31. Convert the total of 1/2 + 1/2 + 1/2 into whole number/…

Questions

31. Cоnvert the tоtаl оf 1/2 + 1/2 + 1/2 into whole number/decimаl form.

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Prоblem 1. (20 pts) Cоnsider the inductоr below. Derive аn expression for the horizontаl slot leаkage permeance in terms of the geometrical variables shown below and the permeability of free space. Assume the depth of the winding is equal to the depth of the slot (dw=ds{"version":"1.1","math":"dw=ds"}). Part (a): Find the portion of the horizontal leakage permeance associated with leakage flux inside the slot. [10 pts] Part (b): Find that potion of the horizontal leakage permeance associated with leakage flux that leaves the core from the front and back faces, such as we considered for the EI inductor in Chapter 5. Your expression should include the impact of the front and back faces with a single permeance. [10 pts] Problem 2. (20 pts) The mesh list of an MEC is Compute RN{"version":"1.1","math":"RN"} and FN{"version":"1.1","math":"FN"}. Use MAFA. Show your work, adding one branch at a time. Problem 3. (20 pts) The MMF across a branch may be expressed Fb=5Φb3{"version":"1.1","math":"Fb=5Φb3"}. If, at our present iteration of the solve Φb=2{"version":"1.1","math":"Φb=2"}, what is the effective source and effective reluctance of the branch model we will use in processing this branch on the next iteration of the nonlinear solve? In other words, find Fseff{"version":"1.1","math":"Fseff"} and Rbeff{"version":"1.1","math":"Rbeff"}. Note, it is not my intention that you use the expressions in the book to calculate these quantities as I don’t remember them off the top of my head myself and wouldn’t expect you to. Rather, I want you to apply the ideas behind this process to come up with values. Your answers should be in terms of literals (like ‘2’). Problem 4. (20 pts) Following the approach we used in class, derive an expression for resistance of a coil in terms of coil volume, coil cross section, packing factor, number of turns, and conductivity. Be sure to define all your symbols so there is no ambiguity for grading. Problem 5. (20 pts) Part (a): Following the approach in the book or the approach we used in class, derive the expression for the field energy contributed by a branch of an MEC. You may assume that this branch does not include a source term. [7 pts] Part (b): Assuming that the branch is magnetically linear and starting from the results of Part (a), find the energy stored in the branch in terms of the branch MMF and the branch permeance. This should be in closed form w/o an integral. [6 pts] Part (c): Find an expression for the differential field energy associated with the branch. Here let x denote the dimension of a mechanical degree of freedom. [7 pts.] Congratulations, you are almost done with this exam. DO NOT end the Honorlock session until you have submitted your work to Brightspace. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF to Brightspace as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to go to Brightspace to submit your work: Exam 1 Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.