[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-656897-105":59,"doc-detail-656897-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","phasor-diagram-and-impedance-in-ac-circuits","Phasor Diagram and Impedance in AC Circuits","","Instructional notes explain constructing phasor diagrams for single-phase AC circuits using passive and sign conventions. It covers relationships between voltage and current phasors, including resistive, inductive, and capacitive behavior, and how impedance and reactance form the complex impedance. The material derives key expressions for series RL, parallel RL/RLC, and discusses power factor, real power, average power, and phase-angle effects using phasor-based methods and impedance triangles.",{"@graph":69,"@context":122},[70,84,105],{"@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":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/phasor-diagram-and-impedance-in-ac-circuits/656897/",{"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/phasor-diagram-and-impedance-in-ac-circuits/656897.png","ImageObject",300,407,{"name":92,"@type":93},"PakDamar76","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-10-25",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you draw a phasor diagram for an AC series circuit using passive sign convention?","Question",{"text":112,"@type":113},"Choose the reference voltage phasor and place the current phasor and component voltage phasors according to phase relations implied by passive sign convention. Superimpose component phasors to obtain the total phasor diagram.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is complex impedance and how is it related to the impedance triangle?",{"text":117,"@type":113},"Complex impedance is expressed as resistance plus j times reactance. Its real part corresponds to resistance and its imaginary part corresponds to reactance, forming the impedance triangle used to compute phase relationships.",{"name":119,"@type":110,"acceptedAnswer":120},"How do phase angle and power factor affect real and average power in AC circuits?",{"text":121,"@type":113},"Average power depends on the cosine of the phase angle between voltage and current. Power factor is that cosine, so lagging or leading phase changes the power factor and thus the computed average real power.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},656897,1792971351,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},962090893057,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","oue-Scngle phase cscuts4oco to dsaw a phaso diagsam:In a ac asuitte Vottagesand currents aensre phasors,so the hvoltages otmust   m a aso  a th c a  o potasity,eitte b an aseo0    usin + and-mask thek t source current I showing its cdirection byan aQQow Asa Conventon,the cuaQontI must leavethe pos86velteamcnal o6 the 8oaoce 5ep  2:Mask the octage acso   and the cuon  ual ot   o(cowcng the  passiveign convontion   have maske$V_R$ and TR$ for the resisteance $R$ stanv, and $I_L$ efor theCaduclance LstepB上 TogetComplete phasox diagram,supexzcmposeau theindividualas m  sthe commonphasoxamong themStep 3:①aw  tte phasor diagram  o cdidualComponen ts,(① Fox resis tan ce,R: The curent s tn phase it theotage ro he oa     diection-awo  the cae phaso   asoalong te reberence diochon    lags ta otta  9 °   rao he Votage phasr   along theYeJeren le di&ochonDraw the cument phasorI   90°   laggg Step4- T0 qet  asor aramSuperimposeall fhe individuaPhasoYdiagvam  \n1.  \nPage No:  \nDate:   /    /  \n   gisg  \nt mo as  \n—  \nmo hem  \n&Eep 5  \nFcnd the phasor e aram  \naddition o   and V   \n0ABC  \nStep6:-  \nonce  the phasor duagram  drawon, e canfake the help 66Complex algebra to makecalculatons  \nmarkcng the  \nrefexenle  \nas posiHve  \nd`&ectón  \nYeal akls  \nthe imaginaryT= TL0°  \naxis to be y  \nancl  \nV,=j IxL = TjxL =IjoL  \n二卫  \nV=VR+  \n三工R十  \n三卫史十卫  \n卫尺十七  \nPhasor duagram o6'R'  \na°  \n本  \nRVk火CUD=πfv  \n@  \ny  \nVR  \n⑥ Phasor dcagram 6bq0°CV工  \nGPhasoa dlagram forL,8otated by 98  \nVL  \n918  \nTL  \n The  complet    hasor  duagram  \nV1=6IxLC  \nVy一平ZQAVR=IRTR  \nL  \n②  \n③  \nWhat is impedance trianglen taie.Fan  tt  o te ottage  phaso to te cuent phas 1   acomplex  qvanttty,called   omplex mpedance  \nThe &eal past is called9Q8istanc andimaginary y is called reactanctae .Thus,Co mplex lmpedance -(resistancae)+jCreactan ce)  \nX  \n100  \niks  \nX= R+jX  \nFog the Seues RL tiscut  \nZ=VR+jwL=zL工00  \nZ=1R²+CL)²  \nQ=tan⁻¹(wL  \n Impedence hian  \n旧ZXL0。