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In summary, the person is seeking help with nodal analysis and has identified one incorrect equation (2) out of the three equations provided. The expert suggests that equation (1) has a duplicate term and involves nodes 2 and 3 incorrectly, while equation (3) has a branch not connected to node 3. They provide a simple method for writing node equations and explain the connections and current directions.

- #1

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- #2

gneill

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Looks like only your equation (2) is a correct node equation.

- #3

alexmath

- 35

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- #4

gneill

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In your equation (1), note that node 1 has only three connections. So there should be just three terms in total, where you have four, and one of them is a duplicate of another while yet another involves nodes 2 and 3 alone for some reason...

In your equation (3), as above it has just three connections so there should be just three terms in total. The last term on the right cancels the term on the left hand side; you only want to account for a given current once. The middle term on the right side seems to involve a branch not even connected to node 3.

A simple way to write node equations is to simply assume that all currents are flowing out of the given node and write their sum. Let's say you want to write the equation for node 2 (for which you have a correct equation already). Then you could write it as:

$$\frac{V2 - 2 - V1}{2} + \frac{V2 - 4}{2} + \frac{V2 - V2}{2} = 0$$

The first term accounts for the current on the branch between nodes 2 and 1, the second term accounts for the current between node 2 and ground, while the third term accounts for the current between node 2 and node 3. That's all three connections accounted for.

The math will automatically take care of the current directions if you do it this way. No need to guess current directions in any branches. Simply assume that all currents are flowing outwards from the chosen node and that the sum of them will be zero.

- #5

rezeew

- 1,257

- 1

I understand the importance of accuracy in solving circuit problems using nodal analysis. It is possible that one or more of the equations used in the analysis may be incorrect, leading to an incorrect solution. In order to determine which equation is incorrect, I would suggest carefully reviewing the steps and calculations used in the nodal analysis. Look for any errors in applying Kirchhoff's current law or in determining the node voltages. Additionally, it may be helpful to double-check the values of the resistors and voltage sources used in the circuit. By carefully reviewing the analysis process, it should be possible to identify and correct any errors that may have occurred.

Nodal Voltage Analysis is a method used in circuit analysis to determine the voltage at each node in a circuit. It is based on Kirchhoff's Current Law, which states that the sum of currents entering a node must equal the sum of currents leaving the node.

To perform Nodal Voltage Analysis, you first need to identify the nodes in the circuit and label them with a unique variable. Then, you can use Kirchhoff's Current Law to set up equations for each node. Finally, you can solve the equations simultaneously to find the voltage at each node.

An error in circuit solution refers to an incorrect or inaccurate result obtained from performing Nodal Voltage Analysis. This can happen due to mistakes in setting up the equations or using incorrect values for the circuit components.

If you notice an error in your circuit solution, you should first double-check your calculations and make sure that all the equations are set up correctly. You should also verify that the values of the circuit components are correct. If the error persists, you may need to use a different method of circuit analysis or seek assistance from a more experienced individual.

Nodal Voltage Analysis is useful in circuits with multiple voltage sources and complex connections, as it allows for a systematic approach to solving for the voltages at each node. It can also be used to analyze circuits with both series and parallel components.

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