# Nodal Analysis with 5 nodes

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#### BartekKowalewicz

##### New Member
Hello.
I need some help in solving a cicuit (https://s30.postimg.org/kd8fscdht/circuit.jpg). This circuit have to be solved by nodal analysis. I do not exactly know how to simplify this circuit to circuit that can be solved by a system of two equations. I will appreciate any help with that.
With best regards,
Bartek

Or better still, as a Moderator, I can add the circuit directly into your post:

JimB

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#### JimB

##### Super Moderator
It makes things much easier if you post the circuit directly here on ETO rather than as a link to some other site.

Like this:

JimB

#### Ratchit

##### Well-Known Member
Hello.
I need some help in solving a cicuit (https://s30.postimg.org/kd8fscdht/circuit.jpg). This circuit have to be solved by nodal analysis. I do not exactly know how to simplify this circuit to circuit that can be solved by a system of two equations. I will appreciate any help with that.
With best regards,
Bartek

Or better still, as a Moderator, I can add the circuit directly into your post:

View attachment 103690

JimB
You don't need to simplify the circuit. You have four unknowns, so you need four equations, one for each node. The sum of the currents present in each branch connected to a node is zero according to the kirchoff current law (KCL). After you derive the equations, you can use a computer equation solver found on the web to get the voltages at each of the four nodes.

Ratch

#### BartekKowalewicz

##### New Member
Hi.
The thing is that I need to simplify this circuit because I can't use any computer equation solver but I have to do that on "paper". I must obtain equestions in this form:

What I found is simplification with current sources but I don't know is that correct:

What can I do with branches with voltage sources and resistores?

#### Ratchit

##### Well-Known Member
Hi.
The thing is that I need to simplify this circuit because I can't use any computer equation solver but I have to do that on "paper". I must obtain equestions in this form:
View attachment 103701
What I found is simplification with current sources but I don't know is that correct:
View attachment 103702
What can I do with branches with voltage sources and resistores?
What do you want to do? What do you want to find out? You can convert any of the ports to a Thevenin or Norton equivalent and use only one equation. Whick port? If you merge the circuit, the nodes will disappear. Let us know what you want.

Ratch

#### BartekKowalewicz

##### New Member
I need to find out a value of R4 when I know that U35=86,34V. All datas for this circuit are in table below:

#### Ratchit

##### Well-Known Member
I need to find out a value of R4 when I know that U35=86,34V. All datas for this circuit are in table below:
View attachment 103704
OK, let me get this straight. You want to find the value of R4 when the voltage at node 3 is 86.34 volts, assuming node 5 is designated ground, right? It looks like the circuit has three nodes. The voltage at one node is given. That leaves two unknown nodes and two equations, which is what the problem specifies. Once you know the voltages at nodes 2 and 4, you should be able to figure the current through R4 and determine the value by the definition of resistance E/I .

Ratch

#### BartekKowalewicz

##### New Member
So my equestions should look like that:

Am I correct?

#### Ratchit

##### Well-Known Member
So my equestions should look like that:
View attachment 103708
Am I correct?
You did not answer my question. There are 3 unknowns, V2,V4,R4. Therefore, you also need a current equation for node 3. That makes three equations for three unknowns. I did not closely proofread your equations, but at first glance, the two equations appear correct.

Ratch

#### BartekKowalewicz

##### New Member
Yes, node 5 is designated ground. And in this case V3=V1=86,34V.

#### Ratchit

##### Well-Known Member
Yes, node 5 is designated ground. And in this case V3=V1=86,34V.
OK, since you appear to have set up the equations correctly, go ahead and solve them after deriving the third equation. You can do it by hand if you want, but I am going to use a computer equation solver. I get V2= 23.004 , V4 = -34.506, and R4 = 12.1246 . If your answers are not the same, then we can compare our equations. Otherwise, your problem will be solved.

Ratch

#### BartekKowalewicz

##### New Member
I made a calculations on paper and my results are the same as your once.
Thank you very much. I appreciate your help.

#### BartekKowalewicz

##### New Member
Hi Ratchit,
Can you look at this circuit which was solved with mesh analysis method:

Is my solution ok?

#### Ratchit

##### Well-Known Member
Hi Ratchit,
Can you look at this circuit which was solved with mesh analysis method:
View attachment 103801
Is my solution ok?
Sure, gladly. My advice is to forget the supernode and supermesh concept. When many textbooks run into a current source between loops or a voltage source between nodes, they go into a tizzy and adopt a topological tangle, coming up with a clunky clumsy concept that confuses and bemuses the problem solver. I like my way of looking at the problem better. Stick to the basics, I say.

OK, here is the basic principle. Every voltage source is capable of carrying a current, and every current source is capable of supplying a voltage.

Your example problem shows a current source between two loops. The circuit has six loops. Write the equations for the six loops using a term labeled something like Vj, designating the voltage across the current source J. So now you have six loop current unknowns, plus one current source voltage unknown Vj. That is seven unknowns and six equations. Add another equation i6 - i5 = J , and you seven equations and seven unknowns. Now you can solve the circuit without any reference to super whatever.

You are invited to submit another problem so I can show you how ordinary methods work best.

Ratch

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