# Combination Circuit Resistances

Discussion in 'Homework Help' started by Serene Potato, Jul 20, 2016.

1. ### Serene Potato Thread Starter New Member

Jul 20, 2016
4
0 What is the equivalent resistance as an algebraic expression (in terms of R) of network as C viewed from its port?

I tried thinking of it as the two parallel resistors being one 1/2 R series resistor, then adding them up, giving 5/2*R.
I also tried thinking of it as parallel of two series resistors, giving R
both were incorrect
I think my failure to grasp the concept of "nodes" has something to do with this, the question looks nothing like the other combination circuit tutorials I found online, can someone give me a intuitive or easy to understand way to understand this question?

2. ### ericgibbs Moderator

Jan 29, 2010
8,134
1,643
hi,
The poorly annotated diagram doesn't help you.
Look at this marked up image, consider R3 and R4 first.

E

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3. ### WBahn Moderator

Mar 31, 2012
24,342
7,602
Do you see either two resistors that are in series or two resistors that are in parallel? If so, combine them so that you have a circuit having three resistors and then repeat that process (looking for two resistors in series or two resistors in parallel that can be combined into a single equivalent resistance).

You can quickly put upper and lower bounds on the total resistance. You know that it has to be at least R since all current must flow through the left-most resistor. But you also know that it must be less than 2R because that's what it would be if the right two resistors were removed and the presence of those two resistors can only decrease the total resistance. So you know the answer must be strictly greater than R but strictly less than 2R. By doing this kind of quick analysis you can rule out both R and 5R/2 as possible answers.

anhnha likes this.
4. ### WBahn Moderator

Mar 31, 2012
24,342
7,602
The diagram isn't poorly annotated -- it clearly shows that all four resistors are the same value, namely R.

It does, admittedly, make it a bit harder to refer to specific resistors.

5. ### RBR1317 Senior Member

Nov 13, 2010
472
90
Just go through a series of combining resistances in series & parallel, doing it in terms of 'R' instead of numbers. As shown in the diagram below, combine resistances in the color-shaded area sequentially as shown to get from four resistors to a single resistance value. shteii01 and anhnha like this.
6. ### ericgibbs Moderator

Jan 29, 2010
8,134
1,643
Reading your last sentence in the above quote, I take it you are agreeing with me regarding the poorly annotated circuit.???

IMO the circuit components should be labelled, so that a student and others can more easily follow the OP's solution.
This is demonstrated by the fact that you had to identify/ refer to the resistor/component by it's location in order to explain the circuit, as in your post #3,

I appreciate all the resistors could be assumed to be the same value, but you repeatedly remind posters, to which I agree, to clearly identify circuit components and to use the standard variable names throughout their equations.

E

I would be interested to hear the OP's opinion

7. ### Serene Potato Thread Starter New Member

Jul 20, 2016
4
0
Thank you so much, I managed to do it just now 8. ### Serene Potato Thread Starter New Member

Jul 20, 2016
4
0
Yeah, it is a bit difficult to describe the circuit using the diagram, as it hasn't been annotated much at all, just that all the resistors are of the same resistance. I just downloaded the image straight from Mitx

9. ### WBahn Moderator

Mar 31, 2012
24,342
7,602
Keep in mind that YOU can always annotate a schematic as needed to get your point across. In fact, you will generally need to do this more often than not.

10. ### Serene Potato Thread Starter New Member

Jul 20, 2016
4
0
Thanks, will keep that in mind =]

11. ### MrAl AAC Fanatic!

Jun 17, 2014
6,230
1,352
Hi,

We do find this nomenclature a lot in electrical schematics. Often when the author wants to show that two or more resistors are the same value they simply use the same part numbering or just "R" as this one does. This is very common.

I cant say that i like it personally, but it's found a lot in the literature so might was well accept it and get used to it because it is going to appear very frequently.

I prefer the R1 through Rn notation also, and if R1=R2 then just state that elsewhere, but i guess for brevity they do it with all the same numbering R1, R1, R1, etc. Without the numbering 1,2,3 we have to refer to the resistors some other way like "the resistor on the far right, the resistor just above that one", etc.

Sometimes the same number is used for several resistors to actually emphasize that they are of the same value, such as in a tuned filter circuit. Another example is in an R-2R digital to analog ladder network, where we really want to show that the resistors have values that are either the same or an exact multiple of another value (2*R).
In the circuit at hand it looks like they wanted to emphasize that all the values were the same AND that the end formula should take advantage of that.

Last edited: Jul 23, 2016