PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

420 Practical MATLAB® Applications for Engineers

Example 4.15

The switch in the circuit diagram of Figure 4.67 is closed for a long time. At t = 0, the

switch is opened and remains opened for t ≥ 0. Analyze by hand the given circuit using

the LT and obtain analytical expressions for

v(t), ir(t), ic(t), il(t) for t ≥ 0

Create the script MATLAB fi le RLC_parallel that returns the plots of the analytical

results as well as the symbolic (Laplace) plots of v(t), ir(t), ic(t), il(t), over the range

− 2 ≤ t ≤ 5, and observe that both solutions are identical.

3 A

switch opens at t = 0

R = 20 Ω

V(s) L = 5 H C = 1/40 F

FIGURE 4.67
Circuit diagram of Example 4.15.

ANALYTICAL Solution

The nodal equation yields

Vs Vs

s

sV s

s

t

() () ()

20 5 40

3

 
for 0

then

Vs

s

s

s

Vs

ss

ss

Vs s s

()

()

()(

1

20

1

540

3

28

40

3

2

2

2

 





















88 
120),solving for voltage Vs()

Vs

ss s

()

()





120

(^22822)
120
7
7
17
⋅