Norton equivalent circuits
  • Explore complex impedance and its applications in AC circuit analysis
  • Investigate methods for calculating power in AC circuits
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Electrical engineering students, circuit designers, and professionals involved in AC circuit analysis and optimization.

Vishera
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Homework Statement



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Homework Equations


The Attempt at a Solution



The text in the black box looks wrong to me. The method below is how I would do it. Why is it wrong?

$$To\quad maximize\quad power,\quad \overrightarrow { Z_{ L } } =\overrightarrow { { { Z }_{ th } }^{ * } } \\ \\ \overrightarrow { { { Z }_{ th } } } =9.412+22.35j\\ \overrightarrow { { { Z }_{ th } }^{ * } } =9.412-22.35j\\ \overrightarrow { Z_{ L } } =9.412-22.35j\\ \overrightarrow { Z_{ L } } ={ R }_{ L }+{ X }_{ L }j\\ \\ Therefore,\quad { R }_{ L }=9.412Ω$$

This is how they did it in the previous example:
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Vishera said:

Homework Statement




The Attempt at a Solution



The text in the black box looks wrong to me. The method below is how I would do it. Why is it wrong?

Because ZL is not what you said. ZL = RL. It's real only. You don't have the freedom to add a reactive component = ZTH* to RL to maximize the power in RL.

In general, if a voltage source has a series impedance Z = ReZ + jImZ, picking the load resistance RL = |Z| maximizes power dissipation in RL.
 
Last edited:
rude man said:
Because ZL is not what you said. ZL = RL. It's real only. You don't have the freedom to add a reactive component = ZTH* to RL to maximize the power in RL.

In general, if a voltage source has a series impedance Z = ReZ + jImZ, picking the load resistance RL = |Z| maximizes power dissipation in RL.

Oh, thank you. I didn't realize the load is purely real. Frustration has been removed. :)
 

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