clc;





% Example Cramer's rule
% application of Kirchhoff's laws

U1=5;
U2=20;
R1=20;
R2=20;
R3=40;


display('Application of Kirchhoff''s laws')
% matrix of the SLAE
A=[1 1 -1;
   R1 0 R3;
   0 R2 R3]
% vector of right-hand side
b = [0; U1; U2]

% solution using Gauss elimination method and inverse matrix, respectively
I= A\b
I=inv(A)*b

% solution of SLAE using Cramer's rule
Ds=det(A) % check our solution of determinant
Ds=-R1*R2-R2*R3-R3*R1 % Sarrus rule

DI1=R3*U2-U1*R2-R3*U1
DI2=U1*R3-R1*U2-U2*R3
DI3=-R2*U1-U2*R1

I1=DI1/Ds
I2=DI2/Ds
I3=DI3/Ds

% check the results (MATLAB solution - our solution)
I-[I1;I2;I3]



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Loop current method 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% (R1+R3)*Ia + R3*Ib = U1
% R3*Ia + (R2+R3)*Ib = U2
display('Loop current method')
A=[R1+R3, R3;
   R3,  R2+R3];
b=[U1;U2];
IaIb=A\b;

IR1=IaIb(1)
IR2=IaIb(2)
IR3=sum(IaIb)

UR1=R1*IR1
UR2=R2*IR2
UR3=R3*IR3

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Node voltage method
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
display('Node voltage method')
Ua=(R1*R3*U1+R1*R3*U2)/(R2*R3+R1*R3+R1*R2);

IR1=(U1-Ua)/R1
IR2=(U2-Ua)/R2
IR3=Ua/R3

UR1=U1-Ua
UR2=U2-Ua
UR3=Ua


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Thevenin's theorem
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
display('Thevenin''s theorem')
Ri=(R1*R2)/(R1+R2);

Ix=(U2-U1)/(R1+R2);
Ui=U1+R1*Ix;

IR3=Ui/(Ri+R3)
UR3=R3*IR3