Thevenin with dependent voltage source

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Discussion Overview

The discussion revolves around finding the Thevenin equivalent resistance (Rthev) as seen by terminals (a,b) in a circuit containing a dependent voltage source. Participants explore various methods such as nodal analysis and mesh analysis, while addressing the challenges posed by the dependent source and the configuration of resistors.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant mentions using nodal analysis and supernode techniques but struggles to obtain the correct answer due to the dependent voltage source.
  • Another participant suggests that injecting 1A to find RTH is standard, noting that the open circuit voltage is 0V due to the absence of independent sources.
  • A participant discusses bypassing certain resistors after injecting current and mentions the need to be cautious about the polarity of the dependent voltage source.
  • There is a question about the applicability of mesh analysis to the problem, with one participant expressing uncertainty about the setup of equations.
  • Multiple participants arrive at a value of 10 ohms for Rth, but there is confusion regarding the correct circuit configuration and the treatment of resistors.
  • One participant expresses uncertainty about whether to use nodal or mesh analysis, indicating a lack of clarity in setting up the equations.
  • A participant questions the validity of combining resistors in a specific manner, emphasizing that certain operations are not permissible.
  • Another participant raises a question about the Thevenin voltage (Vth), suggesting it might be 0 and seeking clarification on the equivalent circuit parameters.

Areas of Agreement / Disagreement

Participants generally agree that the Thevenin resistance is 10 ohms, but there is no consensus on the correct approach to derive this value or on the value of the Thevenin voltage (Vth), which remains uncertain.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the circuit configuration and the treatment of dependent sources. Participants express confusion over the application of nodal and mesh analysis, as well as the correct arrangement of resistors.

savageqm
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Homework Statement


Find Rthev as seen by terminal (a,b)

http://cid-3c099006138591f8.office.live.com/self.aspx/Pictures/IMG^_0337.JPG

Homework Equations



Can somebody point me to the right method to solve this problem. I know how to solve when there is a dependent source, but the dependent voltage source is throwing me off. I tried nodal analysis and supernode but I can't get the right answer.

The Attempt at a Solution


I used nodal analysis and supernode. I applied a 1A to the A,b connector.

Homework Statement


Homework Equations


The Attempt at a Solution


Homework Statement


Homework Equations


The Attempt at a Solution

 
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You usually inject 1A to get RTH. Since I don't see any independent sources, I'd say that the open circuit voltage is 0V.
 
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I am including the 50 ohms.
 
Ok. Sorry for changing things up so much. I just realized what the question was.

After injection, the one next to your terminal pair will definitely be bypassed. I'd also say that the one coming off of the dependent source will also be bypassed and will give you a voltage divider. I'm not sure what the polarity of vx is, so you'll have to be careful about that.
 
so I can get rid of the first 50 and the 25 next to the 3vx?

can mesh analysis be applied to this?
 
Show the equations you derived for nodal analysis so we can see where you went wrong.

I used nodal analysis and got 10 ohms for Rth.
 
I worked out the node voltages and got 0V. For some reason I was thinking short circuit current. That would knock out that resistor, not a current source, sorry...been a long day/night/day.


[PLAIN]http://www.fission-systems.com/images/physics/supernode.png
 
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I come up with this nodal analysis, which is wrong because I know the answer is 10ohms like somebody just mention.

http://cid-3c099006138591f8.office.live.com/self.aspx/Pictures/IMG^_0339.JPG

I guess my problem is setting it correctly. Any ideas where am going wrong?
 
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Which circuit is the correct one, the one in your original post or the one in your latest post? They're not the same.EDIT: Like The Electrician, I found the Thevenin resistance for the original circuit is indeed 10 ohms, so you should start over. It looks like you tried to combine one of the 25-ohm resistors with the 50-ohm resistor, but you can't as they are neither in series nor parallel.
 
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  • #10
The first post is the original problem, my last post was me trying some source transformation to be able to solved the problem.

I still just trying to solve the original post.
 
  • #11
savageqm said:
I come up with this nodal analysis, which is wrong because I know the answer is 10ohms like somebody just mention.

http://cid-3c099006138591f8.office.live.com/self.aspx/Pictures/IMG^_0339.JPG

I guess my problem is setting it correctly. Any ideas where am going wrong?

You can't rearrange your resistors to have 75 ohms in parallel with 25 ohms from the left end of the source to ground. That's not a permissible operation. Try again.
 
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  • #12
Why not use a 1V or 1A test source?
 
  • #13
I always use a 1A test source, but am just out of idea of how to setup the equation. The one I posted is the one I always get back to.

I don't know if I should use Mesh Analysis to calculate the current or Nodal analysis, but then that would mean I would have a supernode which I think am writing wrong.
 
  • #14
The only equations you've posted are in the image you linked to in post 8. As both The Electrician and I pointed out, you can't combine the resistors the way you did, so any equations you derive from that circuit won't yield the correct results.
 
  • #15
i have a question like this one, so i try to solve this question. i also found Req=10 ohm but Vth=0. Is the Vth 0? I mean when we draw the equivalent circuit, do we set Vth=0 and Req=0?
Thanks
 

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