Finding node voltages with KVL and KCL in a resistor network

[nothingsus]

Homework Statement

http://imgur.com/a/L82gU

[Mod note: Inserted image inline for convenience]

Homework Equations

KVL, KCL

The Attempt at a Solution

[/B]
one of my equations will be at one of the nodes and will include all 3 currents.

i can also draw two loops, one for the upper triangle and one for the bottom triangle, however the signs of the terms will depend on the directions of the current, and I don't know which way i_3 will go!So this is a question from my Physics 2 course.

I've googled online for similar problems however most of them use more advanced techniques like mesh currents which I don't think is expected in my course.

We've only learned
1. algebraic sum of voltages about a closed loop is zero
2. current in = current out at a node

So I'm trying to label which way the current splits and the directions so I can write equations with the two above facts in mind, but I'm not really sure.

current is i_0 between the positive terminal of the battery and node A.

At node A, i_0 splits into i_1 (for the branch with R_1) and i_2 (for the branch with R_2).

i_1 should be greater than i_2 since current takes the path of least resistance.

When i_1 and i_2 reach nodes B and C respectively, I'm not really sure what happens. I don't know what direction (left or right) the current i_3 (flowing through R_3) should be.

Also, since the bottom two resistors are also R_1 and R_2 (although R_1 is now on the left and R_2 is now on the right) would they have the same currents i_1 and i_2 through them? What if they were some other resistances?

 

[haruspex]

I don't know which way i_3 will go

You don't need to predict it correctly. Just assume one way and write all the equations accordingly. If you guessed wrongly you will get a negative answer.