ECE210_FA23_HW01

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Stanford University *

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Course

210

Subject

Electrical Engineering

Date

Oct 30, 2023

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pdf

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Uploaded by JusticeKouprey15684

University of Illinois Fall 2023 ECE 210/211 - Homework 1 Due: Tuesday, August 29 by 11.59pm Homework policies: • HWs are due to be submitted via Gradescope. You can find instructions on how to scan/upload your HW on the course website, including the Gradescope’s app. • Late homeworks will only be accepted up to 1 hour after the deadline, with a deduction of 10% of the total points (no negative final score), so please mark your calendar with the deadlines to avoid losing some/all points. Do not wait until the last minute to submit it and then run into internet issues because we will not give you an extension. Submit your HW as soon as you finish it because if you wait and forget to do it on time, we will not give you an extension. • In order to account for sickness, travel or internet issues, the lowest homework grade will be dropped for 211 students and the lowest two homework grades will be dropped for 210 students. • Homeworks constitute an essential component of your learning experience in the course and prepare you for your exams in e ↵ ective ways. Investing time to do your homeworks with care will pay o ↵ when you are taking your exams. – You will be expected to provide detailed explanations of your solutions in order to obtain credit in your homeworks. Graders should not have to guess or make assumptions about why you are using a certain equation, or how you came up with an equation, or what polarity you used, etc. Conversely, solutions lacking full explanations will receive zero credit even when the answer provided may be correct, and may lead to an ’academic integrity violation’ case being opened against you with sanctions. – You are encouraged to collaborate to understand the problems in the assignment, but each student should solve the problems individually for submission even if they work together initially to understand how to solve the problems. Copying a joint solution or someone else’s solution is not acceptable and may lead to an ’academic integrity violation’ case being opened against you with sanctions. – Using previous semester homework solutions and online solutions (Chegg, etc.) may lead to an ’academic integrity violation’ case being opened against you with sanctions. – Sanctions range from a letter grade reduction to an F in the course. – Please keep these cautionary remarks in mind as you are working out your assignments and avoid submitting unsubstantiated solutions to avoid any misinterpretations. • Do not solve the HW directly on the provided pdf because there is not enough space for it and you will most likely lose points due to lack of neatness. • Make sure you box your answers and match problem parts accurately in Gradescope, or you will be deducted points for the corresponding problem part. • Make sure your submission is complete before logging out of Gradescope because we will not give an extension if you do not complete the submission. You will receive an automated email from Gradescope that includes the date and time you turned in the assignment, so make sure you get it. • Make sure that your HW is neat enough to read. Graders has the flexibility to deduct points for lack of neatness. Graders should not have to guess what you wrote and where in the page you wrote it. An easy to follow solution is required. • Solutions will be posted in Canvas 1 hour after the corresponding deadline. • Please report angles in radians and in the range ( - ⇡ , ⇡ ] and simplify fractions to lowest terms. Failure to do so could result in loss of some credit.

Problems: 1. Sign acknowledging you will abide by this course’s and the University’s Academic Integrity policies or face sanctions for not doing so. These policies include, among others, plagiarism: representing the words or ideas of others as your own; cheating: using unauthorized materials and/or information. The possible sanctions include, among others, reduced letter grades and an F in the course. If your solution upload does not include your signature, your homework will NOT be graded, resulting in a zero. sign: . 2. Consider the circuit below, where R 1 = 5 ⌦ , R 3 = 3 ⌦ , V R 2 = 2 3 V and V R 3 = 1V. Let the top-right node be the reference node. Determine the resistance R 2 and the voltage V x in the following circuit, as well all the remaining node voltages. 3. Consider the circuit below, where V s = 8V, I s = 2A and R = 4 ⌦ . Determine the current I and calculate the absorbed power at each circuit element. Clearly indicate if the power is absorbed or injected. 4. Consider the circuit below, where I s = 5A, R = 2 ⌦ and K = 2A/V. Determine the voltage V x and calculate the absorbed power at each circuit element. Clearly indicate if the power is absorbed or injected. 5. Consider the circuit below, where V s = 3V, R 1 = 1 ⌦ , R 2 = 2 ⌦ and K = 2 . Determine the current I and the voltage V x . 6. Consider the circuit below, where R 1 = 6 ⌦ , R 2 = 6 ⌦ , R 3 = 2 ⌦ , V 2 = 18V and I s = 5A. Determine the current I 1 and the voltage V 1 . © 2023 Juan Alvarez. University of Illinois. All rights reserved 2 Haoming Mei ↑ I 23N ① Iont= Iin 0 OKUL: Vx++, = 2 ↑ M ⑮ Is Rs I - 5 t 0 O Iz = 13A 1 = I,3 (+ (23) +(B.) + (s) = 0 - & Ev >s I = 13A = 1, = I = 1313 = 13 IV VR2 = I2 R2 ③ 2/zV = 13A. R2 R 0 0 0 1 I 3 >121 KCL: I + I2 2 0 84K: y-VRy = 0 Prs = 8 I PIsNs.2 PR= IR Ov CA - 4 I = 2-2 y - 12.4 = 0 8 - 4) E i En I2 = 2A 32W - 16W I = (2) 2 =- 4A. ⊥ ⑪ ② e - - 2 IstIxtk.Vy = 0 IIs = V Is Pry= Ix.Vx 5A t 5t + 2.x = 0 ( - 2): 5 ( - 1)( - 2) E Linjest) sorb, YaVx = - 5 Vx = 2 t ~ ① KH: 3+, +KVy+Vy = 0 ② PKx= I.Vx i 2 3t(1.1) + (2)(I)+(1.2) Vx = R2 I 30 I )(2.2)(a) 2 3 + 7I = 0 ⊥ A. ⑭ absorb) gar I 2 kCL: 5 = I2+I 12 = 1 = 3A I W - + - 2 - - (v2: 18-UR, -Vi = 0 6 0 IOV 6 3A I, = 2A L 18 -(61) - V = 0 E 7 1, = 15- 61) W

7. Some of the following circuits violate KVL/KCL and/or basic definitions of two-terminal elements given in Section 1.3. For each one of the circuits, determine if it is correct or ill-specified. If it is ill-specified, explain the problem and indicate what will happen if the incorrect circuit has been built up in your real life? 8. Let A = p 3 - j 2 p 3 and let B = - 3 - j p 3 . (a) Express A in exponential form. (b) Express B in exponential form. (c) Determine the magnitudes of A + B and A - B. (d) Express AB and A/B in rectangular form. 9. This last problem will introduce the basic python programming concepts that will be useful to you in this course, and others. • You will use an IPython notebook via PrairieLearn with unlimited attempts. • Make sure that you complete the PrairieLearn question before this homework’s due date to get credit for it. • You do not need to submit an answer for this question on Gradescope, we will download this problem’s grade from PrairieLearn. • You can access the question by clicking on this link: https://us.prairielearn.com/pl/course i nstance/ 139840 /assessment/ 2357834. • If you do not have access to the question, please email Prof. Alvarez. Conflict exam requests: • Our exam schedule is posted since before the first day of the semester. • Some of you either have classes, labs, other exams or work that overlap with our exams. We will o ↵ er conflict exams for those of you who are in these situations but you need to get Prof. Alvarez’s approval in order to be able to take the conflict exams. • As indicated in the student code, conflict exams are to be granted if the student informs the instructor of the conflict within one week after being informed of the examination schedule. Priority will be given to the examination announced in class the earliest in the semester. • If you have conflicts with one or more of our exams and want to request a conflict exam, you must complete this form by September 6 at 11.59pm: https://forms.illinois.edu/sec/2082281966. • If you do not complete the form by the deadline, we are not required to grant a conflict exam so you might not get one. • If you do not have access to the form, please email Prof. Alvarez. © 2023 Juan Alvarez. University of Illinois. All rights reserved 3 / a) Invalid b.) Invalid, 2A C.) Valid, voltage source in voltage source & IA are in series · OVOr=160 total. in parallel series, violates KVL and they I when they aren't arent equal, equal, This violates KCL. 60y.j Work on next page 25.e A + B = 554 - 3.jA- B= + 3- .j 3 X AB = 123. e 2.97; * (B = 312.2663 Done

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#8) a) 5 + 4.3 = r = 6x>0 3) A + B 55 - 25.j + 3 - 8 = tan(-) = tan-(-2) 3 - i 60.35z - - - 355.j E tr b) - - 54 - 353.j 0 + 3 = 12 E r= Li A - B x <0y303 - 253j) - (- 3- 0 =-Attan( (((5j) 8 = -x+ tan() d.) A.B j.(546 + - 0.352) - x + (+ y) 123e - 5TY -2.97.j - 546.j > A/B = (12.2665 25 C