# optimization problem

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#### Mateusz

##### New Member
Hello.
I need some help in solving a cicuit:

-Find Value R4 for which the voltage U34 = 21,6 [V]
-Create and describe the mathematical model of optimization problem using to describe the dependencies in the DC circuit, the method of nodal readable matrix

I add my solution, but in my teacher opinion everything is wrong

I will appreciate any help with that.
With best regards,
Mateusz

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#### ericgibbs

##### Well-Known Member
hi M,
Your arithmetic is in error, how do you get 5.998 Ohms.

E

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#### JimB

##### Super Moderator
Ian,
I think that IZ1, IZ2 and IZ3 are current SOURCES rather than ammeters.

JimB

#### ericgibbs

##### Well-Known Member
hi,
They are used to demonstrate the students grasp of thevenin and norton theorems in reducing circuits.

E

#### Ian Rogers

##### User Extraordinaire
Forum Supporter
hi,
They are used to demonstrate the students grasp of thevenin and norton theorems in reducing circuits.

E
I Know.... But even when we did nodal analysis in A/C systems, they were more useful circuits..

I wasn't very good at these... I got 1.02 ohm for R4....

#### ericgibbs

##### Well-Known Member
I would agree that the problems should be based on every day circuits and applications.

I am a professional engineer, but I prefer to approach and enjoy engineering in a practical way.

E

#### Ian Rogers

##### User Extraordinaire
Forum Supporter
I have never given analogue electronics much of my time.... Even my projects back in Uni were semi digital even then..

When we sat down and did nodal analysis, I think I was asleep as its really boring to me.. As you know the nearest I get to analogue is a loadcel amp, 4~20mA output, LCD contrast voltage circuits and that's about it!!

#### Ratchit

##### Well-Known Member
Hello.
I need some help in solving a cicuit:
View attachment 104114View attachment 104115

-Find Value R4 for which the voltage U34 = 21,6 [V]
-Create and describe the mathematical model of optimization problem using to describe the dependencies in the DC circuit, the method of nodal readable matrix

I add my solution, but in my teacher opinion everything is wrong

View attachment 104116View attachment 104118

I will appreciate any help with that.
With best regards,
Mateusz
I don't see that as a big problem. You have three unknowns, the current present in E1, V2, and R4. You can easily find three nodal equations to solve for those three unknowns, right? I can't follow what you are doing now, but it appears like you are calculating up a storm. Why don't you start over and write out those three equations so we can see if you are a right thinker. You can solve them later.

Ratch

#### Mateusz

##### New Member
hi M,
Your arithmetic is in error, how do you get 5.998 Ohms.

E
Right, my mistake . Thank you very much.
But i still don't see any mistake in nodal equation ;/

#### Ratchit

##### Well-Known Member
Right, my mistake . Thank you very much.
But i still don't see any mistake in nodal equation ;/
Your answer is correct. ie1 below is the current present in the E1 voltage source.

Ratch

#### ericgibbs

##### Well-Known Member
hi M,
For ref only, LTSpice plot of your circuit

E

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#### MrAl

##### Well-Known Member
Hi,

Check to see that the 5.998 is just due to a rounding during the calculations.

If we solve for the voltage U34 we get:
U34=((I3*R3-I2*R3+I1*R3-E1)*R4)/(R4+R3)

and this is interesting because it is independent of some of the components meaning you can look for reasons why this is so if you want to understand circuits better.

Solving that for R4 we get:
R4=(R3*U34)/((I3-I2+I1)*R3-U34-E1)

Plugging in the given values for the components we get:
R4=6 Ohms

That is an exact value not rounded.

The main idea here is that we first solved for the required voltage and then used that solution to solve for what we really wanted to know, which was R4.

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