I'm reading along on the ebook http://www.allaboutcircuits.com/vol_1/chpt_10/2.html I get about 80% down the page to where it says "solutions:" and I feel like I've missed something. went back and read it again, but still missing something. How did we arrive at those numbers? "multiple unknowns" - what kind of math is that? what can I google that will show me how to solve this? I vaguely remember doing problems like this in school but that was a long time ago. I don't even know what this type of math is called.
All they are doing is solving a system of linear equations. If you google this, you should find lots of material. Often people tend to use matrices to solve these systems of linear equations.
The solutions refer to the 3-variable linear system that is written right above them. There are several ways to solve a linear system. The most basic way is to do some substitutions among the variables, eg: From the 3rd equation find an expression for I2=f1(I3). Take that expression and substitute it in the 1st equation. Now you can derive an expression for I1=f2(I3). Use f1 and f2 in the 2nd equation to have an equation with only I3 and constants. Calculate I3 and trace your steps back to find the other two currents. You can also use linear algebra methods and computer aids. http://www.wolframalpha.com/input/?i=-x1%2Bx2-x3%3D0%2C+4*x1%2B2*x2%2B0*x3%3D28%2C+0*x1-2*x2-x3%3D-7 or http://www.wolframalpha.com/input/?i={{-1%2C1%2C-1}%2C{4%2C2%2C0}%2C{0%2C-2%2C-1}}^%28-1%29*{{0}%2C{28}%2C{-7}}
Woo hoo! small fries for you guys, but a big accomplishment for me! I slept through all my classes. I can still do algebra! after a little refresher you guys pointed me in the direction, and about 4 or 5 tries, I got it figured out. I'm so proud of myself that I decided to post my work:
Learn the matrix method, it blows substitution away in terms of speed and simpleness. Seriously. Don't let the word "matrix" scare you.
I remember running across that in Calculas I, problem is I forgot everything I ever knew about matrix math. I vaugly remember laying out the tables, but that was no help what so ever.
I like the matrix method to solve linear equation for more than 2 variables...Even I wrote a software to do it using Gaussian elimination algorithm... http://en.wikipedia.org/wiki/Gaussian_elimination Good Luck
I have also been taught Crammer's rule in uni, and I have promptly forgotten it, after I passed the course.
There are at least 3 different matrix methods you can use: augmented matrices (the simplist in my opinion), inverse matrices (Cramer's Rule), or matrix equations (coefficient matrix times variable matrix = constant matrix). Graphing calculators have sure taken the horror out of matrix manipulations!
Ok, I should have said "Learn A matrix method", I use Cramer's most, because I have used it since high school.
When I do augmented matrices (say solving for 3 variables in 3 equations) just put it in as a 3 x 4 matrix and then hit the "rref" button under matrix=>math. It's practically magic! It's a really easy way to see no solutions (bottom row zeros except last element) and dependent equations (bottom row all zeros). Sure beats doing it by hand. By the way, back in high school we didn't have graphing calculators or scientific ones either!! (Just a few dinosaurs still roaming around.)