# 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. 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. 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
Sep 27, 2021 at 22:29

Hint: both $$\V_{OC}\$$ and $$\I_{SC}\$$ can be solved in terms of $$\V_S\$$. Remember that $$\R_{th}\$$ = $$\\frac{V_{OC}}{I_{SC}}\$$.
• @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). Sep 30, 2021 at 2:08