# Homework Help: Multi-loop circuit (kirchoffs laws)

1. Jan 29, 2008

### flux110

1. The problem statement, all variables and given/known data

The circuit is attached, i want to know what I4 is ( Answer 15mA ). Been working on this problem for 3h and i always end up when i try to multiply the invert matrix "A" with the matrix "B" then my calculator says "It´s not invertable"..

2. Relevant equations

Kirchoffs Laws

3. The attempt at a solution

junction equations = 2
loop equations = 4

1: I1+I2-I3=0
2: I1+I6-I5=0
a: R*I3-R*I4=6
b: -R*I1-R*I3=-12
c: R*I4+R*I6=6
d: R*I3+R*I6=12

Matrix A:

6x6
1 1 -1 0 0 0
1 0 0 0 -1 1
0 0 100 -100 0 0
-100 0 -100 0 0 0
0 0 0 -100 0 -100
0 0 100 0 0 100

Matrix B:

6x1

0
0
6
-12
6
12

#### Attached Files:

• ###### circuit.JPG
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2. Jan 29, 2008

### pam

It's easier to do with three loops. This gives 3 eqs in 3 unks.
Call the loop currents A,B,C. Then the loop equations are
12-100A-100(A-B)=0
-6-100(B-C)-100(B-A)=0
-6-100(C-B)-100C=0