[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-656893-105":59,"doc-detail-656893-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","520phasor20diagram-passive-circuit-elements-phasor-diagram-series-rl-series-rc-series-rlc-parallel-rl-parallel-rc-parallel-rlc","5%20Phasor%20diagram - Passive Circuit Elements Phasor Diagram - Series RL - Series RC - Series RLC - Parallel RL - Parallel RC - Parallel RLC","","Phasor diagrams for AC electric circuit analysis are developed for passive elements and common R, L, C configurations. The content defines voltage and current phasors in polar and rectangular forms, relates impedance additions for series RL, RC, and RLC networks, and derives resulting voltage phasors across individual components. Parallel RL, RC, and RLC cases are handled through admittance summation with currents phasors, followed by impedance and voltage/current reconstruction. Worked numeric examples compute ZT, VR, VL, VC, and corresponding phasor angles for each topology.",{"@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/520phasor20diagram-passive-circuit-elements-phasor-diagram-series-rl-series-rc-series-rlc-parallel-rl-parallel-rc-parallel-rlc/656893/",{"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/520phasor20diagram-passive-circuit-elements-phasor-diagram-series-rl-series-rc-series-rlc-parallel-rl-parallel-rc-parallel-rlc/656893.png","ImageObject",300,407,{"name":92,"@type":93},"Guten tag","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-25",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How are voltage and current phasors represented for passive circuit elements?","Question",{"text":112,"@type":113},"Voltage and current are expressed as phasors in polar form, and the document notes that the given phasor angles correspond to the in-phase relationship between current and voltage for the passive reference used.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the method for series RL, RC, and RLC circuits in phasor form?",{"text":117,"@type":113},"Impedances are added in series to form ZT, then component voltage phasors are calculated using VR=IZR, VL=IZL, and VC=IZC, with results provided in both polar and rectangular forms.",{"name":119,"@type":110,"acceptedAnswer":120},"How are parallel RL, RC, and RLC circuits analyzed using phasors?",{"text":121,"@type":113},"Admittances are summed to obtain YT, then the total current phasor and branch current phasors are computed. The impedance and resulting branch voltages or currents are then determined from the phasor relationships.","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},656893,1793030799,{"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":24,"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":144,"read_time":145},687212321768,"https://ap-avatar.wpscdn.com/avatar/a0010bdbe886d2fe77?x-image-process=image/resize,m_fixed,w_180,h_180&k=1789897067658708522","Electric Circuits II Phasor Diagram  \nDr. Firas Obeidat  \n1  \nPhasor diagram for the Passive Circuit Elements  \nLet 􀢏 (􀢚) = 􀡵 􀢓􀢉􀢕􀢙(􀣓􀢚 + 􀣘)  \nIn polar form  \n\n| But Vm ∟θ and Im ∟ 􀣘 merely represent the general voltage and current phasors V and I. Thus |  |  |\n| --- | --- | --- |\n|  | |  |\n| The angles θ and 􀣘 are equal, so that the current and voltage are always in phase. |  |  |\n\n Let  􀢏 (􀢚) = 􀡵􀢓 􀢉􀢕 􀢙 􀣓􀢚 + 􀣘  = 􀡵􀢓 􀢋􀢐(􀣓􀢚+􀣘)  \nDr. Firas Obeidat – Philadelphia University  \n2  \nPhasor diagram for series RL circuit  \nExample: for the circuit shown in figure (a), draw the phasor circuit , impedance diagram and voltages phasor diagram.  \nV=100∟0, so the phasor circuit is shown in figure (b) .  \nZT =ZR +ZL=3Ω+j4Ω =5∟53. 13o  \nImpedance diagram is shown in figure (c) .  \n􀜫 = 􀯏􀯓~~ ~~􀯍 = 505∟03~~ ~~1􀯢3o= 20∟−53. 13o  \nVR =IZR=(20∟-53. 13oA)(3∟0Ω)=60∟-53. 13o V. VL=IZL=(20∟-53. 13o A)(4∟90Ω)=80∟36.87o V.  \nPhasor diagram is shown in figure (d) . In rectangular form  \nVR=60∟-53. 13o =36-j48V. VL=80∟36.87o =64+j48V.  \nV=VR +VL=36-j48+64+j48=100+j0V=100∟0 V.  \n4  \nDr. Firas Obeidat – Philadelphia University  \nPhasor diagram for series RC circuit  \nExample: for the circuit shown in figure (a), draw the phasor circuit , impedance diagram and voltages phasor diagram.  \nI=5∟0, so the phasor circuit is shown in figure (b) .  \nZT =ZR +ZC=6Ω-j8Ω=10∟-53. 13o  \nImpedance diagram is shown in figure (c) .  \n􀜸 = 􀜫􀜼 􀯍= (5∟53. 13o)(10∟−53. 13o )=50∟0 V  \nVR =IZR=(5∟53.13o)(6∟0o )=30∟53.13o0 V  \nVC =IZC=(5∟53. 13oA)(8∟-90Ω)=40∟-36.87o V.  \nPhasor diagram is shown in figure (d) . In rectangular form  \nVR=30∟53. 13o=18+j24 V VC=40∟-36.87o =32-j24V.  \nV=VR +VC=18+j24+32-j24=50+j0=50∟0 V.  \n5  \nDr. Firas Obeidat – Philadelphia University  \nPhasor diagram for series RLC circuit  \nExample: for the circuit shown in figure (a), draw thephasor circuit , impedance diagram and voltages phasor diagram.  \nV=50∟0, so the phasor circuit is shown in figure (b) .  \nZT =ZR +ZL+ZC=3Ω+7Ω-j3Ω =3+j4= 5∟53. 13o  \nImpedance diagram is shown in figure (c) .  \n􀜫 = 􀯏􀯓~~ ~~􀯍 = 5∟301􀯢3o= 10∟−53. 13o  \nVR =IZR=(10∟−53.13o)(3∟0o )=30∟−53.13o0 V  \nVL=IZL=(10∟-53. 13o A)(7∟90Ω)=70∟36.87o V.  \nVC =IZC=(10∟-53. 13oA)(3∟-90Ω)=30∟-143. 13o V.  \nPhasor diagram is shown in figure (d) .  \nIn rectangular form  \nVR=30∟−53.13o0 V=18-j24 V  \nVL=70∟36.87o V=56+j42 V.  \nVC=30∟-143. 13o V=-24-j18.  \nV=VR +VL+VC=18-j24+56+j42-24-j18  \nV=50+j0=50∟0 V.  \nDr. Firas Obeidat – Philadelphia University  \n6  \nPhasor diagram for parallel RL circuit  \nExample: for the circuit shown in figure (a), draw thephasor circuit , impedance diagram and currents phasor diagram.  \nV=20 ∟53 .13 , so the phasor circuit is shown in figure (b) .  \nYT =YR +YL=1/3. 33+1/j2. 5=0. 3-j0.4 =0. 5∟-53. 13  \n􀜼􀜶 = 1􀯒􀯍 = 0.5~~ ~~∟53.13 =2 ∟53. 13 Impedance diagram is shown in figure (c) .  \n􀜫 = 􀯏􀯓~~ ~~􀯍 = 220~~ ~~.1313􀯢o= 10∟0o  \n􀜫 􀜴 = 􀯏􀯓~~ ~~􀯋 = 20∟53~~ ~~33.~~ ~~130~~o~~􀯢~~ ~~ = 6∟53. 13o  \n􀜫 􀜮 = 􀯏􀯓~~ ~~􀯅 = 20∟2~~ ~~539.~~ ~~130~~o~~􀯢~~ ~~ = 8∟−36.87o  \nCurrents Phasor diagram is shown in figure (d) .  \nI=IR+IL=3. 6+j4. 8+6. 4-j4. 8=10+j0=10 ∟0.  \nDr. Firas Obeidat – Philadelphia University  \n7  \nPhasor diagram for parallel RC circuit  \nExample: for the circuit shown in figure (a), draw thephasor circuit , impedance diagram and currents phasor diagram.  \nI=10∟0, so the phasor circuit is shown in figure (b) .  \nYT =YR +YC=1/1. 67+1/-j2. 5=0. 6+j0.8 =1∟53. 13  \n􀜼􀜶 = 1􀯒􀯍 = ~~ 1~~∟153.13 =1∟-53. 13 Impedance diagram is shown in figure (c) .  \n􀜸 = 􀜫􀜼 􀯍 = (10 ∟0􀝋 )(1 ∟-53. 13)= 10∟−53. 13o  \n 􀯏   10 ∟−53. 13􀯢  \n􀜫 􀜴 = 􀯓􀯋 = 1. 67∟0o = 6∟−53. 13o  \n􀜫 􀜥 = 􀯏􀯓~~ ~~􀮼 = 10∟~~1 25~~.193􀯢0o= 8∟36.87o  \nCurrents Phasor diagram is shown in figure (d) .  \nDr. Firas Obeidat – Philadelphia University  \n8  \nPhasor diagram for parallel RLC circuit  \nExample: for the circuit shown in figure (a), draw the phasor circuit , impedance diagram and currents phasor diagram.  \nV=100 ∟53 .13 , so the phasor circuit is shown in figure (b) .  \nYT =YR +YL+YC=1/3. 33+1/j1.","cbCaitQ0MQRG8Waj","https://ap.wps.com/l/cbCaitQ0MQRG8Waj","pdf",2598219,18,"English","# Phasor diagram for the Passive Circuit Elements\n# Phasor diagram for series RL circuit\n# Phasor diagram for series RC circuit\n# Phasor diagram for series RLC circuit\n# Phasor diagram for parallel RL circuit\n# Phasor diagram for parallel RC circuit\n# Phasor diagram for parallel RLC circuit\n# Series-parallel AC circuit","[{\"question\":\"How are voltage and current phasors represented for passive circuit elements?\",\"answer\":\"Voltage and current are expressed as phasors in polar form, and the document notes that the given phasor angles correspond to the in-phase relationship between current and voltage for the passive reference used.\"},{\"question\":\"What is the method for series RL, RC, and RLC circuits in phasor form?\",\"answer\":\"Impedances are added in series to form ZT, then component voltage phasors are calculated using VR=IZR, VL=IZL, and VC=IZC, with results provided in both polar and rectangular forms.\"},{\"question\":\"How are parallel RL, RC, and RLC circuits analyzed using phasors?\",\"answer\":\"Admittances are summed to obtain YT, then the total current phasor and branch current phasors are computed. The impedance and resulting branch voltages or currents are then determined from the phasor relationships.\"}]","5%20Phasor%20diagram - Passive Circuit Elements Phasor Diagram - Series RL - Series RC - Series RLC - Parallel RL - Parallel RC - Parallel RLC | PDF",1792971344,45]