Given the functiоn [b] [а] [c], find the percent rаte оf chаnge оf at [x]. Give your answer as a percentage, without typing %, to two decimal places. For example, if the answer is 55.55%, enter 55.55 not 0.5555.
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Prоblem 1. (20 pts) Recаll thаt within а PMAC magnet regiоn we have B=μ0μrm(ϕrm)H+Bm(ϕrm){"versiоn":"1.1","math":"B=μ0μrm(ϕrm)H+Bm(ϕrm)"} where The MMF drop across the magnet may be expressed Fpm(ϕrm)=Rm(ϕrm)Brb(ϕrm)-Fm(ϕrm){"version":"1.1","math":"Fpm(ϕrm)=Rm(ϕrm)Brb(ϕrm)-Fm(ϕrm)"} Derive the expressions for Rm(ϕrm){"version":"1.1","math":"Rm(ϕrm)"} [identifying values for positions under the magnet and for positions not under the magnet] and Fm(ϕrm){"version":"1.1","math":"Fm(ϕrm)"} that we came up with in class [with the one difference is everything is expressed in terms of rotor rather than stator position which makes things easier]. Your expressions should be in terms of μ0, rrb, χm, dm, μrm(ϕrm), {"version":"1.1","math":"μ0, rrb, χm, dm, μrm(ϕrm), "}and Bm(ϕrm){"version":"1.1","math":"Bm(ϕrm)"}. Problem 2. (20 pts) Using relations given to you in Problem 1, the radial flux density may be expressed as B=rrbFm+Fsr Rp+Rg{"version":"1.1","math":"B=rrbFm+Fsr Rp+Rg"} where Fm, Rp, {"version":"1.1","math":"Fm, Rp, "}and Fs{"version":"1.1","math":"Fs"} are functions of position. Derive an expression for the minimum field intensity in the PM (that is the minimum seen anywhere in space) in the positively magnetized portion of magnet. Your expression may be in terms of Fm,pk,{"version":"1.1","math":"Fm,pk,"} and Fs,mn{"version":"1.1","math":"Fs,mn"} but you need to carefully define these (in sentence form). Assume Fs,mn{"version":"1.1","math":"Fs,mn"} is negative and has a magnitude greater than Fm,pk{"version":"1.1","math":"Fm,pk"}. Also, identify at what radius the minimum field intensity occurs.. In addition to Fm,pk{"version":"1.1","math":"Fm,pk"}, and Fs,mn{"version":"1.1","math":"Fs,mn"} your expressions may also include rrb, rrg, Rpm, Rg, Br, μ0,{"version":"1.1","math":"rrb, rrg, Rpm, Rg, Br, μ0,"} and χm{"version":"1.1","math":"χm"}. Problem 3. (20 pts) Consider a three-phase transformer. In abc variables we have Recall and Find the q- and d-axis inductances in terms of Le, Lc, Mec, {"version":"1.1","math":"Le, Lc, Mec, "}and Mee{"version":"1.1","math":"Mee"}. Problem 4. (20 pts) Consider a UI core inductor wherein the U core is completely filled with conductor. The core has a length lc{"version":"1.1","math":"lc"} into the page and a slot depth and width of ds{"version":"1.1","math":"ds"} and ws{"version":"1.1","math":"ws"} respectively. The airgap is denoted g{"version":"1.1","math":"g"}. Derive a closed form expression for the interior corner fringing permeance which includes the impact of conductors being in the fringing path. In choosing your path, consider the desire for a reasonably simple result. Your answer should be in terms of an integral which is ready to be evaluated (but you don’t have to do the integral). Limits of integration should be explicitly stated. Problem 5. (20 pts) 2 pts each. Short Answer. No work required. 5a.) Consider the expression Te=32(λdsiqs-λqsids){"version":"1.1","math":"Te=32(λdsiqs-λqsids)"}. Succinctly describe what conditions an electric machine type must satisfy for this condition to be true. 5b.) What is the impact of inverter load imbalance on inverter input capacitor voltage. What would be the ripple frequency in terms of the fundamental frequency. 5c.) Describe a good method to establish the q-axis current for an operating point in a PMAC optimization. Describe the gene used and the q-axis current is determined from the gene. 5d.) Describe (less than, equal to, greater than) the relationship between the peak air gap flux magnitude and the tooth flux magnitude. 5e.) You run a PMAC optimization. You see that your teeth are not close to the flux density limit at any operating point. What are your thoughts? 5f.) What does the bracket designate in designate? What does the hat designate? 5g.) At a given angular position in the machine, how is the stator circumferential backiron flux magnitude related to the rotor circumferential backiron flux? 5h.) If we decrease wire diameter by a factor of two; but maintain total conductor are by increasing the number of parallel strands appropriately, what is the nex effect on proximity effect loss? 5i.) In the three-phase inductor chapter, why was chosen? 5j.) Under what conditions would be typically use negative d-axis current in a PMAC? 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 3 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.