200 Practical MATLAB® Applications for Engineers
Observe that by changing the value of R (R = 3, 9, and 72 Ω), the three solutions for
the second-order differential equation—over, critical, and underdamped—are obtained.
Observe that the analytical solutions completely agree with the MATLAB solutions.
Example 2.30
Steady-state conditions exist in the network shown in Figure 2.101, at t = 0 −, when the
V 0 = 90 V source is connected to the RCL circuit. At t = 0 +, the switch opens (moves
upward) and the source V 0 = 90 V is disconnected from the RLC structure.
Analyze the transient response (t > 0) of the source-free series RLC circuit for the
following values of R, R = 75, 36, and 3 Ω.
- Determine the analytical response iR(t) for each value of R, for t ≥ 0
- Create the script fi le transient_RLC_series that returns the MATLAB solutions of
part 1, and its plots - Compare the MATLAB solutions of part 2 with the analytical solutions of part 1
FIGURE 2.101
Network of Example 2.30.
C = 1/36 F
V 0 = 90 V
L = 9 H
R = 75, 36, and 3 Ω Switch opens at t = 0
ANALYTICAL Solution
For t ≤ 0 −, the initial conditions are vC(0) = 90 V and iL(0) = 0 A.
Ldi t
dt
()tC 0 Ri() 00 v()
then
di t
dt
vRit
L
v
t L
() CLC( ) () ( ) /s
0
0090
9
10 A
Recall that the loop differential equation is
dit
dt
R
L
di t
dt
it t
2
2
() () (^1) () 00
CL
for