Which Approach is Correct for Nodal Analysis in Electricity Books?

[dijkarte]

In nodal analysis method, two books use different and contradicting approaches and not sure which one is correct. One books says that currents at each nodes should be treated independently from the other nodes so that the same current can have two opposing directions in the same equations. The other book uses the opposite method, where the current direction is consistent which makes more sense. Which one is correct?

 

[carlgrace]

In nodal analysis method, two books use different and contradicting approaches and not sure which one is correct. One books says that currents at each nodes should be treated independently from the other nodes so that the same current can have two opposing directions in the same equations. The other book uses the opposite method, where the current direction is consistent which makes more sense. Which one is correct?

It turns out it doesn't matter in the end how you define current direction (the signs will cancel). It is arbitrary (since it is an unknown) and the equations all work out as long as you are CONSISTENT. I would follow the method that makes more sense to you. For kicks, you can try solving a simple circuit using both methods and you will see they agree.

 

[jean28]

It turns out it doesn't matter in the end how you define current direction (the signs will cancel). It is arbitrary (since it is an unknown) and the equations all work out as long as you are CONSISTENT. I would follow the method that makes more sense to you. For kicks, you can try solving a simple circuit using both methods and you will see they agree.

x2. They are both the same thing. If you try a very simple circuit that requires nodal analysis you will notice that they both turn out the same at the end.

 

[dijkarte]

Should I assume element voltage polarity arbitrarily and independently of the assumed current direction through the same element?

And when doing nodal analysis, since current direction consistency does not matter, what about element polarity? Can I assume different ones when working on a different node?

Thanks.

 

[Jony130]

Here you have two more examples:

First

For this circuit from KCL

I3 = I1 + I2

(Va - 4V)/6Ω = (10V - Va)/10Ω + (6V - Va)/4Ω

And after solve this I get

Va -> 190/31 = 6.12903226V



Second

And again form KCL

(-I1) + (-I2) + (-I3) = 0

Or

- I1 - I2 - I3 = 0

So know all current flow outward (away) from the node.
So this assume that voltage at node Va should be at higher potential.
And current flow from + to - , I assume that if current entering into a node I give him " +"
and current that come out form the node I give "-".
But you can choose whatever you won't but you must be consistent in your choice

So I can write:

-(Va - 10V)/10Ω - (Va - 6V)/4Ω - (Va - 4V)/6Ω = 0

And again the answer is exactly the same

Va -> 190/31 = 6.12903226V

And maybe another example for this diagram I choose

But I also can assume that if current flow out from the node I give a "+" sign.

I1 + I2 + I3 = 0 ( no current entering the node).
Since all current flow out from the node the Va node should be at higher potential.

(Va - 10V)/10Ω + (Va - 6V)/4Ω + (Va - 4V)/6Ω = 0

And the answer is
Va -> 190/31 = 6.12903226V What a surprise

 

[dijkarte]

Thanks a lot!

After reading your example, I tried a different one and this time using at each node different directions for the same current. It worked like a charm! the trick is consistency in applying the sign convention.

 

[dijkarte]

Any idea why NILSSON & RIEDEL book is very popular in academia while it's nothing compared to Sudoki & Alexander?

 

[carlgrace]

No idea. I used Nilsson and Riedel in school...

Wait till you get to Johns and Martin to see how people REALLY design circuits.

 

[dijkarte]

I mean for basic material I would choose something that teaches readers instead of just talking to them or even to itself. Maybe they like the names, sound more academic :D
Nilsson and Riedel!

 

[Jony130]

while it's nothing compared to Sudoki & Alexander?

Can you post the full title of this book. Because Goggle don't help much.
And also here you can find a very good video lecture about circuit theory.
http://www.digilentinc.com/Classroom/RealAnalog/index.cfm

 

[dijkarte]

http://www.amazon.com/dp/0073380571/?tag=pfamazon01-20

I find it the most comprehensive electricity book compared to many others, in terms of context and presentation.