# Circuit analysis with multiple batteries

Discussion in 'Homework Help' started by Terje Hjerpbakk, Oct 9, 2016.

1. ### Terje Hjerpbakk Thread Starter New Member

Oct 9, 2016
2
0
Hello, Im sorry to bother you guys
Im trying to find the current I

Original:

With my notes

incase the Img not working:
1(original):http://imgur.com/a/ujJA6
2(with my notes): http://imgur.com/a/Nyve4

My attempt following the picture with notes:
Loop 1: .3*I2 + 12V = 0 ---> I2 = 4
Loop 2: -24 - 4*I3 + 3*I2 = 0 ---> I3 = -4
Loop 3: 12+6(I1+I2+I3) - 4*I3 =0
12+ 6I1+24-24 = -28 ---> I1 = -4,66

is this correct?

2. ### WBahn Moderator

Mar 31, 2012
20,247
5,758

Why is the resistance in your first loop 0.3 Ω? Did you mean that to be a negative sign? That would be consistent with your conclusion that I2 = 4 A.

You need to start tracking your units properly. I2 = 4 is meaningless. Is it 4 amperes? 4 milliamperes? 4 electrons per month? What?

You might want to check your value for I3 a bit more carefully?

If the current flowing in the 6 Ω resistor in the diagram is I1-I2-I3, then why is it (I1+I2+I3) in your Loop 3 equation?

If I2 = 4 A and I3 = -4 A, then the current in the 12 V battery is 0 A (since it is I2 + I3). This then requires that I2 = -I3. Is that consistent with your answers?

3. ### RBR1317 Active Member

Nov 13, 2010
400
77
Here is another fine example of making life difficult with current loops when the problem is so much easier to solve with node voltages. Note that the circuit consists of a ground and two voltage nodes. Voltage sources set the voltage at each node, therefore the current through each resistor is known. Applying KCL at each node gives the current through each voltage source, so finding the current 'I' is trivial.

4. ### MrAl Distinguished Member

Jun 17, 2014
3,753
791

Hi,

I dont think it would be a bother as many people come here to learn and also to help other people with their circuit questions. You've tried to solve it which is the first step. If you know of a second way to solve it you can try that too and compare results to see if they match.

5. ### Terje Hjerpbakk Thread Starter New Member

Oct 9, 2016
2
0
I really apprecaite the help guys. Im not so good with circuits yet, but trying to do something about it

doing it with KCL i now have:
Loop1:
-3*I2 + 12 = 0
I2 = 4A

Loop2:
3I2 -24 -4I3 = 0

12-24=4I3
-12= 4I3
I3 = -3A

Loop3:
12+6(I1-I2-I3) -4I3 = 0

12+6I1-6I2-6I3-4I3 = 0
12+6I1-24-(-18)-(-12)=0
12+6I1-24+18+12=0
6I1 = -18
I1 = -3A

This seems to fit correctly with RBR1317's solution.
RBR1317: That solution looks way better/less complex! How did you find the current over R2 with nodes? did you just use the

voltage potential between the nodes? Vnode1 - Vnode2 = -24-(-12) = -12 and then found the current I3= -12/4 = -3A?

WBahn: Thanks for all your good tips and for pointing out my mistakes.

Thanks all,
Terje

6. ### WBahn Moderator

Mar 31, 2012
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5,758
This particular circuit is set up so that you can find the voltage at each node by only considering the battery voltages. That makes the analysis of the currents through any of the resistors trivial because you know the voltage on each side of the resistor and, hence, the voltage across the resistor. Since you are also given the values of each resistor, you can use Ohm's Law to calculate the current through each resistor. Then you use KCL to find the current through each battery.

7. ### shteii01 AAC Fanatic!

Feb 19, 2010
3,975
617
Note.
I was taught that mesh currents should all rotate in the same direction.

This is not a requirement, just how I was taught to do it.

8. ### WBahn Moderator

Mar 31, 2012
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Note that he isn't using mesh currents (the drawing makes us think he is at first blush). He is using branch currents and loop equations. He may not have gotten to mesh analysis yet.

9. ### MrAl Distinguished Member

Jun 17, 2014
3,753
791
Hi,

I didnt notice that either until you mentioned it
I took a quick look and thought all the arrow loops where all going in the same direction but now i see they are not. Makes me wonder why someone would want to do that in the first place.
Now for the final question of the day: will the OP come back to check the replies again

10. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,396
355
Why? Let's see. It's October, not too far into fall quarter in the "Introduction to Network Analysis" class. Branch current analysis comes first.

