Detecting if resistances are parallel or series in complex circuits

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Discussion Overview

The discussion revolves around identifying whether resistors in complex circuits are arranged in series or parallel, and how to determine their equivalent resistance in such configurations. Participants explore methods and rules for analyzing these arrangements, particularly in more complicated scenarios beyond simple circuits.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that resistors are in parallel if they terminate on the same two busses, while others describe series resistors as being connected end to end without other connections in between.
  • One participant suggests that the arrangement can be simplified by redrawing the circuit to focus on electrical connections rather than visual layout.
  • Another participant mentions that colors can help in identifying connections between resistors.
  • A participant introduces the idea of labeling connected points with the same letter to clarify parallel connections, noting that some resistor networks may not fit into simple series or parallel categories and may require advanced techniques like Kirchhoff's laws.
  • There is a request for tips on how to approach redrawing complex circuits to better analyze them.

Areas of Agreement / Disagreement

Participants generally agree on the basic definitions of series and parallel arrangements, but there is no consensus on the best methods for analyzing complex circuits. Some viewpoints suggest different approaches and techniques, indicating ongoing debate and exploration of the topic.

Contextual Notes

Participants acknowledge that certain resistor networks may not be easily analyzed using series and parallel rules, highlighting the limitations of these methods in more complex configurations.

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I know how to detect when resistors are arranged in parallel or series arrangement and I can also find their equivalent resistance in simple circuits or when resistances are connected in form of triangle but what happens when the arrangement is complex like this :

5EMUd.png


Which resistors are parallel and which are in series ? How can I find the equivalent resistance in such cases ? Is there rule or method for figuring this out ?
 
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ZapperZ said:
Well, well, well. Isn't this interesting.

Check out Post #5 from our last PF Physics Trivia:

https://www.physicsforums.com/showthread.php?t=680864

Zz.
Actually this is from a book so I know that these resistors are in parallel but I'm more interested to know why i.e. the explanation.
 
They are parallel if they all terminate on the same two busses ... a common wire for one end of each resistor, and another common end for the other end.

Serial means that they are all spliced into a single wire, end to end, with nothing else connected in the middle.

If you can topologically rearrange a set of resistors so that they could all be soldered together at one end, and also at the other, then they form a parallel resistance.
 
You can always change the connecting wires ... make them longer or shorter, rearrange them to your convenience ... at least you can for this kind of problem. Just don't make or break any connections.

If you end up with resistors strung along a single line with each node connecting only the next resistor, then this branch is serial.

If instead you end up with two wires such that you could shorten each of the wires into a "solder knot", and end up with one end of each resistor in one of the solder knots, and the other end of each one in the second solder knot ... then your resistors are in parallel.

This latter statement is equivalent to saying that all of the resistors provide paths connecting a voltage A to a voltage B: parallel resistors connect two independent busses.
 
If two devices are connected to each other at both ends, they are in parallel. If they are connect at one end and nothing else connects there, they are in series.
 
Redraw, keeping the connections as they are. This is the first step of any complicated resistor arrangement. It is the key to solving this sort of problem. All that matters is the electrical connections not how it looks on paper.
 
Sometimes, colors can help:

attachment.php?attachmentid=62360&stc=1&d=1380653372.jpg


All resistors are between yellow and red.
 

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Another way in this case is to give the same letter to points which are connected together by a wire; you'll find that the only letters needed are A and B, so it's very easy to see that all three resistors are connected in parallel.

Note that you can have resistor networks which can't be analysed into series and parallel groupings. An example would be four resistors connected in a ring ABCDA, in which these letters stand for the connections between the resistors. A fifth resistor is connected as a 'bridge' between A and C. The resistance is measured across B and D. This resistance can't be calculated by using series and parallel rules, but Kirchhoff's laws, or some more advanced technique has to be used.
 
  • #10
Thanks everyone for answers.
Integral said:
Redraw, keeping the connections as they are. This is the first step of any complicated resistor arrangement. It is the key to solving this sort of problem. All that matters is the electrical connections not how it looks on paper.
Do you have any tips for redrawing? When I get a complex circuit like this , how should I approach redrawing it? Is there any method ? Thank you
 
  • #11

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