Identifying Serial and Parallel Connections

[rugerts]

Homework Statement

Identify which resistors are in series for the first photo. Which are in parallel for second.

Relevant Equations

Elements connected in series are on the same essential branch. Essential branch = a path that
connects two essential nodes without passing through an essential node.

Elements connected in parallel have both terminals connected to the same essential nodes. Essential node = node where 3 or more circuit elements join.

I think the essential nodes are D, F, C, and F-G-A. R5 and R6 are in series. R1 and R3?

I think R1 and R2 are in parallel

 

[kuruman]

I think the essential nodes are D, F, C, ...

There are two nodes labeled D in the figure.

... and F-G-A.

There is no node labeled G. Check to see if all these meet your criterion of being essential. I can see at least one node in the above where only two circuit elements meet.

R5 and R6 are in series. R1 and R3?

If these pairs are in series, they must be on the same essential branch. Can you identify the essential branch in each case?

 

[rugerts]

There are two nodes labeled D in the figure.

There is no node labeled G. Check to see if all these meet your criterion of being essential. I can see at least one node in the above where only two circuit elements meet.

If these pairs are in series, they must be on the same essential branch. Can you identify the essential branch in each case?

There is a node labeled G.
I think that R5&R8, R1&R9, R1&R3 are in series.
Essential branch 1: D-D-E-F
Essential branch 2: B-A-G-F

 

[berkeman]

There is a node labeled G.
I think that R5&R8, R1&R9, R1&R3 are in series.
Essential branch 1: D-D-E-F
Essential branch 2: B-A-G-F

Wowie, that is a confusing reply. Yes there is a "G" node, but why are there two D nodes? Weird.

Also, IMO you don't need "essential nodes" to figure out series and parallel conversions. Unless the problem asks for them, I would avoid that concept. Just run you finger or eyes along each branch, and each component you go through without reaching a parallel branch is in series. And you will start thinking in terms of combining series and parallel components in problems, so once you see some series components, think about combining them into one total resistance and looking for the next parallel component(s) to combine.

So can you list all series components in circuit #1? I see two sets of series resistors (one set with two resistors and the other set with three resistors), and then once you make those combinations, that sets up other parallel and series combinations...

 

[kuruman]

There is a node labeled G.
I think that R5&R8, R1&R9, R1&R3 are in series.
Essential branch 1: D-D-E-F
Essential branch 2: B-A-G-F

Although I agree with @berkeman that you don't need "essential" nodes and branches, I will reply to your post within that context just to make sure that you see the consistency between what @berkeman recommends and the "essential" approach that (presumably) you were taught. It looks like you ran into trouble because of misapplication of the "essential" rules. This is what you need to do:
1. Identify all essential nodes and label them with different letters. Remember that "Essential node = node where 3 or more circuit elements join." I see 4 of these. How many do you see?
2. Do not identify turning "corners" like A, G and the second D and points between circuit elements like B; they muddle the issue. Identify current paths by their essential nodes and a circuit element. Example: DF through R₇ as opposed to DF through R₆.
3. It looks like you missed the point that a straight wire counts as a circuit element. It may carry current just like any resistor except that it has zero resistance and that there is zero potential difference across its ends.
4. Identify all essential branches. Remember that they have to start and end at an essential node. How many of these do you see? I see 6.

Once you correctly identify essential nodes and branches, it should be easy to figure out what's in series and what's in parallel by applying the criteria that you posted.

 

[rugerts]

Although I agree with @berkeman that you don't need "essential" nodes and branches, I will reply to your post within that context just to make sure that you see the consistency between what @berkeman recommends and the "essential" approach that (presumably) you were taught. It looks like you ran into trouble because of misapplication of the "essential" rules. This is what you need to do:
1. Identify all essential nodes and label them with different letters. Remember that "Essential node = node where 3 or more circuit elements join." I see 4 of these. How many do you see?
2. Do not identify turning "corners" like A, G and the second D and points between circuit elements like B; they muddle the issue. Identify current paths by their essential nodes and a circuit element. Example: DF through R₇ as opposed to DF through R₆.
3. It looks like you missed the point that a straight wire counts as a circuit element. It may carry current just like any resistor except that it has zero resistance and that there is zero potential difference across its ends.
4. Identify all essential branches. Remember that they have to start and end at an essential node. How many of these do you see? I see 6.

Once you correctly identify essential nodes and branches, it should be easy to figure out what's in series and what's in parallel by applying the criteria that you posted.

Okay. Thanks so much for the detailed reply. This has really helped.

I didn't know a wire counted as a circuit element.

Also, to be sure, the large circles don't have to necessarily be there in order for the point to be considered a node, right? I ask this because, under node C, below R10, there is not circle, yet it's still a node.

I can see all of the essential nodes and branches you have mentioned.

 

[berkeman]

Also, to be sure, the large circles don't have to necessarily be there in order for the point to be considered a node, right? I ask this because, under node C, below R10, there is not circle, yet it's still a node.

It depends on what the filled-in circles (large dots) are meant to signify. If they are just meant to label "nodes" for the purposes of solving a circuit question, then they can be placed anywhere you think appropriate.

If they are part of a schematic capture program like OrCAD, then the dots have important significance. They signify the connection of two wires, so the presence or absence of them can make the difference between your PCB implementation of the circuit working or not. So in the example you cite about the missing dot below R10, that would be a design error in most schematic capture packages that I'm familiar with. It would be an error because it sort of looks like the wires are connected, but in fact in the schematic capture drawing they are not. Likewise a dot in the middle of a wire would usually be a design error too, since it can mean that two wires were connected poorly and may hide another problem.

 

[berkeman]

Here an image to show what I mean. See how you can have two wires cross with no dot to show that they are not connected, but if there is a small dot at a "T" or wires crossing, that means they are connected...

http://www.cadxservices.com/samples/images/orcad2.jpg

 

[kuruman]

Also, to be sure, the large circles don't have to necessarily be there in order for the point to be considered a node, right? I ask this because, under node C, below R10, there is not circle, yet it's still a node.

Yes, whoever produced this schematic diagram did a poor job. There is no consistent explanation of what the gray circles are supposed to label. It would have been less confusing not to have them in.

 

[rugerts]

Here an image to show what I mean. See how you can have two wires cross with no dot to show that they are not connected, but if there is a small dot at a "T" or wires crossing, that means they are connected...

http://www.cadxservices.com/samples/images/orcad2.jpg
View attachment 250341

Amazing, thanks for taking the time to explain this. Great to know.