Parallel/Series Circuits Problem

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Discussion Overview

The discussion revolves around the analysis of a circuit involving multiple resistors configured in series and parallel arrangements. Participants explore how to combine resistors and the implications of their configurations on the overall circuit behavior, utilizing Ohm's Law (V=IR) as a foundational principle.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest combining resistors in parallel and series, specifically mentioning configurations of 10k ohm resistors and a 3.3 ohm resistor.
  • One participant notes that a diagonal wire connecting two nodes can be treated as a single node, which may affect how resistors are combined.
  • There is a question about whether two resistors (R2 and R3) are in series if a node between them is removed, with differing views on the implications of node connections.
  • Participants discuss the placement of combined resistors and whether it affects the circuit's configuration, with some arguing that moving resistors along existing wires does not change their connections.
  • One participant raises the concept of current flow through resistors to determine series connections, leading to further clarification on the definitions of series and parallel configurations.
  • There is a discussion about where to place equivalent resistance after combining resistors, with suggestions that it can be flexible as long as connection points are maintained.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding regarding the configurations of resistors and their connections. While some points are clarified, there remains uncertainty about specific arrangements and the implications of moving resistors within the circuit.

Contextual Notes

Limitations include potential misunderstandings of circuit topology and the definitions of series versus parallel connections, as well as the implications of node removal on circuit behavior.

Who May Find This Useful

This discussion may be useful for students and enthusiasts of electrical engineering or physics who are exploring circuit analysis and the principles of combining resistors in various configurations.

eatlsep
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http://imgur.com/QnyUSp4



2. V=IR



3. I tried combining the the two 10kohm resistors furthest away from the source in parallel. Then combined the top 10kohm resistor with the diagonal 3.3 ohm resistor. Then combining the top resistor and the resistor on the right in series then the two remaining resistors in parallel then using V=IR.
 
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eatlsep said:
http://imgur.com/QnyUSp4



2. V=IR



3. I tried combining the the two 10kohm resistors furthest away from the source in parallel. Then combined the top 10kohm resistor with the diagonal 3.3 ohm resistor. Then combining the top resistor and the resistor on the right in series then the two remaining resistors in parallel then using V=IR.

Hi eatlsep, Welcome to Physics Forums.

Combining the rightmost 10K with the bottom 10K is fine, but note that the top 10K is NOT in parallel with the diagonal R.

The diagonal going from bottom left to top right is a straight wire, so those two nodes at either end of it are really just one node. That means you are free to shorten that diagonal wire as much as you like. So imagine that this wire is shortening, dragging the two top-right corner resistor connections with it until the wire vanishes and the resistors are now connected at the bottom left corner of the square. What parallelism can you take advantage of now?
 
Thank you for the response. I'm sorry, I am a little confused what you mean by dragging the top tow resistors as the wire shortens
 
eatlsep said:
Thank you for the response. I'm sorry, I am a little confused what you mean by dragging the top tow resistors as the wire shortens

Like this:

attachment.php?attachmentid=55004&stc=1&d=1359158763.gif


Pull the connections of R2 and R3 down to the other end of the blue wire.
 

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So without the node between R2 and R3 would they then be in series?
 
eatlsep said:
So without the node between R2 and R3 would they then be in series?

Which node would that be? R2 and R3 remain connected together just as before. No connections change simply by rearranging their positions on the drawing.
 
Will R1 and R2 be in parallel?
 
eatlsep said:
Will R1 and R2 be in parallel?

Yup :smile:

What else?
 
So R1 and R2 are in parallel. R3 and R4 are in parallel. Does it matter where I put the combined resistors?. For example, I combine R1 and R2 and put the combined resistor at R1. Then I combine R3 and R4 and put the combined resistor at R3 so that now R1eq and R are in parallel. Can I do this?
 
  • #10
eatlsep said:
So R1 and R2 are in parallel. R3 and R4 are in parallel. Does it matter where I put the combined resistors?. For example, I combine R1 and R2 and put the combined resistor at R1. Then I combine R3 and R4 and put the combined resistor at R3 so that now R1eq and R are in parallel. Can I do this?

No, R1 and R were not in parallel before, so they can't be now. That goes for R1eq as well. Remember, no physical change is made to the circuit by moving connections along existing continuous wires.

If you place the combined resistance R34 = R3||R4 where R3 was originally drawn, then you still have to maintain its connections to the rest of the circuit, no doubt by bending or extending wires. Something like this:

attachment.php?attachmentid=55006&stc=1&d=1359162218.gif


Combine what's in parallel, then combine what's in series,... rinse, repeat :smile:

Probably easier just to place R34 where R4 was...

attachment.php?attachmentid=55007&stc=1&d=1359162347.gif
 

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  • #11
Oh I see what you mean by dragging it down. After combining resistors in parallel. Next, are R12 and R34 in series? Then R1234 and R are in parallel?
 
  • #12
eatlsep said:
Oh I see what you mean by dragging it down. After combining resistors in parallel. Next, are R12 and R34 in series? Then R1234 and R are in parallel?

No, R12 and R34 are not in series; there's something else connected where they join (it's the bottom of Vs). For two components to be in series, where they connect must be to each other and to nothing else. That is, they must exclusively share a node.

However, R is in series with one of the newly combined pairs. Can you spot it?
 
  • #13
Doesn't it also mean if the current is the same through the resistors then it is in series? So R and R1 are not in series because more current wants to flow through the path of least resistance. So R and R4 are in series?
 
  • #14
eatlsep said:
Doesn't it also mean if the current is the same through the resistors then it is in series?
Yes. If the SAME current flows through both components, then they are in series.
So R and R1 are not in series because more current wants to flow through the path of least resistance.
As long as there are alternate paths (no matter what their resistance), then they are not in series; Some current will flow through all available paths so long as they all present some resistance.

Of course, if one of the paths has zero resistance (a so-called "short circuit"), then all the current with take that path. But that's just something to remember for another time.
So R and R4 are in series?
Not as originally drawn. But after combining R2 and R4 into R34, then R and R34 are in series by the definition.

attachment.php?attachmentid=55008&stc=1&d=1359164092.gif
 

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  • #15
Ok great! I am glad I understand those concepts. Now that we combine R34 and R. My next question is where you put the eq resistance. I would guess it goes where R is, but I am not sure why if that is correct
 
  • #16
eatlsep said:
Ok great! I am glad I understand those concepts. Now that we combine R34 and R. My next question is where you put the eq resistance. I would guess it goes where R is, but I am not sure why if that is correct

It's your choice where to put it... remember that the wires are "flexible", so that you don't have to leave them where they're drawn so long as their connection points remain the same. Here it would make sense to redraw the equivalent resistance parallel to R12... :wink:
 
  • #17
Ok. Thank you for all the help. Physics forums is great :D
 

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