Circuitos eletricos laplace

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)
−2s

Figure 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 2Ω

15.30

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
15.37

Obtain 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

2Ω

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) in the 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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