Reducing all circuit resistors to only parallel and series?

In summary, I think that it is possible to connect resistors together in a way that cannot be reduced to some combination of series and parallel combinations. However, if there are more than one voltage source present, it is not clear how this will affect the answer.
  • #1
solour
9
0

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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  • #2
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?
 
  • #3
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.
 

FAQ: Reducing all circuit resistors to only parallel and series?

1. What is the purpose of reducing all circuit resistors to only parallel and series?

Reducing all circuit resistors to only parallel and series is done in order to simplify the circuit and make it easier to analyze and calculate. It allows us to use basic laws and equations to solve for the total resistance and current in the circuit.

2. How do you determine the total resistance of a circuit with only parallel and series resistors?

To find the total resistance in a circuit with only parallel and series resistors, you can use the following equations:
For series resistors: Rtotal = R1 + R2 + ... + Rn
For parallel resistors: 1/Rtotal = 1/R1 + 1/R2 + ... + 1/Rn

3. Can a circuit with only parallel and series resistors have an infinite resistance?

Yes, a circuit with only parallel and series resistors can have an infinite resistance. This can occur when there is an open circuit, where there is a break in the circuit and no current can flow.

4. What is the difference between parallel and series resistors?

Parallel resistors have the same voltage drop across each resistor, but the current is split between them. Series resistors have the same current flowing through each resistor, but the voltage drop is divided between them.

5. What happens if you add more resistors in parallel or series to a circuit?

If you add more resistors in parallel, the total resistance of the circuit decreases. If you add more resistors in series, the total resistance of the circuit increases. This can affect the overall current and voltage in the circuit, so it is important to consider when designing a circuit.

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