EE321, Spring 2011
Homework 4
Problem 1
W
c
1
2
5 2sin 8
θ
rm
⋅
(
)
+
(
)
⋅
i
2
⋅
=
T
e
8 cos
⋅
8
θ
rm
⋅
(
)
⋅
i
2
⋅
=
Problem 2
We may express the system as
λ
1
λ
2
5
3
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.
However, because the partial of lamba 2 with respect
to i1 isn't equal to the partial of lambda 1 with respect to i2, the system
is not conservative.
Problem 3
The given equation is in the linear form
λ
Li
=
therefore
f
e
x
W
c
∂
∂
=
x
1
2
i
T
⋅
L
⋅
i
∂
∂
=
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f
e
1
2
i
T
⋅
x
L
∂
∂
⋅
i
=
1
2
i
1
i
2
i
3
(
)
0
2
−
1 x
+
(
)
2
0
2
−
1 x
+
(
)
2
0
0
0
0
0
⋅
i
1
i
2
i
3
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 Spring '08
 Staff
 Trigraph, −3, leakage inductance Lls, Te θrm, sin RT⋅ θrm

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