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# exam1_solution - EE321 Exam 1 Spring 2011 Notes You must...

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Unformatted text preview: EE321 Exam 1 Spring 2011 Notes: You must show work for credit on Problems 1—3. The last page of exam has a piece of extra paper if needed. Good luck! 1) EOW‘T‘WDME 20 pts. Consider a square loop of wire with 5 turns in a Cartesian coordinate system as shown below. The z-component of the ﬂux density is denoted Bz . The open circuit voltage associated with the coil is given by v = 20000 cos(lOOOt). Given that the ﬂux density is spatially uniform, determine an expression for 32 as a function of time. You may assume 82 has no dc component. y—axis Square loop with 5 turns. Corners marked (x,y,z) wound in direction of arrows. x-axis z-axis is out of page (j’:d)) 2) p); fU’OU’ :/20000 69410001!“ ctt A 2 20 gm (000 t +¢ :0 A10 do Lem/aonwf ‘25 C MAW 2 NBA => 51 9‘ 20400100017 a “(n/wot NA 5A4 2) 21 pts. Consider the magnetic system below. The permeability of the cores is inﬁnite, and you may neglect fringing and leakage ﬂux. The air gap g =1 mm, w: 2 cm, and the depth into the page is 10 cm. Coil 1 has 100 turns (with a direction such that positive current tends to cause ﬂux to go up in the leftmost leg) and a current of 10 A. Coil 2 has 100 turns (with a direction such that positive current tends to cause positive ﬂux go up in the center leg) and a current of 20 A. What is the total flux linkage for winding 2 (i.e. 12)? core I g/{Kg : F'/@g+P”//Pg : Wslom 3 3.) 21 pts. Consider an electromechanical device with the flux linkage equations given below. Suppose i1 =4 A, i2 2—2 A, ﬁrm =1(rad), and the units of the coefﬁcients are such that when the currents are in A, and the position is in radians the ﬂux linkages are in Vs, as normal. What is the numerical value for the electromagnetic torque in Nm. 1 21 = 4i1 + (2 + sin 46 )(i1 +1.2); 1')" l 22 = 41-2 +(2 + sin 46 )(i1+z’2)3 I'm I 6’18 8 0 We, 2 fgldb, + /277[(L‘2 0 0 ’ 452 '4/ “'F ” J t iamchwmw, 5/ Nu — “'4 téq (1+6l'n49rm) 514/9 (re/glam 0'5; by l', [IF 0 l: W42“ 1 \ 2f F \ l / 2’ L’ + 320W 3 4:2: +362+zm49m>(4pt;) “I 0 z 4* : 2£22 7“ 3 2.}. ' ( r n 4/3 .4/ 7; C ”Si/74%) (l/+Lg,) - (I; ) Wm Weﬁwcg. 2 2 (5.1+ (22*) +% (1mm 42%”) (41743940 9W0 . %: 3 (511%))“; @ﬁ 497m NM (o e - W3 /c',:AA “ 3(4‘2) W 4 ” (2f. 4.) 4 pts. Which of the following systems is magnetically linear ? (You may circle more than one) A =i +' System 1: 1 1 12_ 1/2 = l2 + 11 ﬂ 5i,2 + 31'2 A] : 10+x 11=i1+i2+25in8rm System 3: System 4: . . 3i1+7i§ 42 =12+l1 12 = 10 + x 5.) 5 pts. In electromagnetic or electromechanical device design, what is the relationship between mass and loss? mews o< __/___ L055 6.) 5 pts. The a-phase of a VR stepper motor has a ﬂux linkage equation given by ﬁgs 2 (5 + 3 cos(49,.m Dias The b-phase has a maximum inductance at 6m =7r/8. Write the b-phase flux linkage equation. A6; = {9"} L9’g #Lerm~7\"/g)> L.“ V; 7.) 5 pts. Consider a VR stepper motor with 5 phases and 8 rotor teeth. What is the step length. gL 3 2 A? 2 A W 01' ﬂ ;_ 7 O 4' K9. . 20 . *0 dd) 8.) 5 pts. Under what condition 15 the followmg statement not true: J d?” = Te — T, ? if J Jr; a Ina/757; 9.) 4 pts. What is an advantage of ferromagnetic materials over ferrimagnetic materials. What is an advantage of ferrimagnetic materials over ferromagnetic materials. If you could be a ferromagnetic material or a ferrimagnetic material which would you be and why (you can skip this last part if desired). Perm/hag Ara/Ha Mar/s KAI/e lug/m (amraﬂbm 74W “WM/We; than ,Lem‘ FEm'mag/wfi'c Mfr); cm: nan Cardiac/um rem/7‘14: CE fem lO.) t Which ofthe following hold in a material with hysteresis ? (circle all that apply) Ohm’s Property for Magnetic Systems; Lossless e d " ll.) 5 pts. Why do magnetic materials saturate? . ‘ \ . \ 4; (2’9” mt dam/was 4 "3 MAM W’FF‘ ap/yaecl 0449M, W W‘ct? Car/mat 2’8;de i5 /ua“/¢[email protected] c‘n We in 5563M;- ...
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