ee321finals03 - EE321 Spring 03 Final Exam Neatly print...

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EE321 Spring 03 Final Exam Neatly print your full name: Work out problems completely – this won’t get you partial credit but will increase the odds of getting the problem correct. There are 10 questions on the exam. Each question is worth 10 points. Circle only one answer unless otherwise directed.
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(1) Consider the following geometry: The mutual inductance between winding 1 and winding 2 is best described by what form: (a) r b a L L θ sin + , (b) r b a L L θ sin , (c) r b a L L θ cos + , (d) r b a L L θ cos (e) r b a L L θ 2 sin + , (f) r b a L L θ 2 sin , (g) r b a L L θ 2 cos + , (h) r b a L L θ 2 cos (i) r b a L L θ 4 sin + , (j) r b a L L θ 4 sin , (k) r b a L L θ 4 cos + , (l) r b a L L θ 4 cos (m) r b L θ sin , (n) r b L θ sin , (o) r b L θ cos , (p) r b L θ cos (q) r b L θ 2 sin , (r) r b L θ 2 sin , (s) r b L θ 2 cos , (t) r b L θ 2 cos (u) r b L θ 4 sin , (v) r b L θ 4 sin , (w) r b L θ 4 cos , (x) r b L θ 4 cos (2) Consider the flux linkage equations r bs as as r as i i i θ θ λ sin ) ( 3 . 0 ) 2 cos 2 5 ( 5 . 0 + = r bs as bs bs i i i θ λ sin ) ( 3 . 0 7 5 . 0 + = The electromagnetic torque for this system may be expressed (a) r bs as r as i i i θ θ cos ) ( 2 . 0 2 sin 2 5 . 1 2 + (b) r bs as r as i i i θ θ cos ) ( 2 . 0 2 sin 5 . 1 2 + (c) r bs as r as i i i θ θ cos ) ( 2 . 0 2 sin 2 5 . 1 2 + (d) r bs as r as i i i θ θ cos ) ( 2 . 0 2 sin 5 . 1 2 + (e) r as r bs as r as i i i i θ θ θ cos 2 . 0 cos ) ( 2 . 0 2 sin 2 5 . 1 5 . 1 2 + (f) r as r bs as r as i i i i θ θ θ cos 2 . 0 cos ) ( 2 . 0 2 sin 2 5 . 1 5 . 1 2 + + (g) r as r bs as r as i i i i θ θ θ cos 2 . 0 cos ) ( 2 . 0 2
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