Reducing all circuit resistors to only parallel and series?

AI Thread Summary
The discussion centers on whether all resistor configurations can be reduced to series and parallel combinations. The initial thought is that with a single voltage source, any resistor combination can be simplified to one equivalent resistor. However, the complexity increases with multiple voltage sources, leading to uncertainty about the reduction process. A participant mentions the infinite cube of resistors as an example that cannot be reduced, and another notes finding a confirmation of this on Chegg, although they lack access to the details. Overall, the conversation highlights the challenges of resistor combinations in circuit analysis.
solour
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Homework Statement


The problem from the textbook is:

Is it possible to connect resistors together in a way that cannot be reduced to some combination of series and parallel combinations?

Homework Equations


V = IR
kirchhoff's current law
kirchhoff's loop law

The Attempt at a Solution


I am completely lost as to where to begin. My intuition tells me that if there is only 1 voltage source, the answer would be no, all resistor combinations can be reduced to a single equivalent resistor(I do not know whether this statement is true or not). However, if the voltage source becomes more than 1 at different locations of the circuit, I do not know how this will effect the answer.
 
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solour said:

Homework Statement


The problem from the textbook is:

Is it possible to connect resistors together in a way that cannot be reduced to some combination of series and parallel combinations?

Homework Equations


V = IR
kirchhoff's current law
kirchhoff's loop law

The Attempt at a Solution


I am completely lost as to where to begin. My intuition tells me that if there is only 1 voltage source, the answer would be no, all resistor combinations can be reduced to a single equivalent resistor(I do not know whether this statement is true or not). However, if the voltage source becomes more than 1 at different locations of the circuit, I do not know how this will effect the answer.
Welcome tpo the PF.

I think that the classic infinite cube of resistors cannot be reduced. What have you found in your Google searches so far?
 
berkeman said:
Welcome tpo the PF.

I think that the classic infinite cube of resistors cannot be reduced. What have you found in your Google searches so far?

Thankyou for the heart warming welcome!

I managed to find the answer for this question on chegg, and it appears to be a yes. Unfortunately I do not have an account and therefore cannot see how they proved it.

I believe the Resistor Cube you suggested also answers the question, though I need to dig in a little deeper to understand how that one works.
 

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