Calculating Maximum Average Power of AC Circuit

In summary, the conversation involves a discussion about maximizing power in a circuit and the use of load resistance. The speaker suggests a different method for finding the maximum power and questions the method used in the given example. The other person explains that the load resistance must be purely real and provides a general rule for maximizing power in a circuit.
  • #1
Vishera
72
1

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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  • #2
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:
  • #3
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. :)
 

FAQ: Calculating Maximum Average Power of AC Circuit

What is the maximum average power of an AC circuit?

The maximum average power of an AC circuit is the highest amount of power that can be delivered to a load over a period of time. It is typically calculated using the formula Pmax = Vrms x Irms, where Vrms is the root mean square voltage and Irms is the root mean square current.

How is the maximum average power different from the peak power in an AC circuit?

The maximum average power is the average power delivered to a load over a given time period, while the peak power is the highest power delivered at a specific moment in time. The peak power is typically higher than the maximum average power and occurs during the peak of the AC waveform.

What factors affect the maximum average power in an AC circuit?

The maximum average power in an AC circuit is affected by the voltage and current levels, the type of load, and the power factor. Higher voltage and current levels result in a higher maximum average power, while a higher power factor indicates a more efficient use of power.

How do you calculate the maximum average power for a resistive load in an AC circuit?

For a resistive load, the maximum average power can be calculated using the formula Pmax = Vrms^2/R, where Vrms is the root mean square voltage and R is the resistance of the load. This formula assumes that the load is purely resistive, meaning it does not have any capacitive or inductive components.

Can the maximum average power of an AC circuit be increased?

Yes, the maximum average power of an AC circuit can be increased by increasing the voltage or current levels, improving the power factor, or using a more efficient load. However, it is important to consider the limitations of the circuit and ensure that it can handle the increased power without causing damage.

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