# Simple question about the difference between Thevenin resistance and non-Thevenin resistance

In a lecture for an Electrical Engineering course I was taking, the professor did an example on solving a Thevenin circuit.

When he solves the circuit for Thevenin resistance he adds two resistors in parallel between the open circuit "a" port, however when solving to make an equivalent resistor to find the voltage he goes and adds two resistors in series between the same "a" open circuit. I am confused as too how this is allowed.

I would think that for both cases either it could only be added in parallel or series however this seems to not be the case. The only thing that changes is that now there is a voltage source and I am confused on how that has an effect on the calculation of resistance.

Picture for reference of solution:

Edit: Added full solution of the problem using Thevenin:

• yes, I did as I feel that it wasn't relevant to the question but I will edit it into the post if that is helpful to the question. Oct 1, 2020 at 2:44
• the circuit does not change in the second solution ... the resistors can be oriented any way you like ... note: between the open circuit "a" ... you cannot have anything between only one point ... when something is between, it is always between two or more points Oct 1, 2020 at 2:59

When reading what follows, keep in mind that you are always allowed to select one of the wires (nodes) and designate it as $$\0\:\text{V}\$$ (or ground.) That is your prerogative. In my work below, I've chosen to make b the same as ground.

## 1

Just redraw the first circuit:

simulate this circuit – Schematic created using CircuitLab

Now it is completely obvious how it is that $$\R_1\$$ and $$\R_2\$$ can be taken in-parallel and Thevenized that way into $$\\frac{R_1\: R_2}{R_1+R_2}=2\:\Omega\$$. That value is then in series with $$\R_4\$$, so just add the two values together. And that result is in-parallel with $$\R_3\$$. So it's pretty easy.

One of the things that you need to learn early is to realize that our brains are often easily misled. Just get into the practice of patiently sitting down, getting out paper and pencil, and re-drawing what you see in a completely different way. Do this with intention. Make it radically different. But make sure that all the connections (nodes) are correct, of course.

You'll begin to see in a new way, soon enough.

## 2

Again, re-draw:

simulate this circuit

You can now Thevenize $$\R_1\$$ and $$\R_2\$$ with $$\V_1\$$'s voltage. That resulting Thevenin resistance will be in series with $$\R_4\$$, so just add them. Now you have your $$\V_1\$$ source at one end of a voltage divider and your Thevenin source, $$\V_x\$$, at the other end. That means the final resulting Thevenin resistance will be those two values, the earlier result and $$\R_3\$$, taken in-parallel again. You can also easily compute the new Thevenin voltage from the divider pair, as well.

## Redrawing Schematic Appendix

One of the better ways to try and understand a circuit that at first appears to be confusing is to redraw it. There are some rules you can follow that will help get a leg-up on learning that process. But there are also some added personal skills that gradually develop over time, too.

I first learned these rules in 1980, taking a Tektronix class that was offered only to its employees. This class was meant to teach electronics drafting to people who were not electronics engineers, but instead would be trained sufficiently to help draft schematics for their manuals.

The nice thing about the rules is that you don't have to be an expert to follow them. And that if you follow them, even blindly almost, that the resulting schematics really are easier to figure out.

The rules are:

• Arrange the schematic so that conventional current appears to flow from the top towards the bottom of the schematic sheet. I like to imagine this as a kind of curtain (if you prefer a more static concept) or waterfall (if you prefer a more dynamic concept) of charges moving from the top edge down to the bottom edge. This is a kind of flow of energy that doesn't do any useful work by itself, but provides the environment for useful work to get done.
• Arrange the schematic so that signals of interest flow from the left side of the schematic to the right side. Inputs will then generally be on the left, outputs generally will be on the right.
• Do not "bus" power around. In short, if a lead of a component goes to ground or some other voltage rail, do not use a wire to connect it to other component leads that also go to the same rail/ground. Instead, simply show a node name like "Vcc" and stop. Busing power around on a schematic is almost guaranteed to make the schematic less understandable, not more. (There are times when professionals need to communicate something unique about a voltage rail bus to other professionals. So there are exceptions at times to this rule. But when trying to understand a confusing schematic, the situation isn't that one and such an argument "by professionals, to professionals" still fails here. So just don't do it.) This one takes a moment to grasp fully. There is a strong tendency to want to show all of the wires that are involved in soldering up a circuit. Resist that tendency. The idea here is that wires needed to make a circuit can be distracting. And while they may be needed to make the circuit work, they do NOT help you understand the circuit. In fact, they do the exact opposite. So remove such wires and just show connections to the rails and stop.
• Try to organize the schematic around cohesion. It is almost always possible to "tease apart" a schematic so that there are knots of components that are tightly connected, each to another, separated then by only a few wires going to other knots. If you can find these, emphasize them by isolating the knots and focusing on drawing each one in some meaningful way, first. Don't even think about the whole schematic. Just focus on getting each cohesive section "looking right" by itself. Then add in the spare wiring or few components separating these "natural divisions" in the schematic. This will often tend to almost magically find distinct functions that are easier to understand, which then "communicate" with each other via relatively easier to understand connections between them.

The above rules aren't hard and fast. But if you struggle to follow them, you'll find that it does help a lot.

You can read a snippet of my own education by those schematic draftsmen at Tektronix who trained me by reading here.

• Nice answer. +1 Oct 1, 2020 at 3:10
• @relayman357 Thanks! How are you doing with LambertW?
– jonk
Oct 1, 2020 at 3:11
• Haven’t messed with it. Didn’t know it would be research project. :-) Oct 1, 2020 at 3:16
• @relayman357 Okay. Got it. Wolfram has a nice page on the topic. Worth a read, I think. It's how you solve equations that include exponential or logarithm product components to them. Every well-vetted mathematician is well-familiar with the idea and its application.
– jonk
Oct 1, 2020 at 3:17
• @HirokazuMiyashita It's truly my pleasure. Help others when you may be able to do so and pass it along. We all need each other in different ways and times and I owe a debt I cannot ever repay for those who were there for me. I'm just glad I was helpful at all. Thanks for letting me know.
– jonk
Oct 1, 2020 at 10:42