I need to solve a system of equations, without the syms command.

%I have a system of equations based off of Kirchoff law (e1-e6) that are
%all simultaneously true. The code works to solve for i4 which is the
%answer needed, but I have to do it without the syms command.
syms i1 i2 i3 i4 i5 i6
e1=v-R2*i2-R4*i4==0; %given equations 1-6
e2=-R2*i2+R1*i1+R3*i3==0;
e3=-R4*i4-R3*i3+R5*i5==0; 
e4=i6==i1+i2;
e5=i2+i3==i4;
e6=i1==i3+i5;
eqns=[e1,e2,e3,e4,e5,e6];
vars=[i1 i2 i3 i4 i5 i6];
[A,b] = equationsToMatrix(eqns,vars);
X=double(A\b);
i4=X(4)
%How do I change this code so I can do it without the syms command?

Answer 1

[Cris LaPierre]

Set up your system of linear equations and solve using left divide.

[Petch Anuwutthinawin]

How would that look?

What variables would I use? Because they are in terms of i and R, do i have to use V instead?

[Cris LaPierre]

You are still solving Ax=b. You just need to create A and b yourself rather than using equationsToMatrix. There is no special function for this. Write them out manually. Each column of A corresponds to a current , and each row of A corresponds to a kirchoff loop. X is your currents. b is your voltages.

Roughly speaking, somethign like this

[Petch Anuwutthinawin]

%Is something like this correct? It says I have the wrong values for the
%fourth i value.
T= [0 R2 0 R4 0
    R1 -R2 R3 0 0
    0 0 -R3 -R4 R5
    R1 R2 0 0 -R5 
    0 R2 R3 -R4 0
    -R1 0 R3 0 R5]
V=[v v v v v v]';
i=T\V;
i4=i(4,:)

[Cris LaPierre]

What happens when you run it? I get an error because none of your variables are defined. I also couldn't say if it is correct because I don't know what your circuit looks like.

[Petch Anuwutthinawin]

That is the circuit.

R1 = 1;

R2 = 4;

R3 = 5;

R4 = 1;

R5 = 5;

v = 100; %->should give i4 = 27.638

%Ax=b -> R(i)=v

T= [0 R2 0 R4 0

R1 -R2 R3 0 0

0 0 -R3 -R4 R5

R1 R2 0 0 -R5

0 R2 R3 -R4 0

-R1 0 R3 0 R5]

V=[v v v v v v]';

i=T\V;

i4=i(4,:)

[Cris LaPierre]

Ok, so you have 3 loops, so you need to create 3 equations.

[Petch Anuwutthinawin]

But the six equations are all simultaneously true, how do I end up with just 3? Do I have to put all equations in terms of R only?

[Cris LaPierre]

Sorry, I was thinking of using current loops. You can use nodes, too. You already have your equations. Just write them in matrix form. x contains the currents (i1-i6), A contains the value to multiply current by, and b contains the resulting value. Just keep track of how you multiply matrices (march across the row of A, and down the columns of x).

For example, you have the equation v-R2*i2-R4*i4==0. I'd rearrange this to be R2*i2+R4*i4=v. In matrix form, this is

To add one of your current equations, use 1s and 0s to create the math. For example, to add this equation: i6=i1+i2 to the matrix, I would rearrange it to be i1+i2-i6=0. In matrix form, that looks like this:

You have 6 unknowns, so you need six equations. Convert your remaining equations to matrix form, and then solve using left division.