Find Ix, Iy, and Iz in the network

Find I_x, I_y, and I_z in the network.

Image from: Irwin, J. David., and R. M. Nelms. Basic Engineering Circuit Analysis, Tenth Edition. N.p.: John Wiley & Sons, 2010.

Solution:

We will write Kirchhoff’s current law for each of the nodes that we picked (picked arbitrarily, pick ones that are the easiest to write equations for). (Forgot Kirchhoff’s current law?)

Node A:

12mA=3mA+I_x

I_x=9mA

Node B:

I_z+4mA=2mA

I_z=-2mA

Node C:

12mA+I_y+I_2=0

I_y=2mA-12mA

I_y=-10mA

The negative values tells us that the way we represented current leaving or entering a node is the opposite of what we chose.

This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 2, question 2.18.