PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 441

where

Zs

s

s

()





20 10

10 20

















and

Vs

s

()

100

0

 











MATLAB Solution

% Script file: loop _ diffeqs

syms s Zs Is Vs

Zs = [s+20 -10;-10 s+20];

Vs = [100/s;0];

Is = inv(Zs)*Vs;

disp(‘*********************************************’)

disp(‘********* Matlab Symbolic Results **********’)

disp(‘*********************************************’)

disp(‘The loop currents I1(s) and I2(s) are: ‘)

disp(‘I1(s)=’),pretty(Is(1))

disp(‘I2(s)=’),pretty(Is(2))

disp(‘*********************************************’)

i1 _ t = ilaplace(Is(1));

i2 _ t = ilaplace(Is(2));

disp(‘The loop currents i1(t) and i2(t)(in amp) are: ’)

disp(‘i1(t)=’),

simplify(i1 _ t)

disp(‘i2(t)=’),

simplify(i2 _ t)

disp(‘**********************************************’)

disp(‘The initial currents:i1(t=0) and i2(t=0)(in amps)’)

disp(‘using the initial value theorem are evaluated below’)

I1 _ 0 = limit(s*Is(1),s,inf)

I2 _ 0 = limit(s*Is(2),s,inf)

disp(‘**********************************************’)

disp(‘The final currents:i1(t=inf) and i2(t=inf)(in amps)’)

disp(‘using the initial value theorem are:’)

I1 _ inf = limit(s*Is(1),s,0)

I2 _ inf = limit(s*Is(2),s,0)

disp(‘**********************************************’)

figure(1)

subplot(1,2,1)

ezplot(i1 _ t);axis([0 .5 0 7])

title(‘i1(t) vs t’),xlabel(‘time (sec)’)

ylabel(‘i1(t) in amp’)

subplot(1,2,2)

ezplot(i2 _ t);axis([0 .5 0 3.5])

title(‘i2(t) vs t’)

xlabel(‘ time (sec) ‘)

ylabel(‘i2(t) in amp ‘)

The script fi le loop_diffeqs is executed and the results are as follows: