SOLUTION: In applying kirchhoff's laws to the circuit shown to the right, the following equations are found.? iA+iB+iC=0 7iA-5iB =2 5iB-3iC=-1 iA=?,iB=?,iC=? type integers or a frac

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Question 729677: In applying kirchhoff's laws to the circuit shown to the right, the following equations are found.?
iA+iB+iC=0
7iA-5iB =2
5iB-3iC=-1
iA=?,iB=?,iC=?
type integers or a fractions.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
iA%2BiB%2BiC=0......1
7iA-5iB+=2.......2
5iB-3iC=-1.......3
iA=?,iB=?,iC=?

I am going to find A,B, C

start with iA%2BiB%2BiC=0......1...solve for A
A=%28-iB-iC%29%2Fi
A=%28-cross%28i%29B-cross%28i%29C%29%2Fcross%28i%29%0D%0A%0D%0A%7B%7B%7Bhiglight%28A=-B-C%29......plug it in 2

7i%28-B-C%29-5iB+=2.......2
-7iB-7iC-5iB+=2
-12B-7C=2....both side multiply by -1
12B%2B7C=-2....solve for C
7C+=-2-12iB
highlight%28C+=%28-2-12iB%29%2F7%29........plug in 3

5iB-3iC=-1.......3
5iB-3i%28-2-12iB%29%2F7=-1.......solve for B
5iB-%28-6i-12%2A3i%2AiB%29%2F7=-1%0D%0A%0D%0A%7B%7B%7B5iB-%28-6i%2B-36i%5E2B%29%2F7=-1
5iB-%28-6i-36%28-1%29B%29%2F7=-1
5iB-%28-6i%2B36B%29%2F7=-1.......both sides multiply by 7
35iB-%28-6i%2B36B%29=-7
35iB%2B6i-36B=-7
B%2835i-36%29=-7%2B6i
highlight%28B=%28-7%2B6i%29%2F%2835i-36%29%29.........now find C

C+=%282%2B12iB%29%2F7

C+=%282%2B12i%28-7%2B6i%29%2F%2835i-36%29%29%2F7

C+=%282%2B%28-7%2A12i%2B6i%2A12i%29%2F%2835i-36%29%29%2F7

C+=%282%2835i-36%29%2B%28-84i%2B72i%5E2%29%29%2F%2835i-36%29%29%2F7

C+=%2870i-72-84i-72%29%2F%2835i-36%29%29%2F7

highlight%28C+=%28-14i-144%29%2F7%2835i-36%29%29%29

and now find A
A=%28-B-C%29
A=%28-%28-7%2B6i%29%2F%2835i-36%29%29-%28%28-14i-144%29%2F7%2835i-36%29%29%29

A=%287-6i%29%2F%2835i-36%29%2B%2814i%2B144%29%2F7%2835i-36%29

A=%287%287-6i%29%2B14i%2B144%29%2F7%2835i-36%29

A=%2849-42i%2B14i%2B144%29%2F7%2835i-36%29

highlight%28A=%28-28i%2B193%29%2F7%2835i-36%29%29

since you need iA,iB,iC, your solutions are:
iA=i%28-28i%2B193%29%2F%287%2835i-36%29%29
iB=i%28-7%2B6i%29%2F%2835i-36%29 and
iC=i%28-14i-144%29%2F%287%2835i-36%29%29


check:
iA%2BiB%2BiC=0......1
......1




%2828%2B193i%2B7%28-7i-6%29%2B14-144i%29%2F%287%2835i-36%29%29=0

%2828%2B193i-49i-42%2B14-144i%29=0%2A%287%2835i-36%29%29

28%2B193i-28-193i=0

28-28%2B193i-193i=0

0=0