Fourier and Laplace
423
30
20
10
−10
−2
−1
−2
0
0
2
4
6
−2
0
0
1
2
3
1
0
2
3
4
2
4
6
−2
0
2
4
6
−2
−0.5
0.5
0
0
1
1.5
2
4
6
time (sec)
time (sec)
Amplitude (amps)
Amplitude (volts)
Amplitude (amps)
Amplitude (amps)
v(t) versus t (sym. Laplace)
i r (t) versus t (sym. Laplace)
i l (t) versus t (sym. Laplace)
i c (t) versus t (sym. Laplace)
FIGURE 4.69
Plots of the symbolic solutions of Example 4.15.
Example 4.16
The switch of the circuit of Figure 4.70 closes at t = 0, assuming that the circuit is initially relaxed, obtain analytical expressions of i(t), v l (t), v r (t), and v c (t) for t ≥ 0.
Create the script MATLAB fi le RLC_series that returns the analytical and symbolic
(Laplace) plots of i(t), v l (t), v r (t), and v c (t), over the range 0 ≤ t ≤ 10 s. Also verify KVL
given by
v(t) = v l (t) + v r (t) + v c (t) over the given time range
v (t ) = 10sin(3t )
R = 4 Ω
L = 2 H
C =1/20 F
switch closes at t = 0
i (t)
FIGURE 4.70
Circuit diagram of Example 4.16.
CRC_47760_CH004.indd 423
CRC_47760_CH004.indd 423
7/28/2008 12:26:17 PM
7/28/2008 12:26:17 PM