Nodal Analysis Help using matrix

[willow16v]

Hi,
I would be grateful of any advice on how to solve the problem below.

My aim is to find the voltages at nodes 2, 3, and 4, by means nodal analysis and thus creating simultaneous equations and solving them using matricies or matrix

I understand kirchhoffs law etc however its the complex numbers that are throwing me when working out the equations at each node.

I have tried for weeks now and it seems i am beaten yet again on my failure of rearranging algebra.

Any help would be great.

A=60 B=15 C=153


See diagram Below.

Cheers Chris

 

[djeitnstine]

1. where is your working?

2. you should have a labeling convention.

 

[Mene]

Hello Chris, thank you for reaching out for help with nodal analysis using matrices. Nodal analysis is a useful method for solving circuit problems, and using matrices can make the process more efficient and organized.

First, let's start by labeling the nodes in the circuit. We have nodes 1, 2, 3, and 4. Node 1 is the reference node and has a voltage of 0V. Now, we can use Kirchhoff's current law to write equations for each node.

At node 2, we have the following equation:
(A + B)(V2 - V3) + B(V2 - V4) = 0

At node 3, we have:
B(V3 - V2) + (B + C)(V3 - V4) = 0

And at node 4, we have:
B(V4 - V2) + C(V4 - V3) = 0

Next, we can rearrange these equations to solve for the unknown voltages V2, V3, and V4. This is where using matrices can be helpful. We can write the equations in matrix form as:

| A + B -B -B | | V2 | | 0 |
| -B B+C -B | | V3 | = | 0 |
| -B -B C | | V4 | | 0 |

Now, we can use matrix algebra to solve for the unknown voltages. The solution will give us the values for V2, V3, and V4.

I hope this helps you with your problem. If you are still having trouble, I would suggest seeking additional resources or reaching out to a tutor for further assistance. Good luck!