[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-300320-105":59,"doc-detail-300320-en":123},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":116,"head_meta":118,"extra_data":120,"updated_unix":122},105,"en","electrical-engineering-fall-2013-fe-electric-circuits-review","Electrical Engineering Fall 2013 - FE Electric Circuits Review","","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.",{"@graph":69,"@context":115},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/electrical-engineering-fall-2013-fe-electric-circuits-review/300320/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/electrical-engineering-fall-2013-fe-electric-circuits-review/300320.png","ImageObject",300,407,{"name":92,"@type":93},"Patrick","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-18",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109],{"name":110,"@type":111,"acceptedAnswer":112},"How are complex-number operations handled in the review?","Question",{"text":113,"@type":114},"Addition is treated like vector addition (rectangular thinking), while multiplication and division are handled using polar representations with magnitudes and angles.","Answer","https://schema.org",{"og:url":83,"og:type":117,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":119,"canonical":83},"index,follow",{"doc_id":121,"site_id":62},300320,1789773821,{"code":4,"msg":5,"data":124},{"doc_id":121,"user_id":125,"nickname":92,"user_avatar":126,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":127,"file_id":128,"file_url":129,"file_type":130,"file_size":131,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":132,"language":133,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":134,"faqs":135,"seo_title":136,"seo_description":67,"update_tm":122,"read_time":137,"preview_page_count":4},549758146520,"https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470","FUNDAMENTALS OF ENGINEERING (FE) EXAMINATION REVIEW  \n[www.railway-technology.com](www.railway-technology.com)  \nELECTRICAL ENGINEERING  \nCharles A. Gross, Professor Emeritus Electrical and Comp Engineering Auburn University Broun 212 334.844.1812 [gross@eng.auburn.edu](gross@eng.auburn.edu)  \nFE: Electric Circuits © C.A. Gross EE1- 2  \n\n| \u003Cbr> EE Review Problems\u003Cbr>\u003Cbr>\u003Cbr>FE: Electric Circuits © C.A. Gross EE1- | 3 |\n| --- | --- |\n\n1. dc Circuits:  \nFind all voltages, currents, and powers.  \nFE: Electric Circuits © C.A. Gross EE1- 4  \nSolution  \nThe 8􀀺 and 7􀀺 resistors are in series:  \nR1 􀀠 8 􀀎 7 􀀠 15􀀺  \nR1 and 10􀀺 are in parallel:  \nR2 􀀠  \n1  \n1 1  \n~~ ~~ 􀀎 ~~ ~~  \n10 R1  \n􀀠 10 􀀋 R1􀀌  􀀠 6􀀺 10 􀀎 R1  \nFE: Electric Circuits © C.A. Gross EE1- 5  \nSolution  \n4􀀺 and R2 are in series: Rab 􀀠 4 􀀎 R2 􀀠 10􀀺  \nSolution  \nV10 60 I 􀀠  􀀠 ~~ ~~ 􀀠 6 A  \nc 10 10  \n􀀋􀀺L 􀀌  \nFE: Electric Circuits © C.A. Gross EE1- 7  \nKCL :  \nIb 􀀠 Ia 􀀐 Ic 􀀠 10 􀀐 6 􀀠 4 A  \nV8 􀀠 8 􀂘 Ib 􀀠 32V (􀀺L)  \nV7 􀀠 7 􀂘 Ib 􀀠 28V (􀀺L)  \n| Absorbed Powers  \u003Cbr>|  |\n| --- | --- |\n| R4 􀂘 I2a 􀀠 4 􀀋 10 􀀌 2 􀀠 400WR10 􀂘 I2c 􀀠 10 􀀋 6 􀀌 2 􀀠 360WR7 􀂘 I2b 􀀠 7 􀀋 4 􀀌 2 􀀠 112WR8 􀂘 I2b 􀀠 8 􀀋 4 􀀌 2 􀀠 128W\u003Cbr>Total Absorbed Power 􀀠 1000W\u003Cbr>Power Delivered by Source 􀀠 Vs 􀂘 Ia | In General: PABS = PDEV (Tellegen's Theorem)\u003Cbr>􀀠 100 􀀋 10 􀀌 􀀠 1000W |\n| FE: Electric Circuits © C.A. Gross EE1- 8 |  |\n\n2. Complex Numbers  \n9  \nConsider x 2 􀀐 2 x 􀀎 5 􀀠 0  \nx 􀀠  \n2 􀁲 (􀀐2)2 􀀐 4(1)(5)  \n2 􀂘1  \n􀀠  \n2 􀁲 􀀐16  \n2  \n4 􀀐1  \n􀀠 1 􀁲 􀀠 1 􀁲 2 􀀐1 2  \nThe numbers \"1􀁲 2 􀀐1 \" are called complex numbers   \nSummer 2008  \nThe “I”(j) operator  \n10  \nMath Department.... Define i 􀀠 􀀐1 x 􀀠 1 􀁲 2i  \nECE Department Define j 􀀠 􀀐1 x 􀀠 1 􀁲 j2  \nWe choose ECE notation! Terminology…  \nRectangular Form.....  \nZ 􀀠 X 􀀎 jY 􀀠 a complex number X 􀀠􀂃 e 􀀋 Z 􀀌 􀀠 real part of ZY 􀀠 Im 􀀋 Z 􀀌 􀀠 imaginary part of Z  \nSummer 2008  \nPolar Form  \n11  \nMath Department.....  \nZ 􀀠 R 􀂘 e 􀁔i 􀀠 a complex number R 􀀠 | Z |􀀠 modulus of Z  \n􀁔 􀀠 arg 􀀋 Z 􀀌 􀀠 argument of Z 􀀋radians 􀀌  \nECE Department.....  \nZ 􀀠 Z􀂑􀁔 􀀠 a complex number Z 􀀠 | Z |􀀠 magnitude of Z  \n􀁔 􀀠 ang 􀀋 Z 􀀌 􀀠 angle of Z 􀀋degrees 􀀌  \nThe Argand Diagram  \nIt is useful to plot complex numbers in a 2-D cartesian space, creating the so-called Argand Diagram (Jean Argand (1768-1822)).  \n“imaginary” axis (Y)  \n+2   \nZ 􀀠 X 􀀎 jY 􀀠 1􀀎 j2  \n~~ ~~ “real” axis (X)  \n+1  \nSummer 2008  \n12  \nConversions  \n13  \nRetangular 􀁯 Polar Z 􀀠  X 2 􀀎 Y2 􀁔 􀀠 tan􀀐1 􀂧􀂨􀂩 ~~ ~~YX~~ ~~ 􀂷􀂹􀂸  \nPolar 􀁯 Retangular..... X 􀀠 Z 􀂘 cos 􀀋􀁔 􀀌  \nY 􀀠 Z 􀂘 sin 􀀋􀁔 􀀌  \nSummer 2008  \nY  \nX  \nExample:  \n14  \nZ 􀀠 3 􀀎 j4  \nX 􀀠􀂃 e 􀀋 Z 􀀌 􀀠 3 Y 􀀠 Im 􀀋 Z 􀀌 􀀠 4  \nRect 􀁯 Polar    \n4  \nZ 􀀠  32 􀀎 42 􀀠 5 3  \n􀁔􀀠Sumnr10􀂧8􀂨􀂩 ~~ ~~43~~ ~~ 􀂷􀂹􀂸 􀀠 0.9273 rad 􀀠 53.10  \nConjugate  \n15  \nZ 􀀠 X 􀀎 jY 􀀠 Z 􀂑􀁔  \nZ * 􀀠 conjugate of Z 􀀠 X 􀀐 jY 􀀠 Z 􀂑 􀀐 􀁔  \nExample...  \n(3 􀀎 j4)* 􀀠 3 􀀐 j4 􀀠 5􀂑 􀀐 53.10  \nSummer 2008  \nAddition (think rectangular)  \n16  \nA 􀀠 a 􀀎 jb 􀀠 A􀂑 􀁄 B 􀀠 c 􀀎 jd 􀀠 B􀂑􀁅  \n􀀠 3 􀀎 j4 􀀠 5􀂑 53.10  \n􀀠 5 􀀐 j12 􀀠 13􀂑 􀀐 67.40  \nA 􀀎 B 􀀠 (a 􀀎 jb) 􀀎 (c 􀀎 jd)  \n􀀠 (a 􀀎 c) 􀀎 j (b 􀀎 d )  \nA 􀀎 B 􀀠 (3 􀀎 j4) 􀀎 (5 􀀐 j12)  \n􀀠 (3 􀀎 5) 􀀎 j(4 􀀐 12) 􀀠 8 􀀐 j8  \nSummer 2008  \nMultiplication (think  \n17  \npolar)  \nA 􀀠 a 􀀎 jb 􀀠 A􀂑 􀁄 B 􀀠 c 􀀎 jd 􀀠 B􀂑􀁅  \n􀀠 3 􀀎 j4 􀀠 5􀂑 53.10  \n􀀠 5 􀀐 j12 􀀠 13􀂑 􀀐 67.40  \nA 􀂘 B 􀀠 ( A􀂑 􀁄 ) 􀂘 (B􀂑􀁅 )  \n􀀠 A 􀂘 B􀂑 ( 􀁄 􀀎 􀁅 )  \nA 􀂘 B 􀀠 (5􀂑53.10 ) 􀂘 (13􀂑 􀀐 67.40 )  \n􀀠 (5) 􀂘 (13)􀂑(53 .10 􀀐 67 .40 ) 􀀠 65􀂑 􀀐 14.30  \nSummer 2008  \n\n| Division (think polar)\u003Cbr>|  |\n| --- | --- |\n| A 􀀠 a 􀀎 jb 􀀠 A􀂑 􀁄 B 􀀠 c 􀀎 jd 􀀠 B􀂑􀁅 | 􀀠 3 􀀎 j4 􀀠 5􀂑 53.10\u003Cbr>􀀠 5 􀀐 j12 􀀠 13􀂑 􀀐 67.40 |\n| \u003Cbr>AB 􀀠 AB􀂑􀂑~~ ~~~~ ~~ 􀀠 􀂨􀂧􀂩 ~~ ~~AB􀂷􀂹􀂸􀂑( 􀁄 􀀐 􀁅 )\u003Cbr>AB 􀀠  ~~ ~~135􀂑􀂑36.13040~~ ~~􀂷􀂹􀂸 􀀠 􀂧􀂩􀂨 153􀂷􀂹􀂸􀂑 􀀋 53.10 􀀐 􀀋􀀐67.40 􀀌 􀀌􀀠 0.3846􀂑 120.50\u003Cbr>Summer 2008 18 |  |\n\n| \u003Cbr>Multiplication (rectangular)\u003Cbr>\u003Cbr>A 􀂘 B 􀀠 (a 􀀎 jb) 􀂘 􀀋 c 􀀎 jd 􀀌\u003Cbr>􀀠 􀀋 ac 􀀐 bd 􀀌 􀀎 j 􀀋 ad 􀀎 bc 􀀌 A 􀂘 B 􀀠 (3 􀀎 j4) 􀂘 (5 􀀐 j12)\u003Cbr>􀀠 (15 􀀎 48) 􀀎 j (􀀐36 􀀎 20)\u003Cbr>􀀠 63 􀀐 j16 􀀠 65􀂑 􀀐 14.30\u003Cbr>Summer 2008\u003Cbr>19 | EL\u003Cbr>EC\u003Cbr>38 |\n| --- | --- |\n\n10  \nAddition ( polar)  \n5􀂑 53.10  \n20  \nComplex number addition is the same as \"vector addition\"!  \nSumm","cbCaifMoIKlRhorB","https://ap.wps.com/l/cbCaifMoIKlRhorB","pdf",512920,46,"English","# dc Circuits\n## Find voltages, currents, and powers\n# Complex Numbers\n## Terminology and I(j) operator\n## Rectangular and polar form\n## Argand diagram and conversions\n## Conjugate, addition, multiplication, and division\n## Worked examples","[{\"question\":\"How are complex-number operations handled in the review?\",\"answer\":\"Addition is treated like vector addition (rectangular thinking), while multiplication and division are handled using polar representations with magnitudes and angles.\"}]","Electrical Engineering Fall 2013 - FE Electric Circuits Review | PDF",116]