Lect20 - Physics 212 Ph Lecture 20 AC Circuits Maximum...

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Unformatted text preview: Physics 212 Ph Lecture 20 AC Circuits Maximum currents & voltages Phasors: A Simple Tool Simple Physics 212 Lecture 20, Slide 1 Music