How to arrange/draw circuit diagram from fixed resistances

[Dependent]

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.

 

[phinds]

Ohm's Law

 

[sk1105]

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.

 

[Dependent]

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 R_t(17Ω)=(this arrangement of the five resistances)

 

[phinds]

yeah, but what i want to know is R_t(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.

 

[Dependent]

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

R_t(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

 

[phinds]

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".

 

[donpacino]

For more complex problems you can use iterative solving and optimization methods

 

[Windadct]

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.

 

[phinds]

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.

 

[phinds]

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?

 

[Dependent]

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.

 

[donpacino]

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.

 

[psparky]

I actually know the answer, which is

R_t(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.

 

[sophiecentaur]

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.