# node analysis and dependent sources

## calculate current i

• ### Vx

• Total voters
0

#### hassansleiman

Joined Nov 12, 2015
3
Hello every body can you help me to solve this problem

#### Attachments

• 297.7 KB Views: 25

#### WBahn

Joined Mar 31, 2012
24,854
Hello every body can you help me to solve this problem
MOD NOTE: Moved to Homework Help

#### WBahn

Joined Mar 31, 2012
24,854
Hello every body can you help me to solve this problem
Yes, we can HELP you, but we won't just do it for you. YOU need to post YOUR best attempt to solve YOUR homework (regardless of whether it is assigned homework or not). That gives us the ability to see what you are doing right and what you are doing wrong and to help guide you back onto the right path.

#### RBR1317

Joined Nov 13, 2010
502
Before one can begin the node analysis (sorry, I never do mesh), it is necessary to identify the nodes and label them. Why don't you begin there? Then determine which of the nodes should be the ground node.

#### WBahn

Joined Mar 31, 2012
24,854
Given the exclusive use of current sources, nodal analysis is probably the best choice for this circuit anyway.

Using superposition might help, but that isn't totally obvious to me.

#### MrAl

Joined Jun 17, 2014
6,641
Hi,

Just for reference and check point, i get a value for Vx which is between 2 volts and 3 volts so you can use that to get a rough idea if you got the right result. I wont specify any more exact just yet. I made the minus (-) terminal of Vx the ground node (0 volts).
I used Nodal.

#### hassansleiman

Joined Nov 12, 2015
3
can you help me solve this homework and show me the solution

#### MrAl

Joined Jun 17, 2014
6,641
can you help me solve this homework and show me the solution

Hi,

Yes, but did you try it yourself? This forum usually requires the person who asks to post their first attempt to solve it, unless you are totally in the dark in which case we would have to start with a simpler problem first so you can get that going.

My question is, do you know how to write equations for Nodal Analysis, or any other type of analysis really?
Did you learn any circuit analysis techniques yet, and if so, which ones?

#### WBahn

Joined Mar 31, 2012
24,854
can you help me solve this homework and show me the solution
In case you missed Post #3:

Yes, we can HELP you, but we won't just do it for you. YOU need to post YOUR best attempt to solve YOUR homework (regardless of whether it is assigned homework or not). That gives us the ability to see what you are doing right and what you are doing wrong and to help guide you back onto the right path.

#### RBR1317

Joined Nov 13, 2010
502
My question is, do you know how to write equations for Nodal Analysis
There is a simple technique for writing node equations as demonstrated below for a generic 'Node Z'. A node equation is concerned with a single node and its direct connection to adjacent nodes - any other nodes in the circuit have been faded away. Use 'Node Z' as a template for writing the node equations for all remaining nodes (except the ground node). With this method, current flowing out of the node is positive, so if there is a current source forcing current to flow into a node then it will be written as negative in the node equation.

#### MrAl

Joined Jun 17, 2014
6,641
Hi,

Yes, but did you try it yourself? This forum usually requires the person who asks to post their first attempt to solve it, unless you are totally in the dark in which case we would have to start with a simpler problem first so you can get that going.

My question is, do you know how to write equations for Nodal Analysis, or any other type of analysis really?
Did you learn any circuit analysis techniques yet, and if so, which ones?

There is a simple technique for writing node equations as demonstrated below for a generic 'Node Z'. A node equation is concerned with a single node and its direct connection to adjacent nodes - any other nodes in the circuit have been faded away. Use 'Node Z' as a template for writing the node equations for all remaining nodes (except the ground node). With this method, current flowing out of the node is positive, so if there is a current source forcing current to flow into a node then it will be written as negative in the node equation.
View attachment 107121

Hi there,

I am not really sure why you are telling me this, but thanks just the same. I was really asking the OP if *they* knew how to do nodal analysis. I still appreciate your reply with the very nice drawing and all which clearly shows *ONE* nodal method, which might be the easiest to remember.

If the OP knows nodal already they we dont have to teach that, just find out where the errors, if any, are.

#### RBR1317

Joined Nov 13, 2010
502
I am not really sure why you are telling me this...
Sorry, I see now that I should have started my reply with, "For the benefit of the now-absent OP....."

