416
Practical MATLAB
® Applications for Engineers
Example 4.13
The switch sw shown in the circuit diagram of Figure 4.64 has been opened for a long
time. At t = a = 0, the sw closes and remains closed for t ≥ 0. Assume that all the initial
conditions are zero. Determine by hand an expression for i(t). Create the script fi le analysis_RLC that returns i(t) using the LT, and obtain plots of i(t) versus t for t ≥ 0, using a
numerical and symbolic approach.
Also obtain the symbolic expression fot i(t), for t ≥ 0, using Laplace for the case when
the sw closes at t = a = 1.
ANALYTICAL Solution
Z s
R sL
sC
( )
(
)
ϭ ϩ ϩ
1
total impedence
FIGURE 4.64
Circuit diagram of Example 4.13.
50 V
R = 2 Ω
L = 1 H
C = 0.1 F
sw closes at t = a
i(t )
0
0
0
1
2
3
4
5
0.5
1
1
0.5
−0.5
0
1
0.5
−0.5 −1
2
3
4
5
2.5
3.5
4.5
1.5
time (sec)
time (sec)
v 0 (t) versus t (symbolic solution)
v 0 (t) versus t (numerical solution)
Amplitude (volts)
Amplitude (volts)
FIGURE 4.63
Numerical and symbolic plots of v 0 (t) of Example 4.12.
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7/28/2008 12:26:15 PM