Biomedical Engineering Reference
In-Depth Information
For
t
¼
0, as is often the case in solving circuit problems, Eq. (9.20) reduces to
0
Z
t
1
L
i
ð
t
Þ¼
v
ðÞ
d
l þ
i
ð
0
Þ
ð
9
:
21
Þ
0
and for
t
¼1
, the initial current is by definition equal to zero, and therefore Eq. (9.20)
0
reduces to
Z
t
1
L
i
ð
t
Þ¼
v
ðÞ
d
l
ð
9
:
22
Þ
1
The initial current in Eq. (9.20),
i
ð
t
0
Þ
, is usually defined in the same direction as
i
, which
means
i
ð
t
0
Þ
is a positive quantity. If the direction of
i
ð
t
0
Þ
is in the opposite direction
of
i
(as will happen when we write node equations), then
i
ð
t
0
Þ
is negative.
EXAMPLE PROBLEM 9.12
Find
i
for
t
0if
i(0)
¼
2 A and
v
ð
t
Þ¼
4
e
3
t
u
ð
t
Þ
in the following circuit.
i
+
−
v
2 H
Solution
From Eq. (9.20), we have
Z
t
Z
t
1
L
1
2
e
3l
d
l þ
i
ð
t
Þ¼
vd
l þ
i
ð
t
0
Þ¼
4
2
t
0
0
t
2
e
3l
¼
0
þ
2
3
l¼
u
ð
t
Þ
2
3
e
3
t
¼
4
V
