I want to write a function that calculate the voltage for three junctions A,B and C in the picture below if we know the voltage of V. (G=0V). Did anyone write it before?

[DGM]

Express the currents entering and leaving those three nodes as functions of the node voltages V,Va,Vb,Vc. Expand and rearrange to form a simple linear system of equations. Solve.

Answer 1

[Milad Mehrnia]

function ans = voltage(V,R)
E1 = [R(2)*R(7)+R(1)*R(2)+R(1)*R(7) -R(1)*R(2) 0]
E2 = [-R(3)*R(8)*R(4) R(4)*R(8)*R(7)+R(3)*R(8)*R(4)+R(3)*R(7)*R(4)+R(3)*R(7)*R(8) -R(3)*R(7)*R(4)];
E3 = [0 -R(5)*R(6) R(8)*R(6)+R(5)*R(6)+R(5)*R(8)];
E = [E1;E2;E3];
b = V.*[R(2)*R(7);R(4)*R(8)*R(7);R(8)*R(6)];
ans = E\b;
end

[Milad Mehrnia]

I wrote this code about a week ago for one of my assignments. It works, but you can write it, using permutaions and combinations only in this specific problem.

[DGM]

Disregarding the requirement to implement as a function, this is equivalent but perhaps a bit more compact. Sometimes it's neater to use one or the other method.

% some inputs
V = 10;
R = [1 1 1 1 1 1 1 1];

% coefficient terms
A = [-(1/R(1) + 1/R(2) + 1/R(7)) 1/R(7) 0; ...
    1/R(7) -(1/R(3) + 1/R(4) + 1/R(7) + 1/R(8)) 1/R(8); ...
    0 1/R(8) -(1/R(5) + 1/R(6) + 1/R(8))];
% constant terms
b = -[V/R(1); V/R(3); V/R(5)];

Vx = A\b % node voltages

The terms are derived from the expressions of presumed node currents.

Then factored as necessary. Both are equivalent and will give a numeric solution for numeric inputs.

If it's desired to find a fully symbolic solution instead:

syms V Va Vb Vc R1 R2 R3 R4 R5 R6 R7 R8

% these are implicitly treated as equal to zero.
IA = (V-Va)/R1 - Va/R2 - (Va-Vb)/R7;
IB = (V-Vb)/R3 - Vb/R4 - (Vb-Vc)/R8 + (Va-Vb)/R7;
IC = (V-Vc)/R5 - Vc/R6 + (Vb-Vc)/R8;

S = solve([IA,IB,IC],[Va Vb Vc]); % solve

% show the solutions
S.Va
S.Vb
S.Vc

[Benjamin Asakov]

Thank you both guys. I really don’t know how to appreciate it.

Didn’t expect to have the answer less than a day. And not just one but three answers.

Really thank you

[Marko]

حل هزا السؤال