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Circuit Diagram

In order to calculate R_th, you have to made all voltage and current sources equal to 0 (creating open circuits at current sources and shorts at voltage sources), so you will wind up with only resistors. That means that:

$$R_{th}=[(R_1+R_2)^{-1}+1/R_3+1/R_4]^{-1}$$

The dependent voltage source has a transresistance, so it adds on to the value of R_th. This is not being accepted as my answer though. I tried with and without the transresistance, even though it shouldn't be removed.

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  • \$\begingroup\$ Nodal analysis is easier than mesh analysis in this case. \$\endgroup\$ – Chu Mar 31 '18 at 9:36
  • \$\begingroup\$ Why would node analysis be easier? When dealing with the top voltage source, you end up forming a super node, so you sum all of the currents leaving the nodes to the right and left of the voltage source. This leads with you dividing over 0 on the right-hand side because you have the right node-a over that resistor, which is 0. Or do I not make that calculation and assume that the current in that piece of the circuit is 0 because it is an open loop? \$\endgroup\$ – Albert Garcia Mar 31 '18 at 16:00
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For \$\small V_{TH}\$, let \$\small V\$ be the 25/55/25v node, then: \$\frac{V-4I_x}{29}+\frac{V}{55}+\frac{V-25}{20}=0\$, and \$I_x=\frac{V}{55}\$. Hence \$\small V_{TH}=V-25\$.

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When in doubt try to go back to the definitions:

schematic

simulate this circuit – Schematic created using CircuitLab

This means that V_th is just the same as the open-circuit voltage across the load. Similarly you can show from the definition that I_n is the short-circuit current across the load. The equivalent resistance is then V_th / I_N.

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  • \$\begingroup\$ This is misleading, the answer is not 1V/100ohm. \$\endgroup\$ – Chu Mar 31 '18 at 9:32
  • \$\begingroup\$ Yeah this is an extremely misleading answer. Think it needs editing \$\endgroup\$ – MCG Mar 31 '18 at 9:40
  • \$\begingroup\$ Sorry my bad. It was my first time using the schematic tool and I did not realize the default values on the voltage source and the resistor. My intention was to explain the theory so that the OP can try calculating the answer using this method from the definitions as opposed to receiving a meaningless final answer. \$\endgroup\$ – pooya13 Mar 31 '18 at 17:59
  • \$\begingroup\$ Please remove downvotes as I have fixed the schematic and the downvotes would mislead the readers into thinking the answer is false. \$\endgroup\$ – pooya13 Mar 31 '18 at 18:05

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