PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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.

1. Determine the analytical response iR(t) for each value of R, for t ≥ 0


2. Create the script fi le transient_RLC_series that returns the MATLAB solutions of
   part 1, and its plots


3. 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