I can still remember when mesh analysis was my preferred approach and I just didn't grok node equations, probably because I was first taught one of those *OTHER* nodal methods. But now I can say that I have not used mesh analysis in a very long time.

#### WBahn

Joined Mar 31, 2012
24,854
But now I can say that I have not used mesh analysis in a very long time.
That's a shame, because some circuits are trivially easy with mesh but much more complicated with node and other circuits are the other way around. So when you voluntarily limit yourself to using a single technique you are forcing yourself to do a lot more work -- and increase the odds of making a mistake -- than if you are able to choose the right tool for the right job.

#### RBR1317

Joined Nov 13, 2010
502
That's a shame, because some circuits are trivially easy with mesh...
But those circuits are likely contrived homework problems, whereas in my world of analyzing signal voltages the primary concern is not to make the trivial mistakes which I find happens all too often when using mesh analysis or clever transformations. One must find the right path within their own limitations. Also, complexity is not usually a concern when using a symbolic algebra engine for calculation.

#### WBahn

Joined Mar 31, 2012
24,854
Good points. And I must admit that I very seldom use things like delta-wye transforms, even though they can significantly reduce the work load for some problems, because I can't remember the formulas and so first I have to take a couple minutes to derive them. I know people that memorize formulas for mesh and node analysis, and I just shake my head since both are nothing more than formalized, but direct, applications of KVL and KCL, which should be part of the marrow of one's bones by the end of Circuits I -- but then again I have seen plenty of grad EE students that still have to look up KVL and KCL if it has been more than a few weeks since they used them. I can only shake my head and weep.

#### The Electrician

Joined Oct 9, 2007
2,750
Good points. And I must admit that I very seldom use things like delta-wye transforms, even though they can significantly reduce the work load for some problems, because I can't remember the formulas and so first I have to take a couple minutes to derive them. I know people that memorize formulas for mesh and node analysis, and I just shake my head since both are nothing more than formalized, but direct, applications of KVL and KCL, which should be part of the marrow of one's bones by the end of Circuits I -- but then again I have seen plenty of grad EE students that still have to look up KVL and KCL if it has been more than a few weeks since they used them. I can only shake my head and weep.
I seem to remember that you had a derivation of the delta-wye transformation in your blog, but it isn't there now. Am I mis-remembering? If I'm remembering correctly, why did you remove it?

#### The Electrician

Joined Oct 9, 2007
2,750
Sorry, I see now that I should have started my reply with, "For the benefit of the now-absent OP....."

I can still remember when mesh analysis was my preferred approach and I just didn't grok node equations, probably because I was first taught one of those *OTHER* nodal methods. But now I can say that I have not used mesh analysis in a very long time.
I've never seen more than one nodal method. What is a nodal method that is different from the one you show in post #10? Can you briefly explain the difference, or provide a link to an explanation on the web?

#### WBahn

Joined Mar 31, 2012
24,854
I seem to remember that you had a derivation of the delta-wye transformation in your blog, but it isn't there now. Am I mis-remembering? If I'm remembering correctly, why did you remove it?
I didn't have that in the blog, but rather I wrote a Technical Article for the commercial side of the site. I think it's still there.

#### The Electrician

Joined Oct 9, 2007
2,750
Ah, yes. I see it there. I knew I had seen it somewhere in connection with All About Circuits.

#### WBahn

Joined Mar 31, 2012
24,854
I've never seen more than one nodal method. What is a nodal method that is different from the one you show in post #10? Can you briefly explain the difference, or provide a link to an explanation on the web?
They would all be variants on a theme. Some people work with currents flowing into the node, some with currents flowing out. Some put all the terms on one side and some put the terms with unknowns on one side and knowns on the other.

With just a bit of practice, you can write the linear equations directly by inspection. For instance, for the example in Post #10, you can write

$$- \; V_A \( \frac{1}{R_{AZ}}$$ \; - \; V_B $$\frac{1}{R_{BZ}}$$ \; - \; V_C $$\frac{1}{R_{CZ}}$$ \; - \; V_D $$0$$ \; + \; V_Z $$\frac{1}{R_{AZ}} \; + \; \frac{1}{R_{BZ}} \; + \;\frac{1}{R_{CZ}}$$ \; = \; -I_{ZD}
\)