PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Direct Current and Transient Analysis 183

Example 2.25

The switch of the circuit diagram shown in Figure 2.85 is open for t < 0, and it closes at

t = 0 where it remains indefi nitely. Obtain

1. Analytical expressions for vc(t), vR(t), and i(t) assuming that ic(0) = 0 A, for t ≥ 0.


2. Create the script fi le RC that returns the MATLAB symbolic solutions for vc(t), vR(t),
   and i(t) by solving the corresponding loop differential equation for each of the
   following cases: R = 1, 2, and 5 Ω.


3. The plots of
   a. vc(t) versus t
   b. vR(t) versus t
   c. i(t) versus t

FIGURE 2.84

Transient voltage plots across R of Example 2.24.

0 0.5 1 1.5 2 2.5 3

0

1

2

3

4

5

6

7

8

9

10

11

time t/sec

Voltages across R for, R = 1, 2, and 5

voltage

R = 5 ohms

R = 2 ohms

R = 1 ohm

FIGURE 2.85

Network of Example 2.25.

V 0 = 10 V R

Switch closes at t = 0 C = 0.5 F

ANALYTICAL Solution

The loop differential equation and its solution are given as follows:

RC

dv t

dt

C vt VCCvt V Vet t

()


() 00 and ()
 0  for  0