Electric Circuits I Final Examination

Similar documents
Electric Circuits I Final Examination

Electric Circuits I FINAL EXAMINATION

Electric Circuits I. Midterm #1 Examination

Electric Circuits I. Midterm #1

EE221 Circuits II. Chapter 14 Frequency Response

EE221 Circuits II. Chapter 14 Frequency Response

AC Circuit Analysis and Measurement Lab Assignment 8

Homework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1. Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω.

EE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following time-domain circuit to the RMS Phasor Domain.

Electronics II. Final Examination

Electronics II. Final Examination

Sinusoidal Steady-State Analysis

= 32.0\cis{38.7} = j Ω. Zab = Homework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1

Electronics II. Midterm II

Sinusoidal Steady-State Analysis

EE221 - Practice for the Midterm Exam

Sinusoidal Steady State Analysis (AC Analysis) Part I

ECE 201 Fall 2009 Final Exam

Consider a simple RC circuit. We might like to know how much power is being supplied by the source. We probably need to find the current.

Network Graphs and Tellegen s Theorem

Sinusoidal Response of RLC Circuits

1 Phasors and Alternating Currents

To find the step response of an RC circuit

Electronics II. Midterm #1

Chapter 10 AC Analysis Using Phasors

AC Circuits Homework Set

Sinusoids and Phasors

Phasors: Impedance and Circuit Anlysis. Phasors

AC analysis - many examples

SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS

DC and AC Impedance of Reactive Elements

Basic RL and RC Circuits R-L TRANSIENTS: STORAGE CYCLE. Engineering Collage Electrical Engineering Dep. Dr. Ibrahim Aljubouri

Chapter 33. Alternating Current Circuits

Sinusoidal Steady-State Analysis

Digital Logic Design. Midterm #2

Basics of Network Theory (Part-I)

Circuit Analysis-II. Circuit Analysis-II Lecture # 5 Monday 23 rd April, 18

REACTANCE. By: Enzo Paterno Date: 03/2013

Electric Circuit Theory

Electronics II. Final Examination

Electronics II. Midterm #2

EE 40: Introduction to Microelectronic Circuits Spring 2008: Midterm 2

Chapter 9 Objectives

Basics of Electric Circuits

mywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel

ECE 45 Average Power Review

ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT

ECE Spring 2015 Final Exam

Sinusoidal Steady State Analysis

Lecture #3. Review: Power

RLC Series Circuit. We can define effective resistances for capacitors and inductors: 1 = Capacitive reactance:

QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34)

Designing Information Devices and Systems II Fall 2018 Elad Alon and Miki Lustig Discussion 5A

I. Impedance of an R-L circuit.

CIRCUIT ANALYSIS II. (AC Circuits)

Fall 2011 ME 2305 Network Analysis. Sinusoidal Steady State Analysis of RLC Circuits

Three Phase Circuits

Chapter 10: Sinusoidal Steady-State Analysis

Two-Port Networks Admittance Parameters CHAPTER16 THE LEARNING GOALS FOR THIS CHAPTER ARE THAT STUDENTS SHOULD BE ABLE TO:

Alternating Current Circuits

ELEC 2501 AB. Come to the PASS workshop with your mock exam complete. During the workshop you can work with other students to review your work.

R-L-C Circuits and Resonant Circuits

BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING. Alternating Current Circuits : Basic Law

Sinusoidal Steady State Power Calculations

MODULE-4 RESONANCE CIRCUITS

LCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module. What you'll learn in Module 9. Module 9 Introduction

Schedule. ECEN 301 Discussion #20 Exam 2 Review 1. Lab Due date. Title Chapters HW Due date. Date Day Class No. 10 Nov Mon 20 Exam Review.

Electric Circuits Fall 2015 Solution #5

PHYSICS 2B FINAL EXAM ANSWERS WINTER QUARTER 2010 PROF. HIRSCH MARCH 18, 2010 Problems 1, 2 P 1 P 2

Single Phase Parallel AC Circuits

General Physics (PHY 2140)

LINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09

ECE Circuit Theory. Final Examination. December 5, 2008

Introduction to AC Circuits (Capacitors and Inductors)

SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING. Self-paced Course

Solution: K m = R 1 = 10. From the original circuit, Z L1 = jωl 1 = j10 Ω. For the scaled circuit, L 1 = jk m ωl 1 = j10 10 = j100 Ω, Z L

Midterm Exam 2. Prof. Miloš Popović

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Electromagnetic Induction Faraday s Law Lenz s Law Self-Inductance RL Circuits Energy in a Magnetic Field Mutual Inductance

RLC Circuit (3) We can then write the differential equation for charge on the capacitor. The solution of this differential equation is

EECE 2510 Circuits and Signals, Biomedical Applications Final Exam Section 3. Name:

Note 11: Alternating Current (AC) Circuits

Handout 11: AC circuit. AC generator

11. AC Circuit Power Analysis

Physics 115. AC: RL vs RC circuits Phase relationships RLC circuits. General Physics II. Session 33

Lecture 4: R-L-C Circuits and Resonant Circuits

CHAPTER 22 ELECTROMAGNETIC INDUCTION

Sinusoidal Steady State Analysis (AC Analysis) Part II

CHAPTER 45 COMPLEX NUMBERS

4/27 Friday. I have all the old homework if you need to collect them.

