# Calculating Maximum Average Power of AC Circuit

1. Apr 1, 2014

### Vishera

1. The problem statement, all variables and given/known data

2. Relevant equations

3. 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:

2. Apr 1, 2014

### rude man

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: Apr 1, 2014
3. Apr 4, 2014

### Vishera

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