Kirchoff's Rule - circuit with 3 batteries

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SUMMARY

The discussion focuses on applying Kirchoff's rules to analyze a circuit with three batteries and a 22-ohm resistor. The user successfully derived the currents I1, I2, and I3, calculating I1 as -0.428 A, I2 as 1.39 A, and I3 as 0.958 A. Despite these calculations, the user encountered inconsistencies when attempting to find the voltage across points A and B, indicating potential errors in voltage drop calculations across the circuit components. The problem highlights the importance of accurately applying Kirchoff's laws in circuit analysis.

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  • Familiarity with Ohm's Law
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Students studying electrical engineering, hobbyists working on circuit design, and anyone seeking to deepen their understanding of circuit analysis using Kirchoff's rules.

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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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