December 2015
Intermediate to advanced
737 pages
23h 39m
English
Content preview from Network Analysis and Synthesis, 1st Edition by Pearson
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Transient Response of Circuits Using Laplace Transform 329
=
+
--
2000
1
979 8
200 1
22
eL
s
t
(.)
=×
-
2000
1
979 8
200
et
t
.
sin 979.8
∵
L
sa
a
at
-
+
=
1
22
11
sin
=
-
2000
979 8
979 8
200
.
si
n.et
t
i(t) = 2.04 e
-200t
sin 979.8t
8.6 SINUSOIDAL RESPONSE OF R–L SERIES CIRCUIT
We will now find the transient response of circuits to sinusoidal inputs.
Consider the R–L circuit shown in Figure 8.15.
Applying KVL, the following equation is obtained:
VR
it L
di
dt
m
sin()wt
=+
Taking the Laplace transform on both sides, we get the
equation as follows:
VL tRIs Ls
Is
m
[sin ](
)(
)
w =+
or V
s
RsLIs
m
w
w
22
+
=+
()()
or Is
V
sR
sL
()
()
()
=
++
w
w
m
22
=
+- +
w
ww
V
sj sj RsL
m
()()
()
or Is
V
L
sj sj s
R
L
()
()()
=
+- +
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