Kirchoff's Rule - circuit with 3 batteries

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The discussion revolves around solving a circuit problem using Kirchhoff's rules to find the current through a 22-ohm resistor. The user has set up equations based on Kirchhoff's current and voltage laws but is struggling with inconsistencies in the voltage drops across the circuit. After calculating the currents I1, I2, and I3, the user finds that the results do not align with the expected voltage across points A and B. Despite spending considerable time on the problem, the user remains uncertain about the accuracy of their calculations. Assistance is requested to clarify these discrepancies in the circuit analysis.
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Homework Statement


Hello everyone

I need to find the current through the 22 ohm resistor. I've tried to solve this problem for many hours now... I can't find what I'm doing wrong! Please find a rough diagram attached.


Homework Equations


Kirchoffs rules


The Attempt at a Solution


I1 + I2 = I3

top loop:

-8 -22I1+12-14I3 = 0
0.286 - 1.57I1 = I3

perimeter loop:
-8 -22I1 +12 I2 -18 =0
2.17 +1.83 I1 = I2

Inputting these numbers into the first equation:
I1+I2=I3
I1 +2.17 +1.83I1 = 0.286-1.57I1
I1 = -0.428A

I then put the I1 into the loop equations and found:
I2= 1.39 A
I3= 0.958 A

However, when I'm trying to find the voltage across the points A and B, these currents do not yield consistent voltage drops across the three portions of the circuit.

I really appreciate any help!
 

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Sorry- i actually think this is correct. There goes a couple hours!
 
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