% script file node_v_ex3.m
% Edited: 06/05/2005
% Matlab solution to:
%  Circuits/Node-Voltage Method/Example 3

% See accompanying handwritten page for problem setup.

% We use the Node-V method to solve this problem.
% We write a matrix equation:
% Smatrix * vvec = ivec
%  where
%   Smatrix = conductances (1/ohm) values from node-V equation
%              for node v2
%   vvec = vector of node voltages = [v2 v3 v4 v5]'
%   ivec = vector of constant currents that arise from v1 terms
%           (where v1 = 500 V) moved to right side of node
%           equations
%
% The solution of the matrix equation is
%  vvec = inv(Smatrix) * ivec, or
%  vvec = Smatrix \ ivec

% Create the Smatrix per the preceding node-V solution:
Smatrix = ...
  [ 1/4 + 1/2 + 1/3, -1/3,             -1/2,              0              ; ...
   -1/3,              1/3 + 1/2 + 1/6,  0,               -1/2            ; ...
   -1/2,              0,               1/11 + 1/2 + 1/4, -1/4            ; ...
    0,               -1/2,             -1/4,              1/4 + 1/2 + 1/4]

% Create the ivec per the preceding node-V solution:
ivec  = [500/4; 0; 500/11; 0]

% Solve the matrix equation:
vvec = Smatrix \ ivec
vvec = inv(Smatrix) * ivec