Calculating Maximum Average Power of AC Circuit

[Vishera]

Homework Statement

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:

 

[rude man]

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 Z_L is not what you said. Z_L = R_L. It's real only. You don't have the freedom to add a reactive component = Z_TH^* to R_L to maximize the power in R_L.

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

 

[Vishera]

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

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

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