# Circuitos eletricos laplace

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CHAPTER 15
15.27 Calculate the inverse Laplace transform of: (a) 15.28 6(s − 1) s4 − 1 (b) se s2 + 1
−π s

The Laplace Transform
1Ω i(t)

699

(c)

8 s(s + 1)3

u(t)

Find the time functions that have the following Laplace transforms: (a) F (s) = 10 + s2 + 1 s2 + 4 15.35

+ −

1F

1H

e−s + 4e−2s (b) G(s) = 2 s + 6s + 8 (c) H (s) = 15.29 (s + 1)e s(s + 3)(s + 4)
−2sFigure 15.59

For Prob. 15.34.

Find vo (t) in the circuit in Fig. 15.60.
6Ω e−tu(t) + − 1H
1 10

Obtain f (t) for the following transforms: (s + 3)e−6s (a) F (s) = (s + 1)(s + 2) (b) F (s) = (c) F (s) = 4 − e−2s s 2 + 5s + 4 se−s (s + 3)(s 2 + 4)

F

+ vo(t) −

Figure 15.60
15.36

For Prob. 15.35.

Find the input impedance Zin (s) of each of the circuits in Fig. 15.61.
1Ω 2Ω15.30

Obtain the inverse Laplace transforms of the following functions: 1 (a) X(s) = 2 s (s + 2)(s + 3) 1 (b) Y (s) = s(s + 1)2 (c) Z(s) = 1 s(s + 1)(s 2 + 6s + 10)

1H 2Ω 1F

1H

0.5 F

1Ω (a) (b)
For Prob. 15.36.

15.31

Obtain the inverse Laplace transforms of these functions: 12e−2s 2s + 1 (a) (b) 2 s(s 2 + 4) (s + 1)(s 2 + 9) (c) (s 2 9s 2 + 4s + 13)

Figure 15.61
15.37Obtain the mesh currents in the circuit of Fig. 15.62.
1 4

F

1H

15.32

Find f (t) given that: s 2 + 4s (a) F (s) = 2 s + 10s + 26 (b) F (s) = 5s 2 + 7s + 29 s(s 2 + 4s + 29) 2s 3 + 4s 2 + 1 + 2s + 17)(s 2 + 4s + 20) 15.38

u(t)

+ −

i1

i2

+ −

4e−2tu(t)

Figure 15.62

For Prob. 15.37.

15.33

Determine f (t) if: (a) F (s) = (b) F (s) = Find vo (t) inthe circuit in Fig. 15.63.
1H 10e−tu(t) V + − + vo(t) − 4Ω

(s 2

s2 + 4 2 + 9)(s 2 + 6s + 3) (s

2F

3u(t) A

Section 15.5
15.34

Application to Circuits

Determine i(t) in the circuit of Fig. 15.59 by means of the Laplace transform.

Figure 15.63

For Prob. 15.38.

v

v

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Problem Solving Workbook Contents 700
15.39

PART 3
Determine io (t) in the circuit in Fig. 15.64.

15.43 In the circuit of Fig. 15.68, let i(0) = 1 A, vo (0) = 2 V, and vs = 4e−2t u(t) V. Find vo (t) for t > 0.

1F

2H io 2Ω i vs + − 1H 1F 2i −+ + vo −

e−2tu(t) A

Figure 15.64

For Prob. 15.39.

Figure 15.68
15.40 Determine io (t) in the network shown in Fig. 15.65.15.44
1Ω io 5 + 10u(t) V + − 2H
1 4

For Prob. 15.43.

Find vo (t) in the circuit in Fig. 15.69 if vx (0) = 2 V and i(0) = 1 A.
+ vx − 1F e−tu(t) A 1Ω 1Ω 1H

i

F

Figure 15.65

For Prob. 15.40.

+ vo −

15.41

Find io (t) for t > 0 in the circuit in Fig. 15.66.
2Ω + vo − 1Ω 1F 5e−2t V + − 0.5vo + − 1H + − io 3u(−t) V

Figure 15.69
15.45

For Prob. 15.44.Consider the parallel RLC circuit of Fig. 15.70. Find v(t) and i(t) given that v(0) = 5 and i(0) = −2 A.

i 4u(t) A 10 Ω 4H
1 80

F

+ v −

Figure 15.66
15.42

For Prob. 15.41.

Figure 15.70
Calculate io (t) for t > 0 in the network of Fig. 15.67. 15.46
2e−tu(t) V +− 1F io 1H 1Ω + −

For Prob. 15.45.

For the RLC circuit shown in Fig. 15.71, ﬁnd the complete response if v(0) = 2 Vwhen the switch is closed.

t=0

1H
1 9

4u(t) A

2 cos 4t V

F

+ v −

Figure 15.67
v
v

For Prob. 15.42.

Figure 15.71

For Prob. 15.46.

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Problem Solving Workbook Contents

CHAPTER 15
15.47 For the op amp circuit in Fig. 15.72, ﬁnd vo (t) for t > 0. Take vs = 3e−5t u(t) V.
10 kΩ 50 mF 20 kΩvs + −

The Laplace Transform
15.52

701

When the input to a system is a unit step function, the response is 10 cos 2t. Obtain the transfer function of the system. A circuit is known to have its transfer function as s+3 H (s) = 2 s + 4s + 5 Find its output when: (a) the input is a unit step function (b) the input is 6te−2t u(t).

15.53

− +

vo

15.54

When a unit step is...