Hey, I ran into this problem in a textbook that seems to be giving more trouble than it should be. I've tried doing it a few times, but I can't seem to get the right answer with my method. Here's the question

I tried solving it with KVL, but my answers weren't right. Here's my basic working. Can someone show me what I'm doing wrong?

First loop, clockwise.

Second Loop, clockwise

[tex]10000(I_1-I_2)+22000I_2 + 6 = 0
\newline
10000I_1 +12000I_2 = -6
\newline
10000(\frac{10+10000I_1}{25000})+12000I_2 = -6
\newline
4+4000I_2 + 12000I_2 = -6
\newline
I_2 = -10/16000 A
\newline
\therefore
I_1 = \frac{10+10000*\frac{-10}{16000}}{25000} = 0.15*10^{-3} A
\newline
\therefore I = I_1-I_2 = 0.775*10^{-3} A[/tex]
I apologise if I've made some really obvious mistakes. I feel like my approch makes less sense each time I try. Thanks for the help

 

Your problem is that you are not using your loop current definitions consistently.

This is commonly the result when you don't explicitly draw your loop currents as you have defined them on your diagram.

Not doing so also forces the people looking at your work (us, in this case, or the grader when you go to get credit for it) to guess what your loop currents are. What is L1? What is L2? Which direction do they go? Just saying that your loop equation is going clockwise is ambiguous. Does this mean that the loop current is going clockwise, or that the equation is being summed up by going clockwise around the loop?

Also, since you say that these are only loop currents and not mesh currents, you need to be even more explicit in defining them since a loop current can take any closed path through the circuit that does not cross itself. You appear to actually be using mesh currents, so it is best to call them that as readers of your work will interpret the description more readily the same way you meant it.

So annotate your diagram with your I1 and I2 currents and then look at your initial equations for each mesh again. You'll probably slap yourself on the head for your mistake. If not, post the annotated diagram and we can proceed from there.

EDIT: Fixed typos.

 

Your problem is that you are not using your loop current definitions consistently.

This is commonly the result when you don't explicitly draw your loop currents as you have defined them on your diagram.

Not doing so also forces the people looking at your work (us, in this case, or the grader when you go to get credit for it) to guess what your loop currents are. What is L1? What is L2? Which direction to they go? Not that saying that your loop equation is going clockwise is ambiguous. Does this mean that the loop current is going clockwise, or that the equation is being summed up by going clockwise around the loop?

Also, since you say that these are only loop currents and not mesh currents, you need to be even more explicit in defining them since a loop current can take any closed path through the circuit that does not cross itself. You appear to actually be using mesh currents, so it is best to call them that as readers of your work will interpret the description more readily the same way you meant it.

So annotate your diagram with your I1 and I2 currents and then look at your initial equations for each mesh again. You'll probably slap yourself on the head for your mistake. If not, post the annotated diagram and we can proceed from there.

Yeah, you were right. I was inconsistently dealing with the middle resistor, by accidentally flipping the sign when getting the equation for the second mesh. I did it again and ended up with 31/70000 A, which is apparently right. Thanks again

 

Yeah, you were right. I was inconsistently dealing with the middle resistor, by accidentally flipping the sign when getting the equation for the second mesh. I did it again and ended up with 31/70000 A, which is apparently right. Thanks again

There's a super, super valuable lesson to be learned here, so I want to be sure to make it really explicit so that it doesn't get lost in the glow of the successful solution of the problem.

Setting up your equations is critical. Everything flows from there. More to the point, all of the electrical engineering associated with the problem is confined to those equations. Everything after that is "simply" mathematical gyrations. Furthermore, mistakes in setting up those equations usually can't be caught afterward (except by specifically checking that the answers obtained actually are solutions to the problem, something that should always be done and that almost never is).

So, you need to break a problem into three very specific phases. In the first phase you set up the equations needed to solve the problem. Nothing more. Don't simply them or manipulate them. Once you have them, you then carefully check that they are correct since, as already stated, mistakes at this stage are near-impossible to catch until you get to the end. In the second phase you solve the equations and, again, this is just applied math. In the final phase you should check that the answers you got really are solutions to the problem.

In that first phase, you should annotate your diagram with all variables that appear in any of your equations, including voltage and currents (to include polarity) and node designations. Then you write the equations in as clear a fashion as you can -- as you gain practice the format that will qualify as "clear" to you will evolve. But at whatever point you are at, you want to decide on a "standard" format for your equations. This will allow you to quickly determine if they have any obvious problems.

For instance, the mere fact that both equations had (I1-I2) in them should throw a big red flag that something is wrong. For each equation that has (Ix-Iy) in it, there should be another equation that has (Iy-Ix). Furthermore, no other equations should have either of these factors since they are there because of the single branch shared by Ix and Iy.

I usually draw a horizontal line under my setup equations before I start any actual work at solving them. They are that critical that I want to be able to see at a glance where they stop and the grunt work starts.

Two other aspects that, if applied religiously, will drastically improve your work is to always, always, ALWAYS track your units through each and every step of your work -- do not just tack them onto the end. You are going to make plenty of silly mistakes in your work and most of those mistakes will mess up the units, but only if the units are there to get messed up. Second, always, always, ALWAYS ask if the answer makes sense. Get in the habit of trying to ask this at the intermediate steps, too. At many such points it will be hard to tell, but at others it can be very obvious. An example is asking when a denominator in an expression can go to zero and if that makes physical sense.