Hi AAC,

I'm having an issue with the following problem:

As shown from the picture, terminals 'a' and 'b' are open. I know the answer to this problem, but having an issue proving it.

Here is my nodal analysis. I keep getting Vth as 4V. The answer says 6V.

What am I doing wrong?? Any help would be GREATLY appreciated!

 

It's a simple algebra mistake, as it so often is.

In the right hand column, 4th expression down you have:

\(10 V_{th}-4[\frac{24+V_{th}}{2}]=0\)

Next line you have:

\(10 V_{th}-2[24-V_{th}]=0\)

How did the plus sign in the numerator between the square brackets become a minus sign?

 

It's a simple algebra mistake, as it so often is.

In the right hand column, 4th expression down you have:

\(10 V_{th}-4[\frac{24+V_{th}}{2}]=0\)

Next line you have:

\(10 V_{th}-2[24-V_{th}]=0\)

How did the plus sign in the numerator between the square brackets become a minus sign?

Duhhhhhh. Thank you very much. I spent hours on this problem

 

What did you do for those hours?

Did you go back through your work line by line verifying that each line actually leads to the next line? That should come early in your efforts.

Don't be afraid to take everything you have done and push it aside and start from scratch on a clean sheet of paper. You usually won't make the same dumb math mistakes twice.

Also, you need to start tracking your units through your work. Most mistakes we make will mess up the units and let us catch the mistake right when we make it or at least make it much easier to track the error down. It wouldn't have helped with this particular mistake, though.

 

What did you do for those hours?

Did you go back through your work line by line verifying that each line actually leads to the next line? That should come early in your efforts.

Don't be afraid to take everything you have done and push it aside and start from scratch on a clean sheet of paper. You usually won't make the same dumb math mistakes twice.

Also, you need to start tracking your units through your work. Most mistakes we make will mess up the units and let us catch the mistake right when we make it or at least make it much easier to track the error down. It wouldn't have helped with this particular mistake, though.

When I couldn't get the correct answer using KCL, I went ahead and performed mesh analysis to find Vth. I got stuck because I did not know what to do with the current between the two nodes. Then I realized that that current just equal to (i1+i2) (based on selected current direction).

This took me a while, but after struggling with this problem, I've learned as you have mentioned - pay attention to units and signs. In addition, after doing mesh analysis, that math was less involved than using nodal analysis. So I learned to pick my method of attacking the problem wisely.

Thanks again everyone.

 

As you are indeed discovering, different methods have different strengths and weaknesses. No one method is "best" -- which is why you are taught several in the first place -- and a big part of the art of engineering is learning how to pick the 'best' (or at least something on the 'good' end) for a particular situation. There are some general rules, but even those have lots of holes. Quite often a problem that the rules say lends itself to mesh is actually trivially done with nodal analysis because of the peculiarities of that particular circuit. This is especially the case as soon as you are dealing with dependent sources (which, as you will learn, happens a lot because small signal models for transistors are based on them). Lots of experience and frustration and working problems multiple ways (which is an excellent way to check your work, particularly as a practicing engineer where there is no grader or anyone else to check it for you) is the only way to get it down. Good luck to you.