Simplifying a Resistor Circuit

In summary, the circuit is symmetrical and can be simplified using just parallel and series definitions.
  • #1
irivce
11
0
9JJ356s.png


Is it possible to simplify this circuit using just parallel and series definitions ?

* A circuit is parallel to another circuit or several circuits if and only if they share common terminals; i.e. if both the branches touch each other's endpoints

* Resistors can be connected in series; that is, the current flows through them one after another

These are the definitions of resistors in series or parallel and according to these definitions none of these are in series or parallel.

Ct0GdEr.jpg


This was my attempt at making the circuit a bit easier to simplify but still could not see how any would fit into the definitions.
 
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  • #2
irivce said:
9JJ356s.png


Is it possible to simplify this circuit using just parallel and series definitions ?

* A circuit is parallel to another circuit or several circuits if and only if they share common terminals; i.e. if both the branches touch each other's endpoints

* Resistors can be connected in series; that is, the current flows through them one after another

These are the definitions of resistors in series or parallel and according to these definitions none of these are in series or parallel.

Ct0GdEr.jpg


This was my attempt at making the circuit a bit easier to simplify but still could not see how any would fit into the definitions.

Welcome to the PF.

Your 2nd image is missing the 1 Ohm resistor on the right side...

I'm not seeing a way to simplify it offhand, so I would just solve the problem using KCL equations written at the nodes. Can you give that a go to see what answer you get?
 
  • #3
look for delta-Y transforms, which is the only alternative to (and derived from) doing your own loop analysis
 
  • #4
berkeman said:
I'm not seeing a way to simplify it offhand..
There is, look at the node between 6 ohm resistors. :)
 
  • #5
Pranav-Arora said:
There is, look at the node between 6 ohm resistors. :)

Uh ... huh?
 
  • #6
phinds said:
Uh ... huh?

The circuit is symmetrical...can you figure it out now?
 
  • #7
Yes, I saw the symmetry but that doesn't seem to eliminate the need to do a delta-Y transform, which is the crux of the OP's problem.
 
  • #8
If you split the "bottom" 3-ohm resistor into two series 1.5-ohms...
 
  • #9
Pranav-Arora said:
There is, look at the node between 6 ohm resistors. :)

Interesting. Initially I'd dismissed cutting the circuit in half to use its symmetry, but maybe now I see what you mean. I didn't think cutting the bottom resistor in half bought anything, but I think I see what you're getting at.
 
  • #10
lewando said:
If you split the "bottom" 3-ohm resistor into two series 1.5-ohms...

Then you have done nothing, as far as I can see, to avoid the need for a delta-Y transform. I don't see that it buys you anything. Am I missing something. Can you do this without the delta-Y transform (or the equivalent loop analysis) ?
 
  • #11
phinds said:
Then you have done nothing, as far as I can see, to avoid the need for a delta-Y transform. I don't see that it buys you anything. Am I missing something. Can you do this without the delta-Y transform (or the equivalent loop analysis) ?

Yeah, so there is one more trick to the method that they are proposing. I think we should leave it to the OP to figure out what that trick is. And I think they should also try the wye-delta transformation that you are proposing, to see if he gets the same answer with both techniques (he should).
 
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  • #12
Pranav-Arora said:
There is, look at the node between 6 ohm resistors. :)

Alright so I split the 3 ohm resistor, and then could I add a wire to make the 1.5 ohms resitors parallel to the 3 ohm resistors and take it from there ?
ImageUploadedByPhysics Forums1379520496.690797.jpg
 
  • #13
irivce said:
Alright so I split the 3 ohm resistor, and then could I add a wire to make the 1.5 ohms resitors parallel to the 3 ohm resistors and take it from there ? View attachment 61938

Yep!
 
  • #14
Pranav-Arora said:
Yep!

Awesomee thanks a lot guys!
 

Related to Simplifying a Resistor Circuit

1. What is a resistor circuit?

A resistor circuit is a combination of electronic components, specifically resistors, that are connected together in a specific way to control the flow of electric current.

2. Why is it important to simplify a resistor circuit?

Simplifying a resistor circuit helps to reduce the complexity of the circuit, making it easier to analyze and understand. It also helps to optimize the circuit for efficiency and cost.

3. How do you simplify a resistor circuit?

To simplify a resistor circuit, you can use basic electrical laws and principles, such as Ohm's Law, Kirchhoff's Laws, and series and parallel resistor equations. These can help you determine the total resistance and current in the circuit.

4. What are the benefits of simplifying a resistor circuit?

By simplifying a resistor circuit, you can easily identify and troubleshoot any issues in the circuit. It also allows for easier modifications and upgrades to the circuit, as well as reducing the overall cost and complexity of the circuit.

5. Can a resistor circuit be simplified too much?

Yes, a resistor circuit can be simplified to a point where it no longer accurately represents the original circuit. This can happen when the assumptions and approximations made during simplification are too far from the real values. It is important to balance simplicity and accuracy when simplifying a resistor circuit.

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