Electricity & Magnetism Lecture 20 - AC Circuits - Maximum currents & voltages Phasors

Oct 25, 2026

Uploaded by dhado

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.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages27

Reading Time1 h 8 min

AccessFree to download

Today’s Concept: AC Circuits

Maximum currents & voltages

Phasors: A Simple Tool

Resistors, Capacitors, Inductors

RL Clicker Question

Summary

CheckPoint

Driven RLC Circuit

Your Comments This material is a little abstract. Can you explain these phase diagrams and how to draw the right triangles to find phi in more detail? Is there ever going to be more than one loop/ more than one of each piece of the circuit? If so, can we please go through an example? So we just get done with a decently difficult exam and this is what you throw at us??!?!?!?! Between 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. I really like the pretty diagrams. .. I just wish I understood them haha. Sorry, 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 This 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. Electricity & Magnetism Lecture 20, Slide 1 Physics 212 Lecture 20 Today’s Concept: AC Circuits Maximum currents & voltages Phasors: A Simple Tool Electricity & Magnetism Lecture 20, Slide 2 Big Idea Maximum Values (easy V=IR) VRmax = Imax R Imax = emax / Z VLmax = Imax XL VCmax = Imax XC Value at specific time (phasors) y component gives voltage V-Inductor Leads current V-Capacitor Lags current Electricity & Magnetism Lecture 20, Slide 3 Resistors e = Vmax sin (wt) I = VR/R = Vmax/R sin(wt) Amplitude = Vmax/R Electricity & Magnetism Lecture 20, Slide 4 Capacitors e = Vmax sin (wt) 90o Q = CV = CVmax sin (wt) I = dQ/dt I = Vmax wC cos(wt) Amplitude = Vmax/XC where XC = 1/wCis like the “resistance”of the capacitor XC depends on w Electricity & Magnetism Lecture 20, Slide 5 Inductors e = Vmax sin (wt) 90o L dI/dt = VL = Vmaxsin (wt) L where XL = wLis like the “resistance”of the inductor XL depends on w Electricity & Magnetism Lecture 20, Slide 6 RL Clicker Question An RL circuit is driven by an AC generator as shown in the figure. L R For what driving frequency w of the generator will the current through the resistor be largest A) w large B) Current through R doesn’t depend on w C) w small XL = wL As w-> 0 , so does XL As w-> 0 , resistance of circuit R current gets bigger Electricity & Magnetism Lecture 20, Slide 7 Summary Imax = Vmax/R VR in phase with I Because resistors are simple Imax = Vmax/XC VC 90o behind I XC = 1/wC Current comes first since it charges capacitor Like a wire at high w Imax = Vmax/XL XL = wL VL 90o ahead ofI Opposite of capacitor Like a wire at low w Electricity & Magnetism Lecture 20, Slide 8 CheckPoint 1c The phase difference between the CURRENT through the resistor and the CURRENT through the inductor is B C D The CURRENT is THE CURRENT There is only 1 current in this circuit Same everywhere in circuit Electricity & Magnetism Lecture 20, Slide 9 Driven RLC Circuit Makes sense to write everything in terms ofI since this is the same everywhere in a one-loop circuit: Vmax = Imax XCV 90o behind I C L emax R Vmax = Imax RV in phase with I Vmax = Imax XLV 90o ahead ofI Phasors make this simple to see Imax XL Imax R Imax XC Always looks the same. Only the lengths will change Electricity & Magnetism Lecture 20, Slide 10

FAQs

What is the main advantage of using phasors in AC circuits?

Phasors make maximum values and phase relationships easier to see, since the relevant comparisons become geometric on the diagram.

How do the currents and voltages relate for a resistor, capacitor, and inductor?

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°.

How are XC and XL defined, and how do they affect maximum values?

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.

Oct 25, 2026

Uploaded by dhado