Power Factor Improvement

12 Chapter Driven RLC Circuits

Figure Circuit for Question 1. Figure Circuit for Question 2

1.3 Sinusoidal Steady State

Chapter 10: Sinusoids and Phasors

CHAPTER 6. Inductance, Capacitance, and Mutual Inductance

Review of DC Electric Circuit. DC Electric Circuits Examples (source:

Electric Circuits II Sinusoidal Steady State Analysis. Dr. Firas Obeidat

Ch. 23 Electromagnetic Induction, AC Circuits, And Electrical Technologies

EE292: Fundamentals of ECE

Transcription:

The University of Toledo s8fs_elci7.fm - EECS:300 Electric Circuits I Electric Circuits I Final Examination Problems Points.. 3. Total 34 Was the exam fair? yes no

The University of Toledo s8fs_elci7.fm - EECS:300 Electric Circuits I Problem points Given is the electrical circuit model shown in Figure.. I I G V I 3 G G 8 S G 9 S I I 0 A V V ρi G3 V V G 3 V 3 V V VV G3 + - G 4 G 3 6 S G 4 7 S ρ 5 Ω I G3 0 I V Figure. The electric circuit model with positive reference directions for currents and voltages that ought to be calculated. Problem Statement Demonstrate an ability to solve the electrical circuit model of Figure. applying the Nodal Voltage Method to determine: (a) voltage V G3 across resistor G 3 and current I G3 that flows through resistor G 3, (b) currnet I V through the voltage source V V, (c) power P V delivered/consumed to/from the electrical circuit by the voltage source V V. Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected.. Select the reference node, and and indicate in Figure. the positive reference direction nodal volatages Then prepare the set of canonical form nodal-voltage equations. Show your work in the space reserved for equation (-). Canonical NVM equations only can be written for two nodes, since nodal voltage V 3 is equal to the electromotive force V V of the voltage source which is connected between the node numbered 3 and the reference node, as it is shown in Figure.. G V - G V - G 3 V 3 -I I -G V + G V - G 3 V 3 I I with V 3 V V ρi G3 ρg 3 V (-)

The University of Toledo s8fs_elci7.fm - 3 EECS:300 Electric Circuits I. Show the expressions for the self and mutual conductances of the nodes, and calculate their values. Show your work in the space reserved for equation (-). Self conductances of the two nodes for which the nodal voltage method equations (-) have been written are, G G G + G 3 8 + 6 4 S 8 S G G + G 4 9 + 7 6 S G G 4 S 9 S G 6 S G (-) G G 0S 3 6 S G 0S G G G 3 G 3 G 8 S 4 7 S 3 8 S G 3 9 S G 3 G 3 G 9 S.3 Show the solution method for the nodal voltages. Show your work in the space reserved for equations (-3). Substituting the known expression (-) for V 3 into the canonical form nodal voltage equations, and rearranging the terms we obtain a system of two equations in two unknown voltages, V and V, (G - G 3 ρg 3 )V - G V -I I G V - G V - G 3 ρg 3 V -I I -G V + G V - G 3 ρg 3 V I I -(G + G 3 ρg 3 )V + G V I I V 3 V V ρi G3 ρg 3 V (-3).4 Calculate the numerical values, for the nodal voltages. Show your work in the space reserved for equations (-4) The system determinant of equations (-3) and the two needed numerator determinants are, G G - G 3 ρg 8 S 3 -G (G - G 3 ρg 3 )G - G(G + G 3 ρg 3 ) G -G - G 3 ρg 9 S 3 G (4-8. 0. 6)6-0 0-7456 S G 3 6 S -I I -G I I G G 3 ρg 3 8. 0. 6 480 -I I G + I I G -0. 3 + 0 0-60 + 0-60AS G 3 8 S G - G 3 ρg 3 -I I I I (G - G 3 ρg 3 ) - I I (-G - G 3 ρg 3 ) G 3 9 S -G - G 3 ρg 3 I I 0(6-0-0. 6) -0(- 0-9. 0. 6) -3480+0800-680AS (-4). G 4 7 S G 4 S G 6 S G 0S