RA  \nrom the  phasor  diagram,we  can seperate the vo tagel   each d  l is vded   \nI the &esatt is the cmpedence triangle  \nRL  RC℃  \nSesies RL ascut  \nheenc      \n*The VR and V be the voclage  \ndoops across sesistanlo  \n and  cndctance ely  \n V=V+V  \n④  \nPage No:  \nDate:  \n/  \n/  \n老不√IR  \n矩R44L000VR—×Vw=2πf②  \n大 eiseut  \n矛V= TR土TXL  \n三TR+TjaL  \n三TCR+jwoL  \nV=TCR+X  \n8e&ies Rc uscut.-  \n人AAC4Vc十④  \n。二只e工VeV=TZ  \n and v be he oagdrops arosSresistanlR and tnductance L,respechively.  \n V=VR+Vc=TR+IX三T(R+Vjwc)二TCR+xc)  \n n phas a ree    a  Cument T ,bat fox thecapauitance,the voctage vc israwon agthe ct   十V= I CR+xc)  \nPasallel RL and Rc uruuit  \n入ILR冒L  \nThe cunventthro ugh the resistance andtheCum entthroughthe cnductanue is IL  \n*The totallument I= IR+I关The curent,T=VYwthee Yis the complex admit ance of the paratlelRL uut.Ater wattonaluisatton,we can wsete工 at     Yis called Condu ctance and tmaqenarypaxt is calledSvs ceptance Thvs,We Can writey= Gt+jB=Condcuctance+susceptancQ关 工=IR+IL=VY=VCGr+jB)paso aamke Stast the phasor dlagramb akcn the o asor a erence  The  curent 卫1  pase it    Ilags ottage  The oswetantcurrent phasor I is then foonund by addingphasoas TR and I0-工←V工无  \nPage No:  \nDate:  /  \nPasalled Rc uscutThe  ua   teougAenis6oxR andthecuont工ctsoughCapautoxc axeivon as工x2—2C工个=R工尺▽工= Vx →CYw) Vjwcusang  kCl,tte  tota/ cen7三T+十Vcjwc)V,+ j we)=V(Y)whexelouduetauce G=YRSuscptan co B=WCPhasor diagram王王→vJK*Taking voltage akias inphase withotagVbut Ytue uont见leads 肱e  \n⑤  \n ottage 8 cuoQont phaso又7is then found by addinforsorR andTc  \nSesies RLC cxcut上  \nu& aut duagsam  \n尺C—V  \nphasor clagram²  \nwten L> Ywc(0 XL>Xc  \nVL个VL+Vc\u003C6VB工Vc  \nwtonWL \u003CYwc CC)X,∠Xc  \nMV0VL+Ue上VC↓  \nKVL equ atiogwation  \nV=VR+V+Ve=TR+ Icjx)+工C-jxc)=工[R+JxL-jx=工Zhtuse Zi the complex pedante e gen aa  \n⑥  \nPage No:  \nDate:   /  \nZ干R+jCxL一×c)Ltan 1 1=R2co0 -2+(u/RLC uxuutIduchve u'scuit上wten wL> Ywc the phase angle%the cuaent phaso8 is negative·The curent lags thea   ae a   Capacitve u'scuit: wuuenr  phaso  i postve  T e  usent  leas the  vottag","cbCaicNGFLoHph9X","https://ap.wps.com/l/cbCaicNGFLoHph9X","pdf",9527854,25,"English","# Single-phase AC phasor basics\n## Passive sign convention and phasor relationships\n## Impedance triangle and complex impedance\n# RL, RC, and RLC phasor diagrams\n## Series circuits\n## Parallel circuits and admittance\n# Phasor-based power factor and power calculations","[{\"question\":\"How do you draw a phasor diagram for an AC series circuit using passive sign convention?\",\"answer\":\"Choose the reference voltage phasor and place the current phasor and component voltage phasors according to phase relations implied by passive sign convention. Superimpose component phasors to obtain the total phasor diagram.\"},{\"question\":\"What is complex impedance and how is it related to the impedance triangle?\",\"answer\":\"Complex impedance is expressed as resistance plus j times reactance. Its real part corresponds to resistance and its imaginary part corresponds to reactance, forming the impedance triangle used to compute phase relationships.\"},{\"question\":\"How do phase angle and power factor affect real and average power in AC circuits?\",\"answer\":\"Average power depends on the cosine of the phase angle between voltage and current. Power factor is that cosine, so lagging or leading phase changes the power factor and thus the computed average real power.\"}]","Phasor Diagram and Impedance in AC Circuits | PDF",63]