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ECE3025D_Spr2005_Quiz2_Solutions

ECE3025D_Spr2005_Quiz2_Solutions - Name Ev Problem 1(25...

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Unformatted text preview: Name: Ev Problem 1. (25 points) Consider transmission line with a characteristic impedance of Zo = 75 Q . Plots are given below for the standing wave amplitude for two different loading conditions on the same transmission line. The dielectric constant of the line is 8, = 2.1 . A. (5 pts) What is the frequency in Hertz of the generator? 1 3193mm .) 39°Z¢§m 9L ' P/C we z Wow/W eat—gm 2, B. (10 pts) What is the impedance at the generator end of the transmission line for Plot A? March 8, 2005 _ 2 ECE 3025D Exam #2 Mr, Problem 1. (Continued) C. (10 pts) What is the impedance of the load for Plot B? Note that the value of VSWR for Plot B is not the same as that for Plot A! 1 \pl: \lswa—I vewrurl . \Ul=%%=o.l309 mm bra-e kWWR 311T W 0’6 F Z QL+$§ 2gp: ”f ' .ZTF— \OQT 2,». L . (1:04'30‘1‘cw\-‘lrr+éo.\3o‘(rxé~lfl'fi' (“z—0.0%03—30u34 42r— Lfl? - 0.?S‘i7va:o.|LV : o.‘%77e'?o°'m "r' ' W‘ws firms—w W , — (mafia—cam?) L‘Ofll’S—i 3” _ .2 q (9 e =o.‘?137€afo Ll é 2L = ofl 371w '(-o.zq%fl +é‘rimgom 9Q] @L: O. ‘3‘? 3-80.2218 “—2 = L20: empgrnol L March 8, 2005 3 ECE 3025D Exam #2 ML! Problem 2. (25 points) Consider three non-colinear points in space which are located at A(1,2,0), B(0,4,0) and C(2, 4 ,3) These three points define the vertices a triangle. (Note : the triangle illustration is not necessarily drawn to scale) A. (15 pts) Using the definition of the dot product, find each of the interior angles, a, ,3, 7, of the triangle defined by ABC. F3 C M>=(-l)2,,0)3 ”(MA/E 7°12 =- (1,1433 3 Mal-5W3 Mum VE'W YEW B em a: oars-gee :> <>(= leokiowwtégfif fiAz’fHS ’ (l)«z\o)) “94:ij emf-(110193 We]; 13 mix-Heel: WW: 7?: oer/WW: BSBK M: owe-Rf 2‘: 1370‘“ March 8, 2005 ECE 3025D Exam #2 Nam. KEY Problem 2. (Continued) B. (5 pts) Find a unit vector that is along the path from point B to point A. QME”: a (5’2”?) IBM YE C. (5 pts) Find a unit vector that is normal to the plane of the triangle ABC. A. A: A a 2 —> m :2 ’2 CzPrExfrC_ _' z 0 l2 3 March 8, 2005 5 ECE 3025D Exam #2 KEY Problem 3. (25 points) A vector field X has cartesian components (y2 , x2, x2 + y2 + z2 ) Name: Find the following: EX]: :: 8%32 —-<Q~’)L9 +(Z7L-Zg)§ Mar h 8, 200 c 5 6 ECE 3025D Exam #2 KEY c. (2 pts) What is § - K called? Name: March 8, 2005 ECE 3025D Exam #2 KEY Problem 3. (Continued) Name: E. (7 pts) Evaluate (1:; (K 0 n) (10' over a closed surface defined by a cylinder aligned with the z axis from 2 = 0 to 2 =10 with a radius of 2. Here n denotes a unit vector normal to the surface of the cylinder. March 8, 2005 ‘ 8 ECE 3025D Exam #2 KEY Name: Problem 4. (25 points) , B(— d / 2, 0, 0) in free space, and both line char charge centered at point A(d / 2, 0, 0) has a charge per unit length of p A line charge centered at point B(—d / 2, 0, O) has a charge per unit length of pB The 2 axis extent of both line charges is from Z = d = 0.01 meters. A. (15 pts) Write the general the answer into three regions. Two line charges of opposite polarity are centered at points A(d / 2, 0, 0) and V ges are parallel to the z-axis in cartesian coordinates. The line = 150 x 10‘9 Coulombs/meter, and the = —150 x 10’9 Coulombs/meter. — 00 to Z = 00. These line charges are separated by exactly lit 6; expression for the electric field at any point P located along the x axis. Hint: Sp A ,5? A 7 IgoXtO o.6| N/ E _,__. ”L C March 8, 2005 9 ECE 3025B Exam #2 KEY Problem 4. (Continued) Name: B. (10 pts) Plot the value of the x component of E , i.e., Ex , along the x axis and over the interval from —4d S x S 40' . Scale the plot carefully and use complete axis labels to receive full credit. 7c Um) \ —\o.8 X mg ”/0 March 8, 2005 10 ECE 3025D Exam #2 ...
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