how do i find the interception of these two fuctions i1 and i2

% hemuppgift 3
a = 0.5;
ih = 10.^-7;
iz = 10.^-5;
F = 96485;
R = 8.134;
T = 298.15;
h= 0.0001;
x = -1:h:1;
z1 = -1.87:h:0.13;
z2 = -2.32:h:-0.32;
% 
% E1 = @(z) (x - 0.87);
% E2 = @(z) (x - 1.37);
i1 =  @(x) (ih*(exp((a*F*x)/(R*T)) - exp((-a*F*x)/(R*T))));
i2 =  @(x)  (iz*(exp((a*F*x)/(R*T)) - exp((-a*F*x)/(R*T))));
logh = log10(i1(x));
logz =log10(i2(x));
plot(logh,z1, 'b')
hold on
plot(logz,z2, 'r')

Answer 1

[Star Strider]

This was a challenge!

I tried this a couple times before I had an appropriate insight to calculating the intersection. (I made a few minor changes in the code, specifically changing ‘logh’ and ‘logz’ to anonymous functions for clarity, however other than my additions to it that are required in order to calculate the intersection, and that are all commente-documented, it is otherwise unchanged.)

There is only one real intersection, that being (-4.06,-1.21).

% hemuppgift 3
a = 0.5;
ih = 10.^-7;
iz = 10.^-5;
F = 96485;
R = 8.134;
T = 298.15;
h= 0.0001;
x = -1:h:1;
z1 = -1.87:h:0.13;
z2 = -2.32:h:-0.32;
% 
% E1 = @(z) (x - 0.87);
% E2 = @(z) (x - 1.37);
i1 =  @(x) (ih*(exp((a*F*x)/(R*T)) - exp((-a*F*x)/(R*T))));
i2 =  @(x)  (iz*(exp((a*F*x)/(R*T)) - exp((-a*F*x)/(R*T))));
logh = @(x)log10(i1(x));
logz = @(x)log10(i2(x));

common_z = linspace(min([z1,z2],[],2), max([z1,z2],[],2), 1E+3);        % Common 'z' Vector (Created From 'z1' & 'z2')
common_logh = interp1(z1, real(logh(x)), common_z);                     % 'logh' Interpolated To 'common_z'
common_logz = interp1(z2, real(logz(x)), common_z);                     % 'logz' Interpolated To 'common_z'
common_dif = common_logh - common_logz;                                 % Difference
Lidx = ~isnan(common_dif);                                              % Remove 'NaN' Values
z_intx = interp1(common_dif(Lidx), common_z(Lidx), 0)                   % Calculate 'z' Intersection

z_intx = -1.2104

logh_intx = interp1(z1, logh(x), z_intx)                                % Calculate 'logh' Intersection (Can Also Use 'logz')

logh_intx = -4.0590 + 1.3644i

figure
plot(real(logh(x)),z1, 'b')
hold on
plot(real(logz(x)),z2, 'r')
yline(z_intx, '-g')
xline(real(logh_intx), '-g')
legend('logh', 'logz', 'Intersection Lines', 'Location','best')

figure
plot(x, real(logh(x)), 'b')
hold on
plot(x, imag(logh(x)), ':b')
plot(x, real(logz(x)), 'r')
plot(x, imag(logz(x)), '--r')
grid
title('Plotted As Funcitons Of ‘x’')

Experiment to get different results.

.

[Alexander Singh]

thank you this helped alot

[Star Strider]

As always, my pleasure!

.