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The Fundamental of Circuit Theory
Typology: Exercises
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Problem 1
Find the Laplace transform of the function f ( t ) in Fig. 1
Figure 1
Problem 2
Find the Laplace transform of each of the following functions:
a.
f ( t )=sin( ωtt + θ )
b. f
t
= δ
t
t
− 3 e
− 2 t
u ( t )
− 4 t
d. f
t
= t
2
sin
2 t
u ( t )
e. f
t
= 40 e
− 8 ( t − 3 )
u ( t − 3 )
Problem 3
Find the inverse Laplace transform of
a.
F ( s ) =
s
2
s ( s + 2 )( s + 3 )
b.
s
10 s
2
s ( s + 1 )( s + 2 )
2
c. F ( s ) =
5 ( s
2
s
2
d. F
s
5 s
2
s
2
e.
F ( s ) =
10 ( 3 s
2
s
s + 2
2
f.
F ( s ) =
s
2
( s + 5 )
g.
F ( s ) =
250 ( s + 7 )( s + 14 )
s ( s
2
h.
s
11 s
2
( s + 2 )( s
2
i.
s
13 s
3
2
s ( s + 2 )( s
2
j. F
s
18 s
2
( s + 1 )( s + 2 )( s + 3 )
Problem 4
Find the initial and final values of the function whose Laplace transform is
H ( s )=
s + 3
s
2
Problem 5
The switch in the circuit in the following figure has been open for a long time. At t = 0, the
switch closes
a. Derive the integrodifferential equation that governs the behavior of the voltage v 0
for
t ≥ 0
b. Find the simple equation for V 0
(s) and I 0
(s)
c. Suppose that R = 5 kΩ, L = 200 mH, C = 100 nF and V dc
= 35 V. Find v 0
(s) and i 0
(s) (t ≥ 0)
