[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-656899-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-656899-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","electricity-magnetism-lecture-20-ac-circuits-maximum-currents-voltages-phasors","Electricity & Magnetism Lecture 20 - AC Circuits - Maximum currents & voltages Phasors","","Electricity & Magnetism Lecture 20 focuses on AC circuits and introduces phasors as a simple tool for analyzing maximum currents and voltages. The lecture derives relationships for resistors, capacitors, and inductors, including phase relationships (in phase, 90° behind, and 90° ahead). It compares effective impedances using VRmax = Imax R, VCmax = Imax XC with XC = 1/(wC), and VLmax = Imax XL with XL = wL. A driven RL circuit question and a driven RLC circuit discussion illustrate how current remains the same in a one-loop circuit and how phasor diagrams reveal results geometrically.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/electricity-magnetism-lecture-20-ac-circuits-maximum-currents-voltages-phasors/656899/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/electricity-magnetism-lecture-20-ac-circuits-maximum-currents-voltages-phasors/656899.png","ImageObject",300,407,{"name":42,"@type":43},"dhado","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-10-25",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What is the main advantage of using phasors in AC circuits?","Question",{"text":62,"@type":63},"Phasors make maximum values and phase relationships easier to see, since the relevant comparisons become geometric on the diagram.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"How do the currents and voltages relate for a resistor, capacitor, and inductor?",{"text":67,"@type":63},"For a resistor, VR is in phase with I; for a capacitor, VC lags the current by 90°; for an inductor, VL leads the current by 90°.",{"name":69,"@type":60,"acceptedAnswer":70},"How are XC and XL defined, and how do they affect maximum values?",{"text":71,"@type":63},"XC = 1/(wC) acts like a resistance for capacitors, while XL = wL acts like a resistance for inductors. These enter directly into VCmax = Imax XC and VLmax = Imax XL.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},656899,1792971357,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":102,"slug":103},6,50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":101,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":79,"read_time":144},5909893218464,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Your Comments  \nThis material is a little abstract. Can you explain these phase diagrams and how to draw the right triangles to find phi in more detail?  \nIs there ever going to be more than one loop/ more than one of each piece of the circuit?  \nIf so, can we please go through an example?  \nSo we just get done with a decently difficult exam and this is what you throw at us??!?!?!?!  \nBetween this and the exam, I kinda sorta really, really hate E&M now. And did we really setup a differential equation, examine three separate complex instances, introduce phasers (which confuse the int(B * dA) out of me), and graph phasers all to arrive at ... a problem solved by simple geometry and algebra? Not only do I hate E&M, E&M constantly confuses me with how it can be so complex and yet so simple.  \nI really like the pretty diagrams. .. I just wish I understood them haha.  \nSorry, i didn't really do this prelecture/checkpoint. but i'll come back to it in a few days! studying for a CS exam :0  \nThis pre-lecture went way over my head. Going over everything in class will definitely help because I need some general explanation of what things are in order to understand the details of the example.  \nElectricity & Magnetism Lecture 20, Slide 1  \nPhysics 212 Lecture 20  \nToday’s Concept:  \nAC Circuits  \nMaximum currents & voltages Phasors: A Simple Tool  \nElectricity & Magnetism Lecture 20, Slide 2  \nBig Idea  \nMaximum Values (easy V=IR)  \nVRmax = Imax R  \nImax = emax / Z VLmax = Imax XL  \nVCmax = Imax XC  \nValue at specific time (phasors)  \ny component gives voltage V-Inductor Leads current V-Capacitor Lags current  \nElectricity & Magnetism Lecture 20, Slide 3  \nResistors  \ne = Vmax sin (wt)  \nI = VR/R = Vmax/R sin(wt)  \nAmplitude = Vmax/R  \nElectricity & Magnetism Lecture 20, Slide 4  \nCapacitors  \ne = Vmax sin (wt)  \n 90o   \nQ = CV = CVmax sin (wt) I = dQ/dt  \n I = Vmax wC cos(wt)  \nAmplitude = Vmax/XC  \nwhere XC = 1/wCis like the “resistance”of the capacitor XC depends on w  \nElectricity & Magnetism Lecture 20, Slide 5  \nInductors  \ne = Vmax sin (wt)  \n90o  \nL dI/dt = VL = Vmaxsin (wt)  \nL  \nwhere XL = wLis like the “resistance”of the inductor XL depends on w  \nElectricity & Magnetism Lecture 20, Slide 6  \nRL Clicker Question   \nAn RL circuit is driven by an AC generator as shown in the figure.  \nL  \nR  \nFor what driving frequency w of the generator will the current through the resistor be largest  \nA) w large  \nB) Current through R doesn’t depend on w  \nC) w small  \nXL = wL  \nAs w-> 0 , so does XL  \nAs w-> 0 , resistance of circuit R current gets bigger  \nElectricity & Magnetism Lecture 20, Slide 7  \nSummary  \nImax = Vmax/R  \nVR in phase with I  \nBecause resistors are simple  \nImax = Vmax/XC VC 90o behind I  \nXC = 1/wC Current comes first since it  \ncharges capacitor  \nLike a wire at high w  \nImax = Vmax/XL  \nXL = wL  \nVL 90o ahead ofI  \nOpposite of capacitor  \nLike a wire at low w  \nElectricity & Magnetism  \nLecture 20, Slide 8  \nCheckPoint 1c   \nThe phase difference between the CURRENT through the resistor and the CURRENT through the inductor is  \nB  \nC  \nD  \nThe CURRENT is THE CURRENT  \nThere is only 1 current in this circuit  \nSame everywhere in circuit  \nElectricity & Magnetism Lecture 20, Slide 9  \nDriven RLC Circuit  \nMakes sense to write everything in terms ofI since this is the same everywhere in a one-loop circuit:  \nVmax = Imax XCV 90o behind I  \nC L   \nemax   R   \nVmax = Imax RV in phase with I  \nVmax = Imax XLV 90o ahead ofI  \nPhasors make this simple to see  \nImax XL  \n Imax R  \nImax XC  \nAlways looks the same. Only the lengths will change  \nElectricity & Magnetism Lecture 20, Slide 10","cbCaikIaIFKdgBuk","https://ap.wps.com/l/cbCaikIaIFKdgBuk","pdf",771784,27,"English","# Today’s Concept: AC Circuits\n## Maximum currents & voltages\n## Phasors: A Simple Tool\n## Resistors, Capacitors, Inductors\n## RL Clicker Question\n## Summary\n## CheckPoint\n## Driven RLC Circuit","[{\"question\":\"What is the main advantage of using phasors in AC circuits?\",\"answer\":\"Phasors make maximum values and phase relationships easier to see, since the relevant comparisons become geometric on the diagram.\"},{\"question\":\"How do the currents and voltages relate for a resistor, capacitor, and inductor?\",\"answer\":\"For a resistor, VR is in phase with I; for a capacitor, VC lags the current by 90°; for an inductor, VL leads the current by 90°.\"},{\"question\":\"How are XC and XL defined, and how do they affect maximum values?\",\"answer\":\"XC = 1/(wC) acts like a resistance for capacitors, while XL = wL acts like a resistance for inductors. These enter directly into VCmax = Imax XC and VLmax = Imax XL.\"}]","Electricity & Magnetism Lecture 20 - AC Circuits - Maximum currents & voltages Phasors | PDF",68]