Why Is Nodal Analysis Confusing in This Circuit Example?

In summary, the author is trying to solve a circuit using nodal analysis. He is not sure how to solve for the voltages and currents in the left part of the circuit. He is able to eliminate one resistor in series with a current source and solve for the voltages and currents in the right part of the circuit.
  • #1
arhzz
267
52
Homework Statement
Use nodal voltage analysis to solve the circuit
Relevant Equations
Circuit Analysis
Hello! Consider this circuit

Snimka zaslona 2022-06-05 214729.png


Now I am susposed to solve this using nodal analysis. The first step is to "prepare the network" so that I can set up the conductance matrix.

Now I've tried it for a bit and was not really able to do it. So I went ahead and looked at the solutions and this is how it looks like.

weqweqwe.png


Now I think I've figured out how the got the right part of the circuit (the K2). Now the reference node is clear all of the wires are connected to K0 to it. Now looking at the voltage source that is to the right we can transform that into a current source and add the conductances of the resistors (R 2R and 4R).

## \frac{1}{4R} + \frac{1}{R} + \frac{1}{2R} ## this gives us the conductance G ## G =\frac{7}{4R} ## and if we want the resistance we need to take 1/G and we get the solution from the book. Now the current that the source is "emitting" is simply voltage divided through resistance,so and the nodal voltage is from K2 to K0, so its ##U_{20} ## The right part is pretty much clear but the left one is confusing me.

Now we can transform Uq1 just like we did for Uq3 but,I need to add the two resistors that are infront of it and behind it(since they are in series) .If we do that the current will be calculated like Uq1/2R. Now what I do not understand is how they get to the value of R/4? I've tried redrawing the circuit many times and I have not been able to do it. I can see that one of the resistors is short circuted but I can't seem to get to the R/4. This is how I have the circuit drawn
kita.png


Take note that the current source at R1 and R4 are missing since I can't find them in LT spice. Now if I calculate the total resitance here I don't get the R/4 like in the solution.I've tried it a bunch of times and it feels like guessing at this point. What am I doing wrong ?Thanks and excuse the long post.
 
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  • #2
arhzz said:
Now I am susposed to solve this using nodal analysis. The first step is to "prepare the network" so that I can set up the conductance matrix.
Since you haven't received a reply yet...

Are you required to try to simplify the circuit before solving it? For me, the beauty of using KCL to solve networks is that you can write a number of equations that equals the number of unknowns, so you should be able to solve for the circuit voltages and currents without needing to simplify it. Have you tried solving it yet without simplifying? At the very least, it will be a good cross-check of your answers if you do end up simplifying the circuit before writing KCL equations.
 
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  • #3
Just looking at this and wondering which are the knowns and which are the unknowns ...
:rolleyes:

##\ ##
 
  • #4
berkeman said:
Since you haven't received a reply yet...

Are you required to try to simplify the circuit before solving it? For me, the beauty of using KCL to solve networks is that you can write a number of equations that equals the number of unknowns, so you should be able to solve for the circuit voltages and currents without needing to simplify it. Have you tried solving it yet without simplifying? At the very least, it will be a good cross-check of your answers if you do end up simplifying the circuit before writing KCL equations.
Well it is recommened that you simplify the circuit, but it is not mandatory
 
  • #5
BvU said:
Just looking at this and wondering which are the knowns and which are the unknowns ...
:rolleyes:

##\ ##
To ne honest that has not been stated in the question. They want me to set up the conductance matrix, the voltages are than from node 1 to node 0, node 2 to node 0.
 
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  • #6
Resistors in series with current sources and resistors in parallel with voltage sources have no effect on the larger circuit. So the resistor in series with current source Iq2 can be eliminated.

I see 3 resistors of value R connected from node 1 to ground, and 2 resistors of value 2R connected from node 1 to ground. The equivalent resistance of those 5 resistors in parallel is R/4
 
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  • #7
The Electrician said:
Resistors in series with current sources and resistors in parallel with voltage sources have no effect on the larger circuit. So the resistor in series with current source Iq2 can be eliminated.

I see 3 resistors of value R connected from node 1 to ground, and 2 resistors of value 2R connected from node 1 to ground. The equivalent resistance of those 5 resistors in parallel is R/4
I think I see it as well now,I'll try drawing it now,to see if I understood it well
 
  • #8
arhzz said:
I think I see it as well now,I'll try drawing it now,to see if I understood it well

Okay took me a litle long while but this is how I've drawn the circuit.And from this point on I have been able to get to the solution like in the book.

Thanks for the help everybody!

Simplified circuit dark 02.png
 
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Related to Why Is Nodal Analysis Confusing in This Circuit Example?

1. What is nodal analysis?

Nodal analysis is a method used to solve electrical circuits by applying Kirchhoff's Current Law (KCL) at each node in the circuit. It involves setting up a system of equations based on the currents flowing into and out of each node, and then solving for the unknown node voltages.

2. When should I use nodal analysis to solve a circuit?

Nodal analysis is best suited for solving circuits with multiple voltage sources and several nodes. It is also useful for circuits with dependent sources and non-linear elements. For simpler circuits, other methods such as Ohm's Law and Kirchhoff's Voltage Law may be more efficient.

3. What are the steps to solving a circuit using nodal analysis?

The steps for solving a circuit using nodal analysis are as follows:

  • Identify all the nodes in the circuit.
  • Choose a reference node and assign it a voltage of 0.
  • Apply KCL at each node to write equations for the currents flowing into and out of the node.
  • Substitute in known values and solve the resulting system of equations for the unknown node voltages.
  • Check your solution by applying KCL at each node again and ensuring that the currents balance.

4. What are some common mistakes to avoid when using nodal analysis?

Some common mistakes to avoid when using nodal analysis include:

  • Forgetting to include all the nodes in the circuit.
  • Incorrectly labeling the nodes or assigning the wrong reference node.
  • Not properly applying KCL at each node, such as forgetting to include all the currents or using the wrong sign convention.
  • Not checking the solution for errors, such as missing or incorrect units.

5. Are there any tips for making nodal analysis easier?

Here are a few tips to make nodal analysis easier:

  • Label all the nodes and the reference node clearly on your circuit diagram.
  • Choose the node with the most connections as your reference node to minimize the number of equations needed.
  • Use a consistent sign convention for currents, such as entering the node as positive and leaving as negative.
  • Double check your equations and solution for any mistakes.

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