PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

440 Practical MATLAB® Applications for Engineers

4. Use MATLAB and obtain expressions for I 1 (s) and I 2 (s)


5. Use MATLAB to evaluate the initial- and fi nal value of each loop current by apply-
   ing the initial and fi nal value theorems


6. Use MATLAB to obtain solutions for i 1 (t) and i 2 (t), for t ≥ 0


7. Use MATLAB to obtain plots of i 1 (t) versus t and i 2 (t) versus t, for t ≥ 0


8. Discuss the results obtained
   The MATLAB solution is given as follows by the script fi le loop_diffeqs:

ANALYTICAL Solution

Part 1

The loop equations in the time domain for t ≥ 0 are

100 20 10

010 20

1

12

12

2

ut

di t

dt

it it

it it

di t

d

()

()

() ()

() ()

()









tt

Part 2

The loop equations in the frequency domain are

100

20 10

010 20

12

12

s

sIsIs

Is s Is





( ) () ()

() ( ) ()





Part 3

The matrix loop equation of the network in the frequency domain is given by

100

0

20 10

10 20

1

2





ss

s

Is

Is



































 





()

()

V 1 = 100 V

R1 = 10 Ω L1 = 1 H

i 1 (t)

i 2 (t)

sw closes at t = 0

L2 = 1 H

R2 = 10 Ω R3 = 10 Ω

FIGURE 4.85
Circuit diagram of Example 4.21.