Why Are My Kirchhoff Voltage Rule Equations Incorrect?

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AI Thread Summary
The Kirchhoff Voltage Rule equations presented for the circuit analysis are incorrect due to miscalculations in current summation. The equations include terms like I1(8) and I2(5), which may not accurately represent the current distribution at junctions. It is essential to ensure that charge conservation is maintained, meaning the net current at any junction should equal zero. The user’s initial values of I1 = 1, I2 = 2, and I3 = 0.2 are incorrect based on these principles. Properly analyzing the circuit requires careful consideration of how current splits at junctions.
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Homework Statement
Just for practice, not for any assignment
Relevant Equations
Kirchhoff Voltage Rule, Sum of Voltage Drops in Loop is Equal to Zero.
I tried doing three loops. For the bottom I did 9-I1(1) + I2(1) - I3(10) -12 = 0, for the upper left corner I did 12 - I2(1)- I2(5) = 0, for the upper right corner I did 9 - I1(1) - I1(8) = 0. I came to I1 =1, I2 =2 and I3 = .2. This was incorrect, I don't think I am summing the currents correctly. I have attached an image of the problem.
 

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Why do you have a term I1(8)? I1 is the current through the 1.00 Ω resistor. Is all that current also going through the 8.00 Ω resistor or does some of it split at the junction on the right? Same problem with the I2(5) term. To solve such circuits you need to make sure that charge is also conserved. This means that the net current through any junction must be zero.
 

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