Question relating to Kirchhoff's law

[johnknee]

Homework Statement

Determine the magnitudes of the currents through R1 and R2 in (Figure 1) , assuming that each battery has an internal resistance r = 1.2 Ω .
Express your answers using two significant figures separated by commas.

Homework Equations

Junction rule: I3 = I1 + I2 (any current going into one junction must come out with the same amount)
loop rule: The sum of all the potential differences around a complete loop is equal to zero.

The Attempt at a Solution

Please refer to the image I attached.
First I set up the directions for current flow. I got the equations:

I3 = I1 + I2.
For the top loop, I got -18*I2 - 22*I1 +9V = 0.

For the bottom loop, I got 6V + 18*I2 = 0. I isolated I2 to get -6/18 = -0.33333.

Then I plugged in I2(-0.33333) into the top loop's equation to isolate I1. I got I1 = 0.6818.

However, the masteringphysics keeps telling me it's wrong. Can anyone help me with this?

*I've randomly tried changing up the signs of the two numbers, which didn't work so I don't know where I went wrong.

 

[phinds]

So where are I1, I2, and I3, and in what direction? I'd suggest dropping I3 as you only need 2 (and you don't use it anyway)

 

[johnknee]

So where are I1, I2, and I3, and in what direction? I'd suggest dropping I3 as you only need 2 (and you don't use it anyway)

Yes haha I dropped the first equation basically since I3 wasnt needed. I1 i drew to point towards the left from the top loop. As for I2, I drew it pointing towards the right on the middle segment. I3 I drew it point towards the right from the battery on the bottom loop.

 

[phinds]

So how did you work the magic of making I1 not flow through the middle resistor?

 

[johnknee]

So how did you work the magic of making I1 not flow through the middle resistor?

Sorry, not too sure what you mean. I included 18*I2 for the first loop. Is that not the current going through resistor in the middle?

 

[phinds]

Sorry, not too sure what you mean. I included 18*I2 for the first loop. Is that not the current going through resistor in the middle?

Draw a full loop current in each loop. Where do you think I1 goes when it hits the node? Does it just evaporate?

 

[gneill]

The problem asks for the current magnitudes. Magnitudes are never negative.