What is the Maximum Power Transfer Theorem?

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Discussion Overview

The discussion revolves around the Maximum Power Transfer Theorem in the context of a homework problem involving a voltage source with internal impedance supplying power to a complex load impedance. Participants explore how to determine the maximum power transferred to the load, considering the implications of complex impedances.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant emphasizes the importance of focusing on the real power delivered to the load and suggests ignoring the imaginary parts of the impedances to use their magnitudes.
  • Another participant points out that without a numerical definition of the load impedance, the problem lacks a solution.
  • A different participant reiterates that the load impedance does not need to be defined numerically to find the maximum power, indicating a focus on theoretical understanding.
  • There is a suggestion that if the load impedance is the complex conjugate of the source impedance, it simplifies the calculation of current and voltage across the load.
  • One participant notes a misunderstanding regarding the visibility of the term "maximum" in the problem statement, which led to confusion.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of defining the load impedance numerically, with some arguing it is essential for a solution while others believe it is not required for the purpose of finding maximum power.

Contextual Notes

The discussion highlights the dependence on definitions of impedance and the assumptions made regarding the relationship between the source and load impedances. There are unresolved mathematical steps related to calculating current and total circuit impedance.

anand raj
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1. Homework Statement
A voltage source of 240 v having an internal impedance of (3-j4) ohm, is supplying power to a complex load impedance Z1. What will be the maximum power transferred to load?



2. Homework Equations



3. The Attempt at a Solution
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You want to look at the real power delivered to the load. So you don't want to incorporate the imaginary parts of the impedances and use the magnitude.

One quick & dirty shortcut here is that since the two impedances are in series and are complex conjugates, their sum is purely real and comprised of two equal pieces; only the two real components are "seen" by the source since the complex bits cancel. That makes it dead easy to calculate the current and voltage across the load...
 
Since you haven't defined the load impedance numerically, the problem has no solution.

If the load impedance is the complex conjugate of the source impedance then gneill has given you a good hint.
 
anand raj said:
A voltage source of 240 v having an internal impedance of (3-j4) ohm, is supplying power to a complex load impedance Z1. What will be the maximum power transferred to load?
With the load connected, what is the total circuit impedance?

With the load connected, what will be the magnitude of the current?
 
rude man said:
Since you haven't defined the load impedance numerically,
It is not necessary to do so. We are looking for the maximum maximum power.
 
NascentOxygen said:
It is not necessary to do so. We are looking for the maximum maximum power.

OK. I did not see the horizontal scroll bar so the word 'maximum' was hidden.
 

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