# Detecting if resistances are parallel or series in complex circuits

## Main Question or Discussion Point

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 :

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 ?

## Answers and Replies

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ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
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.

UltrafastPED
Science Advisor
Gold Member
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.

UltrafastPED
Science Advisor
Gold Member
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.

Integral
Staff Emeritus
Science Advisor
Gold Member
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.

mfb
Mentor
Sometimes, colors can help:

All resistors are between yellow and red.

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Philip Wood
Gold Member
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.

Thanks everyone for answers.
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