PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

196 Practical MATLAB® Applications for Engineers

Note that the network shown in Figure 2.95 is an ideal circuit (since there is no resis-

tance, R = 0 in the LC loop for t ≥ 0), and the solution clearly indicates that the current

shows an oscillator behavior with W = 12 rad/s = _____^1

√

___

LC

and T = π__ 6 s.

Example 2.29

Steady-state conditions exist in the network shown in Figure 2.97 at t = 0 −, when the

V 1 = 120 V source is connected to the RCL parallel circuit. At t = 0 +, the switch moves

downward, and the source V 1 = 120 V and resistor R = 10 Ω are disconnected from the

parallel (RLC) structure.

Analyze the transient response (t > 0) of the source-free parallel RLC circuit, for each

of the following values of R, R = 3, 9, and 72 Ω.

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


2. Create the script fi le transient_RLC_parallel that returns the MATLAB solutions of
   part 1 and its corresponding voltage plots


3. Compare the MATLAB solutions of part 2 with the analytical solutions of part 1

FIGURE 2.97

Network of Example 2.29.

L = 9 H

R = 10 Ω

R = 3,9 and 72 Ω

V 1 = 120 V

Switch moves down at t = 0

C = 1/36 F

ANALYTICAL Solution

From the circuit diagram of Figure 2.97 for t ≤ 0, the initial conditions are vC(0) = 0 and

iL(0) = 120/10 = 12 A, and

Cdv t

dt

C()tC
 0 


 
 it( 0000 ) iC L R() i() i()

then

dv t

dt

C()tC
 0 


 36 i() 0 36 12( 0 ) 432 V/s

Recall that the node equation is

dv t

dt

dv t

dt

CCvtC t

2

2

()
 11 () () 00

RC CL

for

For R = 3 Ω, the resonant frequency is

w 0 

^12

LC

rad/s