Kirchoffs Law and simple circuit problem

[QuarkCharmer]

Homework Statement

The problem is in the attached image. I can't figure out what is going on. The circuit as given is at the top, I have circled what I am trying to find.

Homework Equations

The Attempt at a Solution

I used the junction law to find the current through the 3 ohm resistor to be 8 amps. Then I took three loops of the system and applied kirchhoffs voltage law, and solved the system of three equations and 3 unknowns, but it's inconsistent. I don't see where I am going wrong but I suspect it has something to do with my loops.

No matter how I do this, it always works out to be impossible?

Thanks

 

[gneill]

I think you're overthinking this

Assign a potential of 0V to the node labeled d (make it a reference node). Then using the known currents and resistances, assign relative potentials to nodes b, h, f. Continue...

 

[QuarkCharmer]

That potential of 0 volts is from which voltage source though? I'm not sure I understand what you mean exactly. I have done about 20 problems like this, finding currents and resistances and emf's without any problems just doing loops and solving. It should work?

If you mean, using node d as the "ground" if I were say, hooking up a multimeter or something, then how do you know that node d has 0 potential?

 

[gneill]

That potential of 0 volts is from which voltage source though? I'm not sure I understand what you mean exactly. I have done about 20 problems like this, finding currents and resistances and emf's without any problems just doing loops and solving. It should work?

If you mean, using node d as the "ground" if I were say, hooking up a multimeter or something, then how do you know that node d has 0 potential?

It's zero because you say it is It's a point of reference, as you say, as if you were to connect the negative lead of your multimeter to it. The same thing is done when you choose a reference node for nodal analysis. The circuit as a whole has no absolute potential reference to anything external, so you're free to assign your own "zero" reference point.

EDIT: Note that your choice of loops did not include the 3 Ω resistor in any path. That's why the system of equations you wrote would not yield a consistent result. Your equations must cover every component.

 

[QuarkCharmer]

I didn't know that you had to hit every component, but that makes sense since most/all of the variables are dependent on the others. To be clear, I need to make sure I cover all the components in my system, but that does not mean I need to do all possible loops right?
(I got the right solution now, knowing that information, thanks!)

 

[gneill]

I didn't know that you had to hit every component, but that makes sense since most/all of the variables are dependent on the others. To be clear, I need to make sure I cover all the components in my system, but that does not mean I need to do all possible loops right?

Correct.

 

[QuarkCharmer]

Got it, thanks Gneill.