How Do You Determine Thevenin Equivalent Circuits and Maximize Power Transfer?

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Discussion Overview

The discussion revolves around determining the Thevenin equivalent circuit for a given circuit, specifically focusing on finding the open-circuit voltage (VOC) and Thevenin resistance (Rth). Participants explore methods for calculating these values and discuss the implications for maximizing power transfer to a load resistor.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant reports using mesh analysis to find VOC, resulting in a value of 2.5V, but struggles with node voltage analysis, yielding a different value of 2.94V.
  • Another participant questions the effectiveness of node voltage analysis in this scenario and wonders if there is an advantage to using a test voltage source versus a test current source.
  • A participant acknowledges forgetting to deactivate the independent voltage source when applying the test method, later correcting their approach and finding Rth to be 6 ohms.
  • It is noted that the controlled source must be accounted for in the node voltage equation to correctly find the open-circuit voltage.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the application of different analysis methods, with some confusion remaining about the node voltage approach and the role of sources in the calculations. No consensus is reached on the best method to use.

Contextual Notes

Participants mention potential errors in their calculations and assumptions, particularly regarding the treatment of sources in the circuit analysis. There is an indication that the node voltage method may require all sources to be active for accurate results.

Who May Find This Useful

This discussion may be useful for students learning about Thevenin equivalents, circuit analysis techniques, and power transfer principles in electrical engineering.

jdawg
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Homework Statement



Find the Thevenin equivalent circuit for the circuit shown. You will need to find VOC and then use the test source method to find the Thevenin resistance. Using the Thevenin equivalent circuit,determine the load resistor that results in maximum power transferred to that load resistor and the amount of that power.

Homework Equations

The Attempt at a Solution


(Fig.1)[/B]I'm a little stuck on this problem. I first used mesh analysis to find VOC, which came out correct: VOC=2.5V.
But I tried to do it with node voltage analysis as well to see if it would work also and it came out a little messed up:
(VA-5)/7 +VA/10=0
VA=2.94V
Is there a reason why node voltage doesn't work in this situation or am I just doing it wrong?
(Fig.2) I tried letting ITest=1A and used mesh analysis:
i2=ITest=1
0.2(V2)-(5ohm)(i1)+5v-(7ohm)(i1)-(10ohm)(i1-i2)=0
Substituted and did some algebra:
i1=0.705
I am super confused at this point :(
Is there an advantage to using a test voltage source vs using a test current source?
Should I have let VTest=2.5V instead?
 

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Oops I forgot to take out the independent voltage source for the test method! I let Vtest=2.5v and found Itest=0.467 so Rth=6ohms! I feel like I understand the test method now, could someone explain how I messed up with the node voltage equation in the Fig. 1 section?
 
jdawg said:
Oops I forgot to take out the independent voltage source for the test method! I let Vtest=2.5v and found Itest=0.467 so Rth=6ohms! I feel like I understand the test method now, could someone explain how I messed up with the node voltage equation in the Fig. 1 section?
You didn't account for the controlled source in the node equation. You need all sources active if you want to find the open circuit voltage.
 
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Thanks!
 

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