Finding Node Voltages Using the Node Method

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In summary, the conversation discusses finding node voltages for a circuit and the equations and attempts at a solution for the problem. The speaker realizes their mistake in handling the currents and adjusts their approach. They also comment on the helpfulness of typing out their thoughts and reasoning.
  • #1
erok81
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Homework Statement



Find the node voltages for the circuit shown.

Homework Equations



See attachment.

The Attempt at a Solution



I have chosen my ground node as the set of nodes in the bottom of the image and labeled all of my unknown voltages as en.

Here is what I have so far. Where G = 1/R

For the node labeled e1:

(e1-v0)G1 + e1(G3) + (e1-e2)I1 + (e1-e2)G2=0

For the node labeled e2:

(e2-e1)(-I2) + e2(G4) + (e2-e1)G2=0

I am pretty sure my problem lies in the way I am handling the currents in the node. I started plugging in numbers after I simplified it all and one of my unknown voltages went away. After that I looked at it again and knew I was doing it wrong. Most of the examples in the book don't deal with a current parallel to a resistor.

I think the way I should have done it is rather than subtracting voltages and multiplying like I am doing with the resistor nodes, is just take the current by itself.

So in my above equation e1)(-I1) would just become -I1 since I am not using ohms law for current. I think I only need current? Does that sound better?
 

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  • #2
erok81 said:
I am pretty sure my problem lies in the way I am handling the currents in the node. I started plugging in numbers after I simplified it all and one of my unknown voltages went away. After that I looked at it again and knew I was doing it wrong. Most of the examples in the book don't deal with a current parallel to a resistor.

I think the way I should have done it is rather than subtracting voltages and multiplying like I am doing with the resistor nodes, is just take the current by itself.

So in my above equation e1)(-I1) would just become -I1 since I am not using ohms law for current. I think I only need current? Does that sound better?

Yup. Much better. Voltage x current yields power, not a current, so is quite unsuitable for a KCL expression!
 
  • #3
Perfect! Thanks for the help.

It seems half the time I post problems, I get them mostly figured out just typing the post up. :)
 
  • #4
erok81 said:
It seems half the time I post problems, I get them mostly figured out just typing the post up. :)

Yup. Typing it out so that it make sense to someone else can often help one re-evaluate one's logic and assumptions. :smile:
 
  • #5


I would suggest that you carefully review your equations and make sure they accurately represent the circuit shown. It is important to consider all components and their relationships in the circuit when using the node method. Additionally, ensure that you are using the correct units for each quantity (e.g. voltage in volts, resistance in ohms). It may also be helpful to draw a diagram of the circuit and label all components and nodes to visualize the problem more clearly. Keep in mind that the node method is a systematic approach and it may be helpful to break down the circuit into smaller sections to make the calculations more manageable. Once you have double-checked your equations and have a clear understanding of the circuit, you should be able to solve for the node voltages using the node method. Good luck!
 

1. What is the Node Method for finding node voltages?

The Node Method, also known as the Nodal Analysis, is a circuit analysis technique used to find the voltage at each node (connection point) in a circuit. It involves applying Kirchhoff's Current Law (KCL) and Ohm's Law to create a system of equations that can be solved to determine the unknown node voltages.

2. When is the Node Method typically used?

The Node Method is typically used when analyzing circuits with multiple parallel branches and complex connections. It is also useful for finding the voltage at a specific point in a circuit, rather than the current flow.

3. How do you set up equations using the Node Method?

To set up equations using the Node Method, start by labeling each node in the circuit with a unique variable. Then, apply KCL at each node by setting the sum of the currents flowing into the node equal to the sum of the currents flowing out of the node. Finally, use Ohm's Law to relate the current to the voltage at each node, creating a system of equations that can be solved for the unknown node voltages.

4. What are the advantages of using the Node Method?

The Node Method allows for a systematic approach to solving complex circuits. It also provides a more accurate analysis compared to other methods, such as the Mesh Method, as it takes into account all the branches and connections in the circuit. Additionally, the Node Method can be used for both DC and AC circuits, making it a versatile tool for circuit analysis.

5. Are there any limitations to using the Node Method?

One limitation of the Node Method is that it can become time-consuming and tedious for circuits with a large number of nodes. Additionally, the Node Method assumes that all the connections between nodes are ideal, which may not always be the case in real-world circuits. In these situations, it may be more practical to use other circuit analysis techniques.

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