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 v c (t), v R (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 v c (t), v R (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. v c (t) versus t
b. v R (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
v t
V
v t
V V e
t
C
C
C
t
( )
( )
( )
ϩ
ϭ
ϭ
Ն
0
0
0
0
and
for
Ϫ
Ϫ ր
CRC_47760_CH002.indd 183
CRC_47760_CH002.indd 183
7/23/2008 1:38:56 PM
7/23/2008 1:38:56 PM