How to arrange/draw circuit diagram from fixed resistances

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Discussion Overview

The discussion revolves around how to arrange fixed resistances to achieve a specific total resistance in a circuit diagram. Participants explore the theoretical and practical aspects of combining resistors, including the application of Ohm's Law and the equations for series and parallel resistances.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks guidance on how to arrange resistors to achieve a total resistance of 17Ω, expressing a desire to understand the formulas involved rather than just receiving an answer.
  • Several participants reiterate Ohm's Law and the equations for series and parallel resistances, suggesting that these are foundational for solving the problem.
  • Some participants argue that the problem is more of a logic or mathematical challenge rather than a straightforward electrical engineering problem, indicating that there may not be a standard algorithmic solution.
  • There are mentions of using iterative solving and optimization methods for more complex resistor arrangement problems, although the applicability of these methods to the current problem is questioned.
  • One participant suggests that the problem can be solved through random guessing and rearranging the circuit until the desired resistance is found.
  • Another participant emphasizes that while Ohm's Law is relevant, Kirchhoff's Laws may also be applicable for combining resistances in this context.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the problem, with some seeing it as a straightforward application of known laws while others view it as a more complex logic problem. There is no consensus on a single method or approach to solve the problem effectively.

Contextual Notes

Participants note that the problem may not have a unique solution and that various arrangements could yield the same total resistance. The discussion highlights the limitations of relying solely on established formulas without considering the specific context of the resistor arrangement.

Who May Find This Useful

This discussion may be useful for students and enthusiasts in electrical engineering or physics who are interested in circuit design and the principles of combining resistances.

Dependent
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How to arrange/draw circuit diagram from fixed resistances to have a specific total resistance? (BTW, I am new to PF so I am just starting to know how to do things here hihi)Sample problem: 2Ω,3Ω,4Ω,5Ω,10Ω - arrange the 5 resistances to form a diagram that will have a total resistance of 17Ω.I know the answer/the arrangement of the resistances, i just want to know how or what formulas to solve this kind of problem.
 
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Ohm's Law
 
If memory serves, the total resistance R in a series circuit is just the linear sum of the component resistors i.e.

##R = R_1 + R_2 + R_3 + ... + R_n##

In a parallel circuit, it's a reciprocal equation:

##1/R = 1/R_1 + 1/R_2 + 1/R_3 + ... + 1/R_n##

Bear in mind you may have to combine series and parallel sections in your circuit to make the required resistance from the values given.
 
sk1105 said:
If memory serves, the total resistance R in a series circuit is just the linear sum of the component resistors i.e.

##R = R_1 + R_2 + R_3 + ... + R_n##

In a parallel circuit, it's a reciprocal equation:

##1/R = 1/R_1 + 1/R_2 + 1/R_3 + ... + 1/R_n##

Bear in mind you may have to combine series and parallel sections in your circuit to make the required resistance from the values given.
yeah, but what i want to know is Rt(17Ω)=(this arrangement of the five resistances)
 
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Dependent said:
yeah, but what i want to know is Rt(17Ω)=(this arrangement of the five resistances)
So, you want us to just give you the answer? This forum doesn't work that way. We help people figure out how to get their own answers and we have done that for you. There have been three statements (Ohms law, the equation for parallel resistance, and the equation for series resistance). That's all you need.
 
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phinds said:
So, you want us to just give you the answer? This forum doesn't work that way. We help people figure out how to get their own answers and we have done that for you. There have been three statements (Ohms law, the equation for parallel resistance, and the equation for series resistance). That's all you need.
I actually know the answer, which is

Rt(17Ω)=10Ω+5Ω+(((2Ω+4Ω)(3Ω))/((2Ω+4Ω)+(3Ω)))my question is what formulas i can use to solve that kind of problem. Because my way is just drawing randomly or guessing the arrangement
 
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Dependent said:
my question is what formulas i can use to solve that kind of problem. 'Coz my way is just drawing randomly or guessing the arrangement
Yes, that is how those problems are solved. There is no "equation".
 
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For more complex problems you can use iterative solving and optimization methods
 
IMO - this is more a logic / math problem than a typical EE circuit problem. So the construct is not real world...I would not expect a standing algorithmic solution.
 
  • #10
Windadct said:
IMO - this is more a logic / math problem than a typical EE circuit problem. So the construct is not real world...I would not expect a standing algorithmic solution.
It is a standard exercise for EE students and is designed to help them become facile in applying Ohm's Law. There is no algorithmic solution nor does there need to be.
 
  • #11
donpacino said:
For more complex problems you can use iterative solving and optimization methods
I have no idea that you mean. Could you expand on this? I mean, what is there to optimize when trying to find an exact value given a set of resistors?
 
  • #12
phinds said:
I have no idea that you mean. Could you expand on this? I mean, what is there to optimize when trying to find an exact value given a set of resistors?
I second this request.
 
  • #13
phinds said:
I have no idea that you mean. Could you expand on this? I mean, what is there to optimize when trying to find an exact value given a set of resistors?

For problems like this, not much. For most problems, not much.
For more complicated problems (6th order notch filters) you can have many many resistors. This coupled with having to solve for 'real' resistor values makes the problems very difficult to solve.

note: optimization techniques won't solve circuit layouts for you, just pick component values. I was making a comment on ways to solve for resistor values other than inspection.

You can use a program (excel w/ visual basic, matlab, C) and implement optimization algorithms. You can set equations governing the resistors relationships with each other (and the allowed resistor values), set initial resistor values (just guesses for orders of magnitude, it doesn't need to be that accurate) and let the optimization tools take over.
 
  • #14
Dependent said:
I actually know the answer, which is

Rt(17Ω)=10Ω+5Ω+(((2Ω+4Ω)(3Ω))/((2Ω+4Ω)+(3Ω)))


my question is what formulas i can use to solve that kind of problem. Because my way is just drawing randomly or guessing the arrangement

You either need to randomly guess and rearange the ciruit until you find the answer.

Or just take a minute and use the hint you have above.

They show you the parallel branches above. 2 +4 ohms in series in one branch and 3 ohms in the other branch.
Give 6 and 3 ohms in parallel which comes out to 2 ohms.

Now just add in the series of 10 + 5 ohms either to the right or left on the wire of your open port ohm reading points.
And wallla, 17 ohms.
 
  • #15
phinds said:
It is a standard exercise for EE students and is designed to help them become facile in applying Ohm's Law. There is no algorithmic solution nor does there need to be.
"Ohm's Law"? I think it's Kirchoff's Laws that you use for this sort of problem - effectively, giving the simple rules for Combining resistances. A solution would have to be found by some sort of iterative method. It has the same sort of potential difficulty as the old 'travelling salesman' type problem. A nightmare unless the problem has been deliberately set with a simple answer.
 

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