% Given Data
l1 =29; % cm
l2 = 28.8; % cm
l3 = 6.9; % cm
lg1 = 1*1E-3; % m
lg2 = 2*1E-3; % m
ur = 2500; % Relative permeability
u0 = 4*pi*1E-7; % Permeability of free space
n1 = 200; % Number of turns
n2 = 500; % Number of turns (Part 2)
I1 = 30; % Current in amperes
A1 = 3*3*1E-4; % Cross-sectional area in m^2
A2 = 3*5*1E-4; % Cross-sectional area in m^2
% Reluctances
r1 = ((l1*1E-2)/(ur*u0*A1));
r2 = ((l2*1E-2)/(ur*u0*A1));
r3 = ((l3*1E-2)/(ur*u0*A2));
rg1 = (lg1/(u0*A2));
rg2 = (lg2/(u0*A1));
% KVL Equations
syms phi1 phi2 phi3
eq1 = r1*phi1 + (r3+rg1)*phi3 == n1*I1;
eq2 = (r2+rg2)*phi2 - (rg1+r3)*phi3 == 0;
% KCL Equations
eq3 = phi1 - phi2 - phi3 == 0;
% Solving the system
sol = solve([eq1, eq2, eq3], [phi1, phi2, phi3]);
phi1 = double(sol.phi1);
phi2 = double(sol.phi2);
phi3 = double(sol.phi3);
% PART(i)
B2 = phi2 / A1; % Flux density in gap two
H1 = phi3 / (A2*u0); % Magnetic field intensity in gap one
% Display Results
disp(['Flux density of gap two = ' num2str(B2) ' Tesla'])
disp(['Flux intensity of gap one = ' num2str(H1) ' AT/m'])
% PART (ii)
clear phi1 phi3 % Only clear necessary variables
clc;
phi2 = 5*1E-3; % Wb (Webers)
% Redefine variables
syms phi1 phi3 I2
% KVL Equations
eq4 = r1*phi1 + (r3+rg1)*phi3 == n1*I1;
eq5 = (rg2 + r2)*phi2 - (r3+rg1)*phi3== n2*I2 ;
% KCL Equations
eq6 = phi1 - phi2 - phi3 == 0;
% Solving Part(ii) Equations
sol = solve([eq4, eq6, eq5], [phi1, phi3, I2]);
% Convert to Numeric
phi1 = double(sol.phi1);
phi3 = double(sol.phi3);
I2 = double(sol.I2);
% Display Results
disp(['Phi1 = ' num2str(phi1) ' Wb'])
disp(['Phi3 = ' num2str(phi3) ' Wb'])
disp(['Current two = ' num2str(I2) ' Amperes'])