Determine I0 and I1 in the circuit

Determine I_0 and I_1 in the circuit.

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. (Forgot Kirchhoff’s current law?) We also labeled I as current leaving node A towards node B (The direction is up to you).

Node A:

4mA+2mA=I

I=6mA

Node B:

I=3mA+I_0

I_0=6mA-3mA

I_0=3mA

Node C:

I_0=I_1+5mA

I_1=-2mA

(Note the negative value means the direction given to us in the question for I_1 is opposite to the current flow in accordance with the passive sign convention.)

This question can be found in Basic Engineering Circuit Analysis, 10th edition, chapter 2, question 2.16.