# AC Mesh Analysis Exercise

#### gianx80

Joined Jan 23, 2011
14
Hi,
I'm trying to solve this exercise:

But I find:

I'm not finding the correct solution. What am I doing wrong? Am I writing the wrong equations?

#### WBahn

Joined Mar 31, 2012
26,139
It would help if you defined the variables you are using instead of making everyone guess.

What are I1, I2, and I3? Both location and direction.

If you do that, and then look at your initial set of equations carefully in light of it, you may well find your mistake.

Always set up your equations carefully and then check them carefully before going any further. This is where ALL of the EE magic is -- everything after that is just algebra. If you make a mistake in the setup, all the careful math in the world can't help you because you are solving the wrong problem at that point.

#### The Electrician

Joined Oct 9, 2007
2,782
The situation is even kinkier than what WBahn suggests. You did indeed make an error in your initial equations, and propagated that error to the last equations shown:

But then you didn't solve these equations correctly. The solution you show:

is not the solution for the equations you show; it is the solution for the equations without the error WBahn alludes to. Apparently you did set up your equations correctly on paper and solved them, obtaining the solution you show here. But when you put them in a format suitable for posting here, you didn't copy the first ones correctly, and propagated that error to the end.

And after all that, you have a solution that apparently doesn't match the given answer.

Last edited:

#### gianx80

Joined Jan 23, 2011
14
Hi,
excuse me, yesterday was late (01.00 a.m here, more or less), and I was so tired.
I did again all the calculations, I'm attaching a pdf with all the new data.

What am I doing wrong?

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#### WBahn

Joined Mar 31, 2012
26,139
The situation is even kinkier than what WBahn suggests. You did indeed make an error in your initial equations, and propagated that error to the last equations shown:
You walked it through a lot further than I generally will (and noticed something interesting as a result).

Once an error is made, I figure that there's little point going any further since anything that follows is virtually guaranteed to be wrong and is thus wasted time and effort, unless a fortuitous additional error cancels it out (which is another error in its own right) or the part with the error happens to not affect the answer. Both situations involve the use of luck and I don't consider luck to be a valid analysis technique. Better to develop the practice of checking your work as you go so that you can spot errors soon after they are made, stop right there, and fix them before proceeding.

#### WBahn

Joined Mar 31, 2012
26,139
Now that you've fixed the error in your set up equations and gotten an answer, check if the answer is correct. Don't do this by comparing it to someone else's solution, since in the real world if the person paying you to solve the problem already had someone else's solution, they probably wouldn't be paying you to solve it in the first place.

Take your solution and assume it is correct and then use that to work the problem backwards -- this is almost always possible to do even in the real world.

There are two obvious ways to do this in this case. Assume you know Io and that you don't know the value of the current source or, alternatively, that you don't know the value of the voltage source. Then solve for it and see if you get the stated value. If you do, then there is a very high likelihood that you are correct. If not, then there is a very high likelihood that you are wrong.

If your answer works out, but doesn't match the "correct" answer, then do the same thing with the "correct" answer to verify that it is, indeed, correct. Authors and publishers make mistakes, too.

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#### The Electrician

Joined Oct 9, 2007
2,782
In post #1, your second equation began with j4(I2 + I1); you fixed that in post #4. The solution you get is the same solution I get. It would appear that "correct" answer you have been given is not correct after all. Perhaps somebody else will chime in here and verify.

Edit: WBahn beat me to it by 3 minutes.

#### The Electrician

Joined Oct 9, 2007
2,782
Another technique for checking your answer is to solve the problem by another method. You were required to use mesh analysis, but you are not prohibited from using nodal analysis for checking. Doing so has the side benefit of giving you practice at nodal analysis.

#### WBahn

Joined Mar 31, 2012
26,139
In post #1, your second equation began with j4(I2 + I1); you fixed that in post #4. The solution you get is the same solution I get. It would appear that "correct" answer you have been given is not correct after all. Perhaps somebody else will chime in here and verify.

Edit: WBahn beat me to it by 3 minutes.
Actually, I didn't. I haven't worked it through to a solution. Just stated the process that I almost always use (and have gotten bit on numerous occasions when I didn't). I never assume that the answer I get is correct -- I know the kinds of mistakes I have made and have seen others make to justify that level of hubris. So I always ask if the answer makes sense (and, of course, I've already confirmed that the units work out since I religiously track my units throughout my work). But then I usually plug my solution back into the problem -- or at least a limiting case of the problem -- to validate it. Or I solve the problem via a different means, if that's simpler. Thus if my solution doesn't match someone else's (such as the author or a student or a coworker or a customer) then I have some confidence that mine is correct. But I then check theirs to confirm that. And there have been times when it turned out that the other solution was correct, "too", and then I've spent significant time trying to understand the situation. In the end I've always tracked it down, though I recall one time that took several days to do so -- sometimes I was right and sometimes I wasn't, but I've always learned something valuable in the process.