Electrical Engineering Fall 2013 - FE Electric Circuits Review

Sep 18, 2026

Uploaded by Patrick

FE (Fundamentals of Engineering) examination review material focused on Electrical Engineering topics, especially DC circuit analysis and complex numbers used in circuit theory. The review guides problem-solving steps to find voltages, currents, and powers in resistive networks using series/parallel reduction, and then applies KCL and power relations to validate results. It also explains complex-number notation, rectangular and polar forms, Argand diagrams, conversions, conjugates, and arithmetic operations (addition, multiplication, division) through worked examples.

LanguageEnglish

CategoryExam

FormatPDF

Pages46

Reading Time1 h 56 min

AccessFree to download

dc Circuits

Find voltages, currents, and powers

Complex Numbers

Terminology and I(j) operator

Rectangular and polar form

Argand diagram and conversions

Conjugate, addition, multiplication, and division

Worked examples

FUNDAMENTALS OF ENGINEERING (FE) EXAMINATION REVIEW [www.railway-technology.com](www.railway-technology.com) ELECTRICAL ENGINEERING Charles A. Gross, Professor Emeritus Electrical and Comp Engineering Auburn University Broun 212 334.844.1812 [gross@eng.auburn.edu](gross@eng.auburn.edu) FE: Electric Circuits © C.A. Gross EE1- 2 |
EE Review Problems

