final exam

# final exam - EE321 Final Exam Spring 2004 Name Student ID...

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EE321. Final Exam Spring 2004 Name: Student ID: Instructions: Work ALL Problems. Show your work. Each problem is worth 25 pts. There was a physics student named bright. He thought a lot about light. He went out one day in the usual way and came back the previous night. – Garrison Keillor

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Problem 1 – MEC Modeling Starting with the definition of flux, and the definition of MMF drop, derive Ohm’s law for linear magnetic material. In particular, show that Φ = R F b a , , where ( ) A l R µ / = where b a F , is the MMF drop from node a to node b, R is reluctance, Φ is the flux into node A, l is the length from node a to node b, A is the cross sectional area of the path, and µ is the absolute permeability. Problem 2 – Energy Conversion Consider a magnetic system with the following flux linkage equations 2 1 2 2 1 1 4 3 5 i i i i + = + = λ λ Initially, both currents are zero. If first winding 1 is energized to 1 A, and then winding 2 is energized from 0 to 2 A, what is the co-energy? Now, consider the situation if winding 1 goes from 0 to 1 A (linearly in time) and winding 2 goes from 0 to 2 A at the same time (again, as a linear function of time).
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