The University of Toledo s8fs_elci7.fm - 4 EECS:300 Electric Circuits I, and the solutions for the nodal voltages are V -60-7456 0.08 V V -680-7456.7V V 3 V V ρg 3 V 0. 6. 0.08 4.8V (-4).5 Using the shown positive reference direction for the current I G3 of the resistor G 3, and applying the passive convention for coupled positive reference directions of the current and voltage of G 3, indicate in Figure. the positive reference direction for the voltage V G3 across the resistor G 3 ; and calculate the value of the voltage V G3 and the current I G3. Sshow your work in the space reserved for equation (-5). V G3 V 0.08 V I G3 V G3 G 3 0.08. 6 0.48A (-5).6 Applying the active convention for coupled positive reference directions of the current and voltage of circuit elements, show in Figure. the positive reference direction for the current I V of the voltage source V V ; then calculate the value of the current I V and the power P V delivered to the circuit by the voltage source V V. Show your work in the space reserved for equation (-6). KCL3: I V (V 3 - V )G + (V 3 - V )G (4.8-0.08)8 + (4.8 -.7)9 37.76+7.965.7A P V I V V V 65.7. 4.8 35 W (-6).7 Based on the result of calculation in part.6, determine whether the voltage source V V delivers, or receives power in the circuit of Figure.. Check the correct answer on both lines below, yes no not applicable x voltage source V V delivers power to the circuit of Figure., x voltage source V V receives power from the circuit of Figure.. Since the active convention has been selected for the coupled positive reference directions of the current and voltage of the voltage source V V, the positive sign of the numerical value of the power P V implies that the voltage source V V delivers power to the circuit of Figure.

The University of Toledo s8fs_elci7.fm - 5 EECS:300 Electric Circuits I Problem points v S + - C (a) i L L v R R R Ω C 0 mf L 5 mh v S 0cosωt V f 60 Hz Figure. An electric circuit specification. (a)electrical model. (b)phasor representation. Z C V il S + - Z L V R (b) Z R Problem Statement For the electrical circuit model of Figure.(a), demonstrate an ability to: (a) prepare its phasor domain representation, (b) determinethe phasor domain representation V R of voltage v R across resistor R, as specified under.,.3 and.4 below, (c) determinethe phasor domain representation of current I L through inductor L, as specified under.5 below, (d) calculate the reactive power component Q L of the complex power S L delivered to the phasor domain impedance Z L of the inductor L, as specified under.6 below. Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected.. For the electrical circuit model of Figure.(a), prepare the phasor domain representation in which the parameters of passive elements R, C, and L are denoted respectively by impedances Z R, Z C, and Z L. Show your work in the space reserved for Figure.(b).. Applying the voltage divider formula to the circuit of Figure.(b), express the real and imaginary parts of the voltage V R across the impedance Z R in terms of circuit element parameters R, L, and C. Show your calculation in the space reserved for equation (-). V R V S Z R Z L Z RL Z R +Z L Z R Z L V Z S V S RL + Z C Z R Z L Z + Z R Z L +(Z R +Z L )Z C (-) Z C R +Z L jωlrv sm -ω LCRV sm R + jωl jωlr + -ω LCR + R + jω L jωc ω L CR V sm [R(ω LC -) + jωl] R (ω LC -) + ω L

The University of Toledo s8fs_elci7.fm - 6 EECS:300 Electric Circuits I.3 Using the derived expression (-), determine numerical values of the real and imaginary parts of the voltage V R. Show your calculation in the space reserved for equation (-) It does make the computations less prone to errors, and faster, if the following five expression evaluated in advance, ω L C (0π) 5 0-3 0 0-3 4. 50 0 7. ω L C - 7. - 6. ω L 0π 5 0 3.885Ω ω L.885 3.6 Ω R (ω L C - ) 6. 37. Ω ω L CR V sm (ω L C -) Re{V R } R (ω L C-) + ω L 7. 0 6. (-) 0.6 V 37. + 3.6 Im{V R } ω L CR V sm ωl R (ω L C-) + ω L 7. 0.9 37. + 3.6 3.3 V.4 Calculate the numerical values of the module and argument of the voltage V R in the circuit of Figure.(b). Show your calculation, and the numerical value of the phasor V R in the space reserved for equation (-3). modv R V R 0.6 + 3.3 argv R arctg 3.3 0.6 V R. _ / 0.3 V. V 7.3 o 0.3 rad (-3).5 Determine the expression for the phasor representation of the current through inductor L. Show your calculation in the space reserved for equation (-4) I L V R Z L V R. /_ 0.3 jω L.885 /_ π/ 5.84 _ / -.7 A 5.84 _/ -7.8 o (.73 - j5.57)a.6 Determine the expression for the reactive power component Q L of the complex power S L delivered to the phasor domain impedance Z L of the inductor L. Show your calculation in the space reserved for equation (-5). (-4) Q L X L I Lef ω L I Lef ω L I L.885 5.84 3. VAR (-5)

