PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Direct Current and Transient Analysis 165

Example 2.20

The switch shown in Figure 2.64 has been at position a for a very long time. At t = 0, the

switch is moved to position b where it remains for 2 s and then moves back to position a

where it remains indefi nitely.

1. Obtain analytical expressions of i 1 (t), i 2 (t), i 3 (t), and vL(t) for all t.


2. Create the script fi le analysis_exam that returns the following:
   a. The network time constants
   b. The maximum currents I 1 , I 2 , and I 3
   c. The maximum voltage drop across L
   d. The current plots of i 1 (t) versus t, i 2 (t) versus t, and i 3 (t) versus t over the range
   0 s ≤ t ≤ 5 s
   e. The voltage plot vL(t) versus t over the range 0 s ≤ t ≤ 5 s


3. If the applied source voltage is V 0 = 100 V, can the voltage drop across L exceed
   100 V?

ANALYTICAL Solution

For t < 0, the switch has been in position a for a long time, then

i 1 (t) = i 2 (t) = i 3 (t) = 0

and

vL(t) = 0

During the interval 0 s < t < 2 s, the switch is in position b. Therefore,

it

V

R

1 et

1

()
^0 *() 1 /

eq

 ^1

it

R

RR

2 3 it

23

()
  * 1 ()

it

R

RR

3 2 it

23

()
  * 1 ()

FIGURE 2.64

Network of Example 2.20.

b

a

L = 10 H

i 1 (t)

i 3 (t) i 2 (t)

VL(t)

R 1 = 8 Ω

R 4 = 18 Ω R 3 = 3 Ω R 2 = 6 Ω

V 0 = 100 V

+

−