Can Symmetry Simplify a Hard Resistor Network?

In summary, the method of symmetry can be used to simplify the given problem of finding the net resistance across points A and B. By recognizing that nodes on the center-line have the same potential, new parallel resistance opportunities can be identified. Additionally, using delta-star transformations and parallel/series resistor simplifications can lead to a solution. It is important to note that the symmetry method relies on the fact that separate nodes at the same potential can be connected or components can be removed without changing the circuit's behavior.
  • #1
mooncrater
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the question is , to find the net resistance across the points a and b as marked in the figure(attached).Here I think that the method of Symmetry should work . But I am not sure about it and moreover its not clear to me how to use it.

The Attempt at a Solution


IMG_20150211_191911.jpg
IMG_20150211_192056.jpg
 
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  • #2
Was it foggy in your room when you took these pix? They're barely legible. :(
 
  • #3
I can hardly see your diagram at all (this is bad form, by the way ... posting illegible diagrams and expecting people to be able to decipher them). Do you know about delta-Y transforms? I seem to recall that there is a trick to the pyramid construct and you are right that it involves symmetry but I don't remember for sure that there is and certainly not how to do it. Delta-Y transforms will give you a brute-force method for getting it.
 
  • #4
Here's a depiction of the problem:

Fig1.gif


To begin with all line segments between nodes represent a 1 Ohm resistors.

By symmetry all points on the center-line (dotted blue vertical line passing through point C) are at the same potential if a potential difference is applied between A and B. So use that fact to recognize new parallel resistance opportunities. Hint: Don't be afraid to cut a 1 Ohm resistor into two 1/2 Ohm resistors in series.

The problem should reduce to something more tractable at least. Still may require an application of Delta-Y or other other circuit analysis methods, but it will be on a trivial circuit.
 
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  • #5
I studied you post , actually i didn't understand the symmetry method , moreover i didn't know about delta star methods . So i searched about them , studied them , applied them(delta star) in the problem , and in 3 long(+hard) tries I DID IT . Thank you.
 
  • #6
@mooncrater : The symmetry method relies on the fact that when separate nodes are at the same potential you can connect them together with a wire or remove components connected to both without changing the circuit behavior in any way.

The simplest case is that of a bridge circuit where the arms of the bridge are balanced and there is no potential across the "bridge".

Fig1.gif
These circuits have identical characteristics

No current can flow if there is no potential difference, so if there's a component on the bridge it can be removed. If there's no component there you can add what you want, even a shorting wire, and no change will occur to the circuit's operation. In the above diagram the placement of resistor R between the nodes a and b has no effect. Recognizing that two nodes previously thought separate can be treated as one can lead to new parallel component reduction opportunities, or serial reduction opportunities if you can remove a redundant component.
 
  • #7
You need at most one delta-star transformation at the very end, everything else can be solved with parallel/series resistor simplifications (after using the symmetry).
 

1. What is a hard resistor network?

A hard resistor network is a type of electronic circuit that consists of multiple resistors connected in a specific configuration. It is designed to provide a specific resistance value to a circuit and can be used in a variety of electronic devices.

2. How does a hard resistor network work?

A hard resistor network works by connecting multiple resistors in series or parallel to achieve a specific resistance value. The resistors are made of materials with high resistance, such as carbon, and the network is designed to provide a consistent resistance despite changes in temperature or current flow.

3. What are the advantages of using a hard resistor network?

Using a hard resistor network allows for precise control of resistance within a circuit, making it an essential component in many electronic devices. It also provides stability and accuracy in resistance values, and can be used in a wide range of applications.

4. What are the different types of hard resistor networks?

There are several types of hard resistor networks, including fixed resistor networks, variable resistor networks, and integrated resistor networks. Fixed resistor networks have a set resistance value, while variable resistor networks allow for adjustment of the resistance. Integrated resistor networks are built into other electronic components, such as integrated circuits.

5. How do I choose the right hard resistor network for my project?

Choosing the right hard resistor network depends on the specific requirements of your project. Consider factors such as the desired resistance value, power rating, and physical size. It is also important to select a network that can withstand the environmental conditions of your project, such as temperature and humidity.

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