11. ### WBahn Moderator

Mar 31, 2012
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My first thought when I noticed that was that he wanted his loops to go through the batteries in the same way, but he didn't achieve that if that was, indeed, the goal. It's hard to say -- could be that those directions just caught his eye for some reason. Of could be that he didn't realize that one of them wasn't in the same direction of rotation as the other two.

12. ### MrAl Distinguished Member

Jun 17, 2014
3,753
791
Hi,

Well, cant i ask the same question, "why", as in why you would think that a circuit analysis course has to do one type of analysis before the other. In the only circuit analysis book i have with me at the moment, they go in the following order:
Single loop circuit
Nodal
Mesh
Superposition
Loop

That book was written by two fairly well known circuit analysis moguls, but im not sure the order matters that much really.

Do you think there is an advantage to doing these in a different order?

It's not that i am totally against doing that one loop the other way, it just seems like a very non symmetrical thing to do unless there is a plausible reason for it, which i was hoping to yank from the OP with that subtle inquiry. So the query was more directed toward the OP rather than the subject of circuit analysis in general.

13. ### WBahn Moderator

Mar 31, 2012
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So that book didn't present KVL and KCL at all?

Almost all books (can't make a complete blanket statement) develop KVL for single loop circuits first. Then they present KCL for two loop circuits. They then usually show how to use a combination of KVL and KCL to develop a set of equations using loop voltages and branch currents. It's at that point that they have set the stage for introducing mesh current analysis and node voltage analysis and these are often done in a different order between two authors.

14. ### The Electrician AAC Fanatic!

Oct 9, 2007
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I would think that one type of analysis might be taught before another for the same reason that you learn to ride a bicycle before you learn to drive a car.
I'm postulating that since the current date is early in the academic quarter, the TS probably hasn't yet learned mesh analysis, and discovered that keeping all the mesh current orientations the same has some advantage when setting up the equations. Of course the answers obtained are the same no matter what orientations are chosen; the only advantage to consistent orientation is helping get the signs right which probably isn't yet apparent to the TS. So the answer to your question "why someone would want to do that in the first place" is that he hasn't yet learned a reason not to--it's too soon in the quarter.

15. ### MrAl Distinguished Member

Jun 17, 2014
3,753
791
Hi,

Yes, but that was more basic so i did not mention that. I didnt want to have to type out the whole table of contents. What i did type however was in the same order that the book gives.

Last edited: Oct 11, 2016
16. ### MrAl Distinguished Member

Jun 17, 2014
3,753
791
Hi,

Ride a bike, drive a car, two very different things of a different class. We were talking about things that are much more similar. Of course one MIGHT learn to ride a bike first, but maybe that person never did that. But the main point is that we are comparing two or more things of equal value or equal complexity, more or less.
For that the difference is minimal nothing like the difference between a bike and a car.

It's possible that you are correct in your thought about someone not having learned something yet, but if so i really wanted the OP to clarify, not just a guess.

I dont think this line of discussion is that interesting anyway, it would be more interesting just to talk about the different ways to do the circuit, and perhaps the more recommended ways such as keeping all the loop currents going in the same direction

If it keeps up this may end up becoming another South Park episode (har har).

Last edited: Oct 11, 2016
17. ### WBahn Moderator

Mar 31, 2012
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But I think it's relevant to this point because I think the TS is in the KVL/KCL stage and thus working with loops and branches. I don't think they've gotten to mesh/nodal analysis yet and so these are the tools in their tool kit at this stage.

18. ### MrAl Distinguished Member

Jun 17, 2014
3,753
791
Hi,

Ok, well as EXPECTED those come before the single loop circuit.

It doesnt really matter to me if he learned it yet or not at this point. If he didnt learn it then he will say so, maybe, eventually, and if he did learn it then he may tell us that instead.
Either way, i'm fine with it. Thanks for thinking about it though.

Also, note the South Park reference in the previous reply

19. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,396
355
For my purpose they are the same class--transportation.

I don't think we are comparing things of equal complexity. That's the point; the thing of lesser complexity, more or less, is taught first. You may think mesh analysis is the same complexity as branch analysis; I don't. My textbooks don't and my classes didn't. Mesh analysis may not be 100 times more complex than branch analysis, but its greater complexity of whatever ratio provides the rationale for teaching it first.

20. ### WBahn Moderator

Mar 31, 2012
20,247
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Since I've never watched the show, I have no idea what the reference is to which you refer.