EE321, Spring 08 Homework 4
Problem 16
W
c
1
2
5
2 cos 2
θ
rm
⋅
(
)
+
(
)
⋅
i
2
⋅
=
T
e
2
−
sin 2
θ
rm
⋅
(
)
i
2
⋅
=
Problem 17
P
λ
1
Pi
2
0.8 i
1
⋅
i
2
0.2
−
⋅
5
x
+
=
P
λ
2
Pi
1
3 i
2
0.8
⋅
5
x
+
=
where P is used for partial.
Clearly the two partial derivatives are not equal and
so the system description is not feasible
Problem 18
We may express the system as
λ
1
λ
2
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
5
7
5
x
2
+
7
5
x
2
+
2
⎛
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎠
i
1
i
2
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
⋅
=
which is of the form
λ
1
λ
2
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
L
i
1
i
2
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
⋅
=
where L is independent of both current and flux linkage.
Thus, this system
is magnetically linear.

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