Solve a Circuit Problem: Node-Voltage Method

[Novean]

Homework Statement

Here's a link to a picture of the problem:
http://i.imgur.com/zMAiR.png

V(delta) is above the 7 Ohm resistor, and V(x) is described by the positive Node between the 7 Ohm resistor and the 5 Amp Source, and the negative Node between the 9 ohm resistor and 150 Volt Source.

i(omega) runs down the 4 Ohm source on the left.

The top dependent voltage source is 3*V(x)
The left dependent voltage source is 5*i(omega)
The right dependent voltage source is 13*v(delta)

Homework Equations

I advise to use the node-voltage method to solve this. Plus, it will help me understand it since that and the Current-mesh are the tools our professor expects us to know for the coming exam.

The Attempt at a Solution

I have spent far too many hours and countless papers and methods trying to solve this problem in a way that gave me the answer that the book has. I've begun to think that the book may be wrong in regards to their answer?

Anyway, I'll detail my usual procedure:

Using the node-voltage method:

I chose to ground the node in the top between the 1 Ohm and 2 Ohm resistors. Since a wire connect that node to the one under it, I concluded that both of those nodes are grounded. I pretty much erased that wire and connected both nodes into one.

I then created node-voltage equations, and use a program called MATLAB to solve matrices that I created out of the linear equations (As my professor has told us to do for every problem).

The answer in the answer manual says that the Power absorbed is 23.68 W.
They show a procedure to doing it, but they always skip the 150 Volt source in their equations. It's as if it doesn't exist. Why is this?

If someone could either do it and get the right answer, or tell me why they chose to omit the 150 Voltage source in their calculations, that'd help me greatly. Also, you could just tell me a different method to doing the problem and I'll give it a go.

What really has me confused is the usage of the Voltage and Current source on the bottom wire. I don't know how to represent those in a node-voltage equation correctly.

Thank you if you can help me in anyway.

 

[szynkasz]

We have voltage source and current source in series. This configuration gives constant current at any voltage so it is actually current source.

 

[Novean]

We have voltage source and current source in series. This configuration gives constant current at any voltage so it is actually current source.

So what you're saying is that they are right in that they ignore the 150 Voltage source?
Cause the way I'm thinking is that the voltage source would also create a current through the bottom resistor, such that the current in the bottom can be represented as a sum of the Current source and Voltage source through the resistor.

 

[szynkasz]

The current source produces 100 mA current regardless of what is connected to it.

 

[rezeew]

I would like to first commend you for your persistence and dedication in trying to solve this circuit problem. It shows your determination to understand and master the node-voltage method, which is a valuable tool in circuit analysis.

Now, to address your concerns about the 150 Volt source and the bottom wire with the voltage and current sources:

1. The 150 Volt source can be omitted in the calculations because it is not connected to any of the nodes that you have chosen. Since the voltage at the node between the 9 ohm resistor and 150 Volt source is already known (it is 150 V), it does not affect the node-voltage equations for the other nodes.

2. The bottom wire with the voltage and current sources can be treated as a single node, just like you did with the top wire. This means that the voltage at that node is also known (it is 0 V, since it is connected to ground). Therefore, it does not need to be included in the node-voltage equations for the other nodes.

Now, as for the procedure to solve this problem:

1. Choose a reference node and label it as 0 V. This can be any node, as long as it is connected to the ground (usually the bottom node is chosen).

2. Write node-voltage equations for each of the remaining nodes. These equations should be in terms of the unknown node voltages.

3. Use Kirchhoff's Current Law (KCL) to write equations for each of the nodes. These equations should be in terms of the unknown node voltages and the known currents (i.e. the 5 Amp source and the 4 Ohm source).

4. Solve the resulting equations using a program like MATLAB or by hand.

5. Once you have the values for the node voltages, you can use them to find the power absorbed by any of the components in the circuit (using P=V*I or P=I^2*R).

I hope this helps you in solving the problem. Remember, practice makes perfect, so keep practicing and don't get discouraged. Good luck!