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Other
Control Systems
Mathematical Modelling-2
For the syste...
Question
For the system shown in figure below, what is the transfer function
V
o
(
s
)
V
i
(
s
)
?
A
V
o
(
s
)
V
i
(
s
)
=
s
L
s
2
R
L
C
+
s
L
+
R
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B
V
o
(
s
)
V
i
(
s
)
=
s
L
R
s
2
R
L
C
+
s
L
R
+
R
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C
V
o
(
s
)
V
i
(
s
)
=
s
2
L
s
2
R
L
C
+
2
s
L
+
1
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D
V
o
(
s
)
V
i
(
s
)
=
s
s
2
R
L
C
+
s
L
+
R
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Solution
The correct option is
A
V
o
(
s
)
V
i
(
s
)
=
s
L
s
2
R
L
C
+
s
L
+
R
Applying Laplace transform and taking the parallel combination of L and C gives
L
s
C
s
L
s
+
1
C
s
Applying voltage division rule we get,
V
o
(
s
)
=
L
/
C
L
s
+
1
C
s
R
+
L
/
C
L
s
+
1
C
s
V
i
(
s
)
V
o
(
s
)
V
i
(
s
)
=
s
L
s
2
R
L
C
+
s
L
+
R
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1
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o
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i
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