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## Homework Statement

Sorry for edit, accidentally posted.

Circuit is show in my attachment. I have 3 loops with three unknown currents.

8 Ohms of resistance down the left side.

6 Ohms of resistance and a 4V battery down the center.

4 Ohms of resistance and a 12V battery down the right side.

I honestly have no idea if I'm even approaching this correctly.

## Homework Equations

Kirchhoff's Rules

## The Attempt at a Solution

See attachment:

Loop A (Big Loop)

-8I1 +12V +4I1 +4I3 = 0

-4I1 +4I3 = -12V

Loop B (Left)

-8I1 +4V -6I1 +6I2 = 0

-14I1 + 6I2 = -4V

Loop C (Right)

-6I3 - 6I2 - 4V + 12V - 4I3 = 0

-10I3 - 6I2 = -8V

combine in a matrix

I1 I2 I3 V

a -4 0 -4 -12

b -14 6 0 -4

c 0 -6 -10 8

rref()

I1 = 1.083

I2 = 1.861

I3 = -1.917

Im not entirely sure, but I think these are voltages for the loops, so from there I would set

V= IR for each of the loops to find the current, but this produces the wrong answer. This is the easiest circuit in my textbook, and I have been searching the web for problems which is only making matters worse I think.

Any help would be greatly appreciated.

#### Attachments

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