# Branch Current Method

Discussion in 'Homework Help' started by Bill Allman, Apr 20, 2009.

1. ### Bill Allman Thread Starter New Member

Apr 20, 2009
1
0
Doing a quick refresher on Branch current method. I'm fine until I reach the final part of the lesson and he figures the current values from these final equations.

-1I1 + 1I2 - 1I3 = 0 KCL
4I1 + 2I2 + 0I3 = 28 KVL
0I1 - 2I2 - 1I3 = -7 KVL

I1 = 5A
I2 = 4A
I3 = -1A

Could someone show the algebraic equation that shows how we get 5 amps, 4 amps, and -1 amp from these equations above.

2. ### guitarguy12387 Active Member

Apr 10, 2008
359
12
You have to simultaneously solve each equation. I usually do it by the substitution method. Solving one equation in terms of the other variables and then back substitute. Or if you have a TI-89, it can do it quick and easy.

3. ### Jack Bourne Active Member

Apr 30, 2008
39
1
I have seen some people solve it by using Matricies. I personally do not know how to do it this way so I would either use my calculator as it has a solve function on it or just use the substitution method.
So Basically, you've got these equations 4I1 + 2I2 = 28, - 2I2 - 1I3 = -7, -1I1 + 1I2 - 1I3 = 0 . These are easy to use as you can have I2 = 14-2I1 -> into second -2(14-I1) = I3-7 so -I3= 21+2I2 -> into third and it gives you the answers.

4. ### jasperthecat Member

Mar 26, 2009
20
0
Another way of solving the set of equations is to use the linear programming approach This is relatively straight forward for 3 or 4 unknowns . You aim to get 2 co-efficients as zero on one line and one coefficient as zero on another.

-1 +1 -1 = 0

+4 +2 0 = 28

0 -2 -1 = -7

Multiply equation 1 by 4

-4 +4 -4 = 0

+4 +2 0 = 28

0 -2 -1 = -7
Add equation 1 to eqn 2

0 +6 -4 = 28

+4 +2 0 = 28

0 -2 -1 = -7

Multiply eqn3 by 3

0 +6 -4 = 28

+4 +2 0 = 28

0 -6 -3 = -21

0 0 -7 = 7

+4 +2 0 = 28

0 -6 -3 = -21

From eq 1 gives I3 = -1

Substitute in eqn 3

I2 = 4

Substitute in 2
4 I1 = 20

I1 = 5

J

5. ### hgmjr Retired Moderator

Jan 28, 2005
9,029
219
Matrix algebra is another technique for solving such a system of linear equations.

hgmjr