Direct Current Circuits and Kirchoff's rules

[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 I've drawn my diagram and I've 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).

 

[M98Ranger]

It seems like you have set up the equations correctly, but there may be a sign error in one of your substitutions. Here are some steps you can take to double check your work:

1. Make sure you are using the correct signs for each component in your equations. For example, if a current is flowing in the opposite direction of your chosen direction, the sign should be negative.

2. Check your substitution for equation #2. It should be: 8 = -2.0I1 - I3. You have written 8 = -2.0I1 - (I1 + I2). This may be where the sign error is occurring.

3. When substituting for I2 in equation #2, you should get: 8 = -2.0I1 - (-I1 - 6). Notice the negative sign before -I1. This should give you the correct answer of +3.5 for I1.

4. Double check your calculations for I2 and I3 using the values you found for I1. If you are still getting a negative answer, there may be an error in your calculations.

5. If you are still having trouble, try using a different method to solve the problem, such as using a matrix or using nodal analysis.

Overall, it's important to be careful with signs and double check your work when solving circuit problems using Kirchoff's rules. It can also be helpful to draw the circuit diagram with the direction of current flow clearly marked to avoid any confusion. Good luck!