# Solve Circuit Analysis Homework: Find v1, v2, v3 with Nodal Analysis

• Engineering
• Dunder
In summary, the problem is that the book says to use nodal analysis, but you haven't written any complete nodal equations. You should use the node equations to find v1, but you found that v1 = 0.
Dunder

## Homework Statement

Find v1, v2, v3
Must be done with nodal analysis

I=V/R

## The Attempt at a Solution

So i started by saying i1 = v2/4, i = v1/2, i3 = v3/3
i + i1 + i2 = 0
v3-v2=51
v1-v2=0

I am not really sure to what to do from here, i can't seem to come across the right solution, the answer given in the book is v1=3.043, v2=-6.956, v3=0.6522

Any help would be much appreciated

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Dunder said:

## Homework Statement

Find v1, v2, v3
Must be done with nodal analysis

I=V/R

## The Attempt at a Solution

So i started by saying i1 = v2/4, i = v1/2, i3 = v3/3
i + i1 + i2 = 0
v3-v2=51
v1-v2=0

I am not really sure to what to do from here, i can't seem to come across the right solution, the answer given in the book is v1=3.043, v2=-6.956, v3=0.6522

Any help would be much appreciated

The problem says to use nodal analysis. You haven't written any complete nodal equations.

Hint: The nodes designated by V1, V2, and V3 are all separated by voltage sources. This implies that you can treat all three nodes as one supernode. Write the nodal equation for the supernode by referencing v1, and note that i = v1/2Ω. (v2 = v1 - 10V; v3 = v1 - 10V + 5i).

So is my nodal equation with the super node i + i1 + i2 = 0 ?
The branch including the 6 ohm resister is negligible since it theoretically exits the node and enters it as well?
Using this, I ended up solving for v1, but ended up finding v1 = 0, so I must be going in the wrong direction

Dunder said:
So is my nodal equation with the super node i + i1 + i2 = 0 ?
The branch including the 6 ohm resister is negligible since it theoretically exits the node and enters it as well?
That is true.
Using this, I ended up solving for v1, but ended up finding v1 = 0, so I must be going in the wrong direction

Node equations involve the node voltages and the resistances connected between nodes (including the reference, or "ground" node). You shouldn't need to designate any particular current as "i1", or "i2", etc. The exception here is that the current given the label "i" is important for the dependent voltage source. You should be able to replace it with a node branch current expression (v1/2).

Okay thank you, I worked to the right answer. Thank you again

## 1. What is Nodal Analysis?

Nodal Analysis is a method used to analyze electric circuits by determining the voltage at each node (connection point) in the 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.

## 2. How do I use Nodal Analysis to solve a circuit?

To use Nodal Analysis, you must first choose a reference node and label all the other nodes in the circuit. Then, write equations for each node by applying Kirchhoff's Current Law. Solve the resulting equations to find the voltage at each node.

## 3. Can Nodal Analysis be used for any type of circuit?

Yes, Nodal Analysis can be used for both DC and AC circuits, as long as the circuit is linear and contains only independent sources. It is a general method that can be used for any type of circuit.

## 4. What are the advantages of using Nodal Analysis?

Nodal Analysis is a systematic approach that simplifies the analysis of complex circuits. It can also be used to solve circuits with multiple voltage sources and dependent sources. Additionally, it provides accurate results and can be easily programmed into computer software.

## 5. Are there any limitations of Nodal Analysis?

One limitation of Nodal Analysis is that it can become tedious and time-consuming for circuits with a large number of nodes. In addition, it cannot be used for circuits with non-linear elements, such as diodes or transistors. In these cases, other analysis methods, such as Mesh Analysis, may be more suitable.

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