PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 437

Is = [2/s+2;8*s/(s^2-9)+1/s];

Vs =inv(Ys)*Is;

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

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

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

disp(‘The node voltages V1(s) and V2(s) are: ‘)

disp(‘V1(s)=’),pretty(Vs(1))

disp(‘V2(s)=’),pretty(Vs(2))

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

disp(‘The initial value voltages V1(t=0) and V2(t=0) (in volts)’)

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

V1 _ 0 = limit(s*Vs(1),s,inf)

V2 _ 0 = limit(s*Vs(2),s,inf)

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

disp(‘The final value voltages V1(t=inf) and V2(t=inf) (in volts)’)

i 1 (t) = 5 A

i 2 (t) = 8 cos(3t) A

R 1 = 3 Ω

R 2 = 4 Ω

R 3 = 9 Ω

C1 = 0.5 F

L1 = 3 h

sw closes at t = 0

L2 = 5 H

v 1 (t)

v 1 (t)

v 2 (t)

+

VC1(0) = 4 V

−

IL1(0) = 3 A

IL2(0) = 2 A

FIGURE 4.81

Circuit diagram of Example 12.20.

I 1 (s) = 5/s

I 2 (s) =

R 1 = 3

ZC1(S ) = 2/s

R2 = 4

ZL1(s) = 3 s

sw Closes at t = 0

ZL2(S) = 5s R3 = 9

V 1 (s) V 2 (s)

2 A

3/s

2/s

s^2 +9

8s

FIGURE 4.82

Equivalent s-domain circuit of Figure 4.81.