How to make this circuit easier?

[Earthland]

Homework Statement

I need to find voltages and currents in the following circuit, using Kirchoff laws. The purpose is not to gain knowledge in electricity, but to write a program that solves a system of equations using Gauss elimination method. I think I wrote correct program, but I also need to get correct equations.

Supervisor advised to draw the circuit in simpler fashion to find the voltages, and only then use Kirchoff laws, so that I can be sure I have found right equations that give right values. However, I'm kind of lost in this electricity stuff and since that is not the point of the exercise at all, I'm looking for some help.

Homework Equations

The Attempt at a Solution

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I thought that maybe resistor 25 is in parallel with 23, 34 and 45, and 12 and 56 are in series with this part of the circuit. And that the voltage over the whole circuit is 200 V. It gave me following values:

U_25 = 123.07692307692308
U_56 = 46.15384615384616
I = 30.76923076923077
U_12 = 1.5384615384615385
I1 = 4.615384615384616
I2 = 6.153846153846154

Are these correct?

 

[gneill]

Hi Earthland,

Your observations about the parallel and series connections of the resistors are fine. While I don't believe that your results are correct, I do see a few of the values that would match some of the correct values for different components. For example, you show a current I = 30.77 A (rounded) that would actually match a voltage U_12 in my calculations.

Can you spell out your calculations in more detail? Maybe start with the net equivalent resistance and the total current from the voltage source.

 

[Earthland]

I think I reasoned as follows:

First, that current trough resistors 12 and 56 is the same (current "I"), thus equations for corresponding voltages

U_12/5 = U_56/20

Second, that voltage in the parallel part is equal, thus currents I1 over 25 and I2 over 2-3-4-5 satisfy the eauation

I_1*10=I_2*30

Current I itself can be written of course as

I = U_12/5

According to Kirchoff

I = I_1+I_2

Voltage over the whole circuit is 200, so

U_12+U_25+U_56=200

For I_1 I can write

I_1 = U_25/10

And this is a system of equations that can be solved.

 

[gneill]

Okay, that looks reasonable. Perhaps your results just ended up getting mislabeled somehow.

But I was thinking of a more direct approach. If you can reduce the resistor network to its equivalent resistance then you can determine the total current that the source provides. Then immediately you can find the potential drops across R12 and R56 since that current flows through them. That gives you one current and two voltages already found, and also leads to a simple way to find U_25. From there the other currents and voltages should be simple.

 

[gneill]

Perhaps I should have asked for clarification on what you were trying to accomplish here. I assumed that you were looking to find all the currents and potentials across the components so that you could compare the results with what you obtain using your Gaussian Elimination program. Perhaps I erred in that assumption? Are you instead trying to develop the simultaneous equations for the program?

 

[Earthland]

You understand me correctly. Anyway, it seems I got right answers, only the order of the variables was messed up. The correct values are

U_56 = 123.07692307692308
U_25 = 46.15384615384616
U_12 = 30.76923076923077
I2 = 1.5384615384615385
I1 = 4.615384615384616
I = 6.153846153846154

Thank you for help, gneill :)

 

[gneill]

You understand me correctly. Anyway, it seems I got right answers, only the order of the variables was messed up. The correct values are

U_56 = 123.07692307692308
U_25 = 46.15384615384616
U_12 = 30.76923076923077
I2 = 1.5384615384615385
I1 = 4.615384615384616
I = 6.153846153846154

Thank you for help, gneill :)

That looks better! You're very welcome.