Kirchoff's Rule - circuit with 3 batteries

[brazen2]

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!

 

[brazen2]

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

 

[baba89]

I can see that you have correctly applied Kirchoff's rules to solve for the current through the 22 ohm resistor. However, it seems like there may be a mistake in your calculations for the voltage drops across the different portions of the circuit.

To double check your work, you can use Ohm's Law (V=IR) to calculate the voltage drops across each resistor using the currents you have found. The total voltage drop across each loop should be equal to the voltage of the battery in that loop.

If you are still having trouble, it may be helpful to redraw the circuit and label all the currents and voltage drops to make sure everything is accounted for. Sometimes a fresh perspective can help identify any mistakes.

Overall, it seems like you have a good understanding of Kirchoff's rules and how to apply them to solve circuit problems. Keep practicing and double checking your work, and you will continue to improve your skills in circuit analysis.