Solving for I2 in a Circuit: What Am I Doing Wrong?

[radji]

Homework Statement

I am attempting to solve the circuit for three currents (I1, I2, I3). I am starting with I1 in terms of I2, then using a third equation to solve for I2 in terms of E and R. I wrote my loops at the bottom of the page. I am using Loop 1 @ B, Loop 2 @ B, and Junction at B to solve for I2.

Homework Equations

ΣIin=ΣIout
∫dv=0

The Attempt at a Solution

Page 2 has all my algebra to solve for I2 first. I reversed the sign of Loop 3 at B, but I don't think that is what is throwing off my answer. I have a measured I2 value to compare against and my answer is nowhere near it. Not sure what I am doing wrong.

 

[NFuller]

The first issue is that A is not a junction. Also the system looks over determined. There are only two loops so you only need two currents.

 

[radji]

Thank you for your reply. This is a lab experiment so I have to follow (i.e. use) the circuit diagram I am given. You are absolutely right, I need only the two loops and one junction at B to solve for the 3 currents. I am more looking to see if my loop equations are setup correctly. Then I can move on to what I did wrong in my calculations.

 

[NFuller]

Okay, in that case the nodes A and C are incorrect.

 

[radji]

Thank you for your observation. I was able to correct the nodes and solve for each unknown current. Even found out how to solve using only one node!