Im having a bit of trouble with some problems using Kirchoff's rules.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Direct Current Circuits and Kirchoff's rules

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