Solving Resistor Problems: How to Find Equivalent Resistances

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Homework Help Overview

The discussion revolves around finding all possible equivalent resistances that can be created using four resistors, each with a resistance of 45 ohms. Participants are exploring both mathematical approaches and circuit drawings to determine these equivalent resistances.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • The original poster inquires about the best method to find equivalent resistances, questioning whether a mathematical approach or drawing circuits would be more effective. Some participants suggest starting with all resistors in parallel and modifying the arrangement, while others propose a systematic breakdown of arrangements based on the number of resistors in parallel versus series.

Discussion Status

Participants are actively discussing different methods to approach the problem, with some favoring drawing circuits and others considering mathematical solutions. There is no explicit consensus on the best method, but various strategies are being explored.

Contextual Notes

Participants are considering the constraints of the problem, such as the requirement to list all ten equivalent resistances and the potential complexity of arrangements. The discussion reflects an understanding of the need to categorize different configurations of resistors.

robphysics
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Four resistors all have resistance 45 W . Find all the possible equivalent resistnaces that can be created (there are ten) and list them from largest to smallest equivalent resistance.

Is there a way to solve this mathmatically or do i have to draw out the 10 circuits and figure it out that way?
 
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Yes.

I think you want to do the second option, it would be easier. Just start with all four in parallel and change one at a time to end up with four in series.
 
Could you point me in the right direction for solving it mathematically?
Thanks
 
Well.. The best way that i still think is the best is to draw out all 10 cicuits.. However, you can still try to do this using some maths.

Let's not make this too complicated.. Split up the types of arrangements first.
Let resisitors in parallel be considered as 1 resistor.
Therefore, we have:
...4R...3R...2R...1R...
....|...|...|...|...
...1...1...1...1...

For 4 resistors in parallel, we have only 1 type of arrangement(4 R in Parallel)

For 3 resistors in parallel, we will have 2 types of arrangement (1 R in series with the other 3 R in parallel)(Rotate bout the positions of the resistors in series to get 2)/ You can also permute 2 with 2..

For 2 R in parallel, we will have 6 types of arrangement (2 R in series with the other 2 in parallel) Taking the 2 parallel R as 1 R, Permute the 3 R with the 3 slots. ie: 3P3=6

For all resistors in series, we will have only one type of arrangement.

Therefore adding all arrangements.. 1+2+6+1=10!
 
Last edited:

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