How to find Thevenin equivalent resistance with dependent sources?

For this problem, Vs and Io are not given. Beta is equal to 8.

I want to learn how to find the Thevenin equivalent resistance with respect to terminals a and b. The correct answer is 27.33 kilo-ohms, but for the life of me, I can not figure out why.

I've tried disabling the independent voltage source and supplying a test voltage (Vt) between terminals a and b, as well as trying to apply a test current between a and b.

I then tried to leave the sources alone, and instead tried to find the open circuit voltage at the node next to terminal a, and tried to find the short circuit current between the terminals. However, I just keep ending up with too many variables and too few equations to work with. In class we did a similar example, except in that case, the source voltage was given to us.

Any help is appreciated.

EDIT: I ended up just assigning the source voltage to be 1 volt. If the Thevenin resistance is not dependent on sources, then I should just be able to put any real, nonzero value for the source.

This method worked and I received the right answer, but I also considered one of the comments that said to basically leave both the open-circuit voltage and short circuit current in terms of the source voltage, which should go away when looking for the final answer for equivalent Thevenin resistance.

• We don't give out solutions to homework problems, we only give hints or suggestions if you ask a specific question. However, you should know that you can find $R_{TH}$ without trying to disable sources or combine resistors, but you need to know the open-circuit voltage and short-circuit current first. Commented Sep 27, 2021 at 21:26
• I already know that the answer is 27.33 kilo-ohms. This question has already been submitted and graded :( so this is just for me to understand how to solve these in the future. I've tried solving for V_oc at the node next to node "a" using an open circuit, and tried solving for I_sc using a short between node "a" and "b" and using the ratio between the two to determine R_th. I suppose a specific question would be: is the source voltage really not needed to solve this problem? I always end up with too many variables and not enough equations. Commented Sep 27, 2021 at 22:00
• @snooFlamingo Please edit your question with that additional information. Your question is at risk of closure because we don't accept homework questions with no attempt at a solution -- we do accept homework with an attempt at solution (and your question meets that standard IMO), but the more work you show the more likely people will recognize your effort and vote for your question to stay open.
– Null
Commented Sep 27, 2021 at 22:29

If the circuit has dependent sources then you need to calculate the open circuit voltage and the short circuit current then divide the short circuit current from the open circuit voltage.

So in realty you need to do 2 things :open the circuit where will be the load and use nodal analysis to find the open circuit voltage,short the circuit where will be the load and use mesh analysis to find the short circuit current.

• I've been trying to find an answer to this one for hours and found something in our zybook. The problem presented in this question is basically a copy from the textbook. However, in the textbook, the voltage source (V_s) is given an actual value. This is the case with my instructor's in class examples as well. This is the first time that the voltage was not given. No matter how many equations I come up with, the solution to the system always ends up having a free variable thrown in there. Is there a method to calculate V_s so that I can do node analysis? Commented Sep 28, 2021 at 2:34
• The method you described was pretty much the process I went through, but I went through the process again, except this time I assigned the source voltage to have a value of 1. This ended up giving me the right answer. Commented Sep 28, 2021 at 20:10

Hint: both $$\V_{OC}\$$ and $$\I_{SC}\$$ can be solved in terms of $$\V_S\$$. Remember that $$\R_{th}\$$ = $$\\frac{V_{OC}}{I_{SC}}\$$.

• I ended up working out the problem and got the right answer by using the fact that the equivalent resistance is not dependent on source voltage. But your method should also work, if both the short circuit current and open voltage are in terms of the source voltage. At least, I think that's right :') Commented Sep 28, 2021 at 20:03
• @snooFlamingo Setting $V_s = 1$ will work for this particular circuit, but the only way to do this in general for any circuit is to solve for $V_{OC}$ and $I_{SC}$ in terms of $V_s$. You really should get comfortable with algebra and solving equations (instead of needing everything to be numerical). Commented Sep 30, 2021 at 2:08

Short circuit any independent voltage source, open circuit any independent current source (leave dependent sources alone). Apply a 1 A current source at the port where you are determining the Thevenin equivalent and compute the voltage across that current source. That voltage, expressed in ohms, is the Thevenin resistance.

I have been teaching this stuff at an Ivy League university EE program (I won't say which) for more than twenty years (among other things). The classic method of OCT and SCT, work every time too, but I've found that even if students quickly find Voc, they seem to have trouble with the computation of the short circuit current, so I chose to teach them the way I wrote above (which I label the "kill the round sources" method, just to give it a name easy to remember).