FE: Electric Circuits © C.A. Gross EE1- | 3 | | --- | --- | 1. dc Circuits: Find all voltages, currents, and powers. FE: Electric Circuits © C.A. Gross EE1- 4 Solution The 8􀀺 and 7􀀺 resistors are in series: R1 􀀠 8 􀀎 7 􀀠 15􀀺 R1 and 10􀀺 are in parallel: R2 􀀠 1 1 1 ~~ ~~ 􀀎 ~~ ~~ 10 R1 􀀠 10 􀀋 R1􀀌 􀀠 6􀀺 10 􀀎 R1 FE: Electric Circuits © C.A. Gross EE1- 5 Solution 4􀀺 and R2 are in series: Rab 􀀠 4 􀀎 R2 􀀠 10􀀺 Solution V10 60 I 􀀠 􀀠 ~~ ~~ 􀀠 6 A c 10 10 􀀋􀀺L 􀀌 FE: Electric Circuits © C.A. Gross EE1- 7 KCL : Ib 􀀠 Ia 􀀐 Ic 􀀠 10 􀀐 6 􀀠 4 A V8 􀀠 8 􀂘 Ib 􀀠 32V (􀀺L) V7 􀀠 7 􀂘 Ib 􀀠 28V (􀀺L) | Absorbed Powers
| | | --- | --- | | R4 􀂘 I2a 􀀠 4 􀀋 10 􀀌 2 􀀠 400WR10 􀂘 I2c 􀀠 10 􀀋 6 􀀌 2 􀀠 360WR7 􀂘 I2b 􀀠 7 􀀋 4 􀀌 2 􀀠 112WR8 􀂘 I2b 􀀠 8 􀀋 4 􀀌 2 􀀠 128W
Total Absorbed Power 􀀠 1000W
Power Delivered by Source 􀀠 Vs 􀂘 Ia | In General: PABS = PDEV (Tellegen's Theorem)
􀀠 100 􀀋 10 􀀌 􀀠 1000W | | FE: Electric Circuits © C.A. Gross EE1- 8 | | 2. Complex Numbers 9 Consider x 2 􀀐 2 x 􀀎 5 􀀠 0 x 􀀠 2 􀁲 (􀀐2)2 􀀐 4(1)(5) 2 􀂘1 􀀠 2 􀁲 􀀐16 2 4 􀀐1 􀀠 1 􀁲 􀀠 1 􀁲 2 􀀐1 2 The numbers "1􀁲 2 􀀐1 " are called complex numbers Summer 2008 The “I”(j) operator 10 Math Department.... Define i 􀀠 􀀐1 x 􀀠 1 􀁲 2i ECE Department Define j 􀀠 􀀐1 x 􀀠 1 􀁲 j2 We choose ECE notation! Terminology… Rectangular Form..... Z 􀀠 X 􀀎 jY 􀀠 a complex number X 􀀠􀂃 e 􀀋 Z 􀀌 􀀠 real part of ZY 􀀠 Im 􀀋 Z 􀀌 􀀠 imaginary part of Z Summer 2008 Polar Form 11 Math Department..... Z 􀀠 R 􀂘 e 􀁔i 􀀠 a complex number R 􀀠 | Z |􀀠 modulus of Z 􀁔 􀀠 arg 􀀋 Z 􀀌 􀀠 argument of Z 􀀋radians 􀀌 ECE Department..... Z 􀀠 Z􀂑􀁔 􀀠 a complex number Z 􀀠 | Z |􀀠 magnitude of Z 􀁔 􀀠 ang 􀀋 Z 􀀌 􀀠 angle of Z 􀀋degrees 􀀌 The Argand Diagram It is useful to plot complex numbers in a 2-D cartesian space, creating the so-called Argand Diagram (Jean Argand (1768-1822)). “imaginary” axis (Y) +2 Z 􀀠 X 􀀎 jY 􀀠 1􀀎 j2 ~~ ~~ “real” axis (X) +1 Summer 2008 12 Conversions 13 Retangular 􀁯 Polar Z 􀀠 X 2 􀀎 Y2 􀁔 􀀠 tan􀀐1 􀂧􀂨􀂩 ~~ ~~YX~~ ~~ 􀂷􀂹􀂸 Polar 􀁯 Retangular..... X 􀀠 Z 􀂘 cos 􀀋􀁔 􀀌 Y 􀀠 Z 􀂘 sin 􀀋􀁔 􀀌 Summer 2008 Y X Example: 14 Z 􀀠 3 􀀎 j4 X 􀀠􀂃 e 􀀋 Z 􀀌 􀀠 3 Y 􀀠 Im 􀀋 Z 􀀌 􀀠 4 Rect 􀁯 Polar 4 Z 􀀠 32 􀀎 42 􀀠 5 3 􀁔􀀠Sumnr10􀂧8􀂨􀂩 ~~ ~~43~~ ~~ 􀂷􀂹􀂸 􀀠 0.9273 rad 􀀠 53.10 Conjugate 15 Z 􀀠 X 􀀎 jY 􀀠 Z 􀂑􀁔 Z * 􀀠 conjugate of Z 􀀠 X 􀀐 jY 􀀠 Z 􀂑 􀀐 􀁔 Example... (3 􀀎 j4)* 􀀠 3 􀀐 j4 􀀠 5􀂑 􀀐 53.10 Summer 2008 Addition (think rectangular) 16 A 􀀠 a 􀀎 jb 􀀠 A􀂑 􀁄 B 􀀠 c 􀀎 jd 􀀠 B􀂑􀁅 􀀠 3 􀀎 j4 􀀠 5􀂑 53.10 􀀠 5 􀀐 j12 􀀠 13􀂑 􀀐 67.40 A 􀀎 B 􀀠 (a 􀀎 jb) 􀀎 (c 􀀎 jd) 􀀠 (a 􀀎 c) 􀀎 j (b 􀀎 d ) A 􀀎 B 􀀠 (3 􀀎 j4) 􀀎 (5 􀀐 j12) 􀀠 (3 􀀎 5) 􀀎 j(4 􀀐 12) 􀀠 8 􀀐 j8 Summer 2008 Multiplication (think 17 polar) A 􀀠 a 􀀎 jb 􀀠 A􀂑 􀁄 B 􀀠 c 􀀎 jd 􀀠 B􀂑􀁅 􀀠 3 􀀎 j4 􀀠 5􀂑 53.10 􀀠 5 􀀐 j12 􀀠 13􀂑 􀀐 67.40 A 􀂘 B 􀀠 ( A􀂑 􀁄 ) 􀂘 (B􀂑􀁅 ) 􀀠 A 􀂘 B􀂑 ( 􀁄 􀀎 􀁅 ) A 􀂘 B 􀀠 (5􀂑53.10 ) 􀂘 (13􀂑 􀀐 67.40 ) 􀀠 (5) 􀂘 (13)􀂑(53 .10 􀀐 67 .40 ) 􀀠 65􀂑 􀀐 14.30 Summer 2008 | Division (think polar)
| | | --- | --- | | A 􀀠 a 􀀎 jb 􀀠 A􀂑 􀁄 B 􀀠 c 􀀎 jd 􀀠 B􀂑􀁅 | 􀀠 3 􀀎 j4 􀀠 5􀂑 53.10
􀀠 5 􀀐 j12 􀀠 13􀂑 􀀐 67.40 | |
AB 􀀠 AB􀂑􀂑~~ ~~~~ ~~ 􀀠 􀂨􀂧􀂩 ~~ ~~AB􀂷􀂹􀂸􀂑( 􀁄 􀀐 􀁅 )
AB 􀀠 ~~ ~~135􀂑􀂑36.13040~~ ~~􀂷􀂹􀂸 􀀠 􀂧􀂩􀂨 153􀂷􀂹􀂸􀂑 􀀋 53.10 􀀐 􀀋􀀐67.40 􀀌 􀀌􀀠 0.3846􀂑 120.50
Summer 2008 18 | | |
Multiplication (rectangular)

A 􀂘 B 􀀠 (a 􀀎 jb) 􀂘 􀀋 c 􀀎 jd 􀀌
􀀠 􀀋 ac 􀀐 bd 􀀌 􀀎 j 􀀋 ad 􀀎 bc 􀀌 A 􀂘 B 􀀠 (3 􀀎 j4) 􀂘 (5 􀀐 j12)
􀀠 (15 􀀎 48) 􀀎 j (􀀐36 􀀎 20)
􀀠 63 􀀐 j16 􀀠 65􀂑 􀀐 14.30
Summer 2008
19 | EL
EC
38 | | --- | --- | 10 Addition ( polar) 5􀂑 53.10 20 Complex number addition is the same as "vector addition"! Summ

FAQs

How are complex-number operations handled in the review?

Addition is treated like vector addition (rectangular thinking), while multiplication and division are handled using polar representations with magnitudes and angles.

Sep 18, 2026

Uploaded by Patrick