The University of Toledo s8fs_elci7.fm - 7 EECS:300 Electric Circuits I Problem 3 points Figure 3. shows the electrical circuit model with two capacitors C and C. V V + - t 0 - t 0 + Q C 60 ff S C v C C v C R C 360 ff V C (0 - ) 5V V V 5V Figure 3. Electrical model of an electric cirucuit. Problem Statement Capacitors C and C have been independently precharged: - capacitor C has been precharged in the configuration of the circuit which existed before the moment t 0; - capacitor C has been precharged to the voltage V C (0 - ) in different circuit (not shown in Figure 3.). Considering that switch S is switched at time t0s from the position shown in Figure 3. to its other position, demonstrate an ability to determine the amounts of: - quantity of charge transfer Q (with respect to the indicated positive reference direction of charge flow) which will occur in the circuit between the time t0, and the time t, when transient current completely stops flowing in the circuit; - voltages across capacitors C and C, V C ( ) and V C ( ) with respect to positive reference directions indicated in Figure 3., at the time when transient current completely stops flowing in the circuit; - the energy stored in the capacitor C at t. Hint # For full credit: all equations, all answers to questions, all circuit models and other graphical representations are expected to be entered into the space designated for them; all shown numerical results must be preceded by the symbolic and numeric expressions whose evaluation produces the shown results. Problem Solution For full credit, explicit demonstration of understanding the following solution steps is expected. 3. Determine the voltage V C (0 + ) across capacitor C at t 0 +. Show your calculation in the space reserved for equation (3-). Since the voltage across a capacitor can not change instantaneously, and V C (0 ) V V 5V, V C (0 + ) V C (0 ) V V 5V (3-)

The University of Toledo s8fs_elci7.fm - 8 EECS:300 Electric Circuits I 3. Determine the charge Q C (0 + ) stored in the capacitance C at t 0 +. Show your calculation in the space reserved for equation (3-). Q C (0 + ) C V C (0 + ) 60 0 5 70 fc (3-) 3.3 Determine the charge Q C (0 + ) stored in the capacitance C at t 0 +. Show your calculation in the space reserved for equation (3-3). Since V C (0 ) is known, Q C (0 + ) C V C (0 + ) C V C (0 ) 360 0-5 5 800 fc (3-3) 3.4 Determine the total charge stored in capacitors C and C at t 0 +. Show your calculation in the space reserved for equation (3-4). Q C (0 + ) + Q C (0 + ) 70 + 800 50 fc (3-4) 3.5 Prepare the relation between voltages V C ( ) and V C ( ) across capacitors C and C at t. Show the prepared relation in the space reserved for equation (3-5). V C ( ) V C ( ) (3-5) 3.6 Prepare the expression for total charge stored on capacitors C and C at t as a function of the voltages V C ( ) and V C ( ), and capacitances C and C. Show your calculation in the space reserved for equation (3-6). Q C ( ) + Q C ( ) C V C ( ) + C V C ( ) (3-6) 3.7 Determine the total quantity of charge stored in capacitors C and C at t. Show your

The University of Toledo s8fs_elci7.fm - 9 EECS:300 Electric Circuits I calculation in the space reserved for equation (3-7). Any charge flow (the current in the circuit) after t0 + only causes a redistribution of charge between C and C ; i.e. the charge only flows from one capacitor to the other, but the total quantity of charge stored on C and C does not change. (3-7) Q C ( ) + Q C ( ) Q C (0 + ) + Q C (0 + ) 50 fc 3.8 Combine equations (3-5) and (3-6) to obtain an equation in which V C ( ) is the only unknown, then solve the equation for V C ( ) and calculate its numerical value. Show your calculation in the space reserved for equation (3-8). Q C ( ) + Q C ( ) C V C ( ) + C V C ( ) (3-8) Q C ( ) + Q C ( ) 50 V C ( ) 6V C + C (60 + 360) 0 5 3.9 Determine the charge Q C ( ) stored on the capacitor C at t. Show your calculation in the space reserved for equation (3-9). Q C ( ) C V C ( ) 360 0-5 6 60 fc (3-9) 3.0 Determine the change in charge Q C in the capacitance C between t0 + and t. Show your calculation in the space reserved for equation (3-0). Q C Q C ( ) - Q C (0 + ) 60-800 360 fc (3-0) 3. Determine the energy stored in the capacitor C at t. Show your calculation in the space reserved for equation (3-).. W C ( ) C V C ( ) 360 0-5 6 6480 fj (3-)

2024 © sciencedocbox.com Privacy Policy | Terms of Service | Feedback