420
Practical MATLAB
® Applications for Engineers
Example 4.15
The switch in the circuit diagram of Figure 4.67 is closed for a long time. At t = 0, the
switch is opened and remains opened for t ≥ 0. Analyze by hand the given circuit using
the LT and obtain analytical expressions for
v(t), i r (t), i c (t), i l (t) for t ≥ 0
Create the script MATLAB fi le RLC_parallel that returns the plots of the analytical
results as well as the symbolic (Laplace) plots of v(t), i r (t), i c (t), i l (t), over the range
−2 ≤ t ≤ 5, and observe that both solutions are identical.
3 A
switch opens at t = 0
R = 20 Ω
C = 1/40 F
L = 5 H
V(s)
FIGURE 4.67
Circuit diagram of Example 4.15.
ANALYTICAL Solution
The nodal equation yields
V s
V s
s
sV s
s
t
( )
( )
( )
20
5
40
3
ϩ
ϩ
ϭ
for
0
Ն
then
V s
s
s
s
V s
s
s
s
s
V s s
s
( )
( )
( )(
1
20
1
5
40
3
2
8
40
3
2
2
2
ϩ ϩ
ϭ
ϩ ϩ
ϭ
ϩ ϩ

 

 

 

 
8 8
120
)
,
( )
ϭ
solving for voltage V s
V s
s
s
s
( )
(
)
ϭ ϩ ϩ
ϭ
ϩ
ϩ
120
2
2
2
2
8
120
7
7
1
7
⋅
CRC_47760_CH004.indd 420
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7/28/2008 12:26:16 PM
7/28/2008 12:26:16 PM