Direct Current Circuits

[biglake]

Im having a bit of trouble with some problems using Kirchoff's rules.

The problem states for me to calculate each of the unknown currents: I1, I2, & I3 for the circuit diagram attached.

Now Ive drawn my diagram and ive gotten my three equations for three unknowns, but i keep getting a negative number for the final answers for I1 and I2. I3 ends up being way off.

Equations:

1. I3 = I1 + I2
2. 8 = -2.0 I1 – I3
3. 4 = I3 – 2I2
4. 6 = -I1 – I2

The equations come from the following:

1. Conservation of energy rule
2. Top loop
3. Bottom Loop
4. Outside Loop

This is the way that my professor was having us practice them in class.

Using equation #2 and substituting equation #1 into #2 I arrive at the following:

Work:

8 = -2.0I1 – I3
8 = -2.0I1 – (I1 +I2)
8 = -3.0I1 – I2

Then Solving for I2 on equation #4 I got:

I2 = -I1 – 6

Including this into the previous equation I got

8 = -3.0I1 – (-I1 – 6)
8 = -3.0I1 - I1 - 6
8 = -4.0I1 -6
14 = -4.0I1
Dividing
-3.5 = I1

The proper answer is +3.5

Ive worked the problem over and over and I can't seem to see where I got a sign mixed up. If someone could steer me in the right direction I would be very thankful.

[jamesrc]

Your first equation does not fit with the other 3 and those last 3 equations use the opposite sign convention of the figure. The main thing with sign conventions is that you stay consistent. I would write KCL looking at the node on the middle right as I1 = I2 + I3 (sum of the currents into the node equals the sum of the currents out of the node). Your 3 loop equations have the signs flipped from what I've got (I wrote out the equations according to the sign conventions given in the diagram).