Detecting if resistances are parallel or series in complex circuits

In summary: Nope, that was a one-time event. Thanks for asking. In summary, the resistor arrangement in this example is complex, and it is not possible to determine which resistors are in series and which are in parallel without further analysis. To solve this problem, first determine the electrical connections between the resistors, and then use Kirchhoff's laws or another more advanced technique to calculate the resistance.
  • #1
agoogler
81
0
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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  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
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.
 
  • #8
Sometimes, colors can help:

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


All resistors are between yellow and red.
 

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  • #9
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

Related to Detecting if resistances are parallel or series in complex circuits

1. How do I determine if resistances are in series or parallel in a complex circuit?

In order to determine if resistances are in series or parallel in a complex circuit, you must first identify all of the resistances in the circuit. Then, you can use the following rules:
- If all resistances are connected end-to-end, they are in series
- If all resistances are connected at the same two points, they are in parallel
- If resistances are connected in a combination of series and parallel, you can simplify the circuit using equivalent resistances.

2. What is the difference between resistances in series and parallel?

The main difference between resistances in series and parallel is how the current flows through the circuit. In series, the current must pass through each resistance in order, while in parallel, the current splits and flows through each resistance simultaneously. Additionally, the equivalent resistance of a series circuit is the sum of all individual resistances, while the equivalent resistance of a parallel circuit is less than the smallest individual resistance.

3. Can I use Ohm's Law to calculate resistances in series or parallel?

Yes, Ohm's Law can be used to calculate resistances in series or parallel. In a series circuit, you can use the equation R = R1 + R2 + R3... to find the total resistance. In a parallel circuit, you can use the equation 1/R = 1/R1 + 1/R2 + 1/R3... to find the total resistance.

4. How do I know if a complex circuit can be simplified into a series or parallel circuit?

To determine if a complex circuit can be simplified into a series or parallel circuit, you can use the following steps:
1. Identify all of the resistances in the circuit
2. Determine if they are connected in a series or parallel configuration
3. Use the appropriate equations to calculate the equivalent resistance
4. Compare the equivalent resistance to the original circuit
If the equivalent resistance is the same, the circuit cannot be simplified. If the equivalent resistance is different, the circuit can be simplified.

5. Why is it important to know if resistances are in series or parallel in a complex circuit?

Knowing if resistances are in series or parallel in a complex circuit is important because it allows you to accurately calculate the total resistance and current in the circuit. This information is crucial for designing and troubleshooting circuits, as well as for understanding the overall behavior of the circuit. Additionally, the correct placement of resistances in a circuit can affect its efficiency and performance.

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