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), ir(t), ic(t), il(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), ir(t), ic(t), il(t), over the range
− 2 ≤ t ≤ 5, and observe that both solutions are identical.
3 A
switch opens at t = 0
R = 20 Ω
V(s) L = 5 H C = 1/40 F
FIGURE 4.67
Circuit diagram of Example 4.15.
ANALYTICAL Solution
The nodal equation yields
Vs Vs
s
sV s
s
t
() () ()
20 5 40
3
for 0
then
Vs
s
s
s
Vs
ss
ss
Vs s s
()
()
()(
1
20
1
540
3
28
40
3
2
2
2
88 120),solving for voltage Vs()
Vs
ss s
()
()
120
(^22822)
120
7
7
17
⋅