What is the Norton equivalent current for terminals a and b in this circuit?

[gomezfx]

Homework Statement

Find the norton equivalent with respect to terminals a and b
[PLAIN]http://img821.imageshack.us/img821/7177/nortonequivalent.jpg

Homework Equations

KVL, KCL

The Attempt at a Solution

I set i1 = .008 A
Then I found the rest of the currents.

KVL@ loop i2:
2000(i2-i1)+30=0
i2 = .0065 A

KVL@ loop i3:
-30+15000i3=0
i3=.002 A

KCL@ node D
i3-i4-.010=0
(.002)-i4-.010=0
i4= -.008 A

KVL@ loop iab:
30000(iab-i4)=0
iab= -.008A

I got the same current for i4 and iab, unless I did my math wrong.
Can someone check my equations and set up to make sure I'm even finding the right current for the norton equivalent circuit?

EDIT. I redid i4 by doing (i4-i3)=.010 A
I got i4 = .012 A so I'm not sure which current to o use.

 

[vela]

There's nothing wrong with having i_ab = i₄. The current will choose the path of least resistance, so if you short a and b, all the current flows through the short. Equivalently, you can think of it this way. If you short a and b, the voltage across the 30k-ohm resistor will be 0, so no current flows through it. Applying KCL to E then gives you that i_ab = i₄.

Your initial attempt to find i4 is correct. In the second try, you introduced a sign error. At node D, i₃ enters and i₄ and 10 mA exit, so you have i₃ = i₄ + 0.010 A.

I didn't check everything in the rest of the problem, but I'll note that given how you drew the direction of i₁, you should have used i₁=-0.008 A.

 

[gomezfx]

How come I can just assume that the 30k ohm resistor will be 0 when I short a and b. My professor made did this same thing in class with another problem and a lot of things I've been reading do the same.

I'll redo the problem with the -0.008 A as well.

 

[vela]

How come I can just assume that the 30k ohm resistor will be 0 when I short a and b.

It doesn't make sense when you say the "resistor will be 0." What is that supposed to mean?

 

[gomezfx]

It doesn't make sense when you say the "resistor will be 0." What is that supposed to mean?

Sorry, I meant to say that the voltage across the resistor will be 0.

 

[vela]

Oh, OK. When you short a and b, the two ends of the resistor are connected to the same node in the circuit, so the voltage across the resistor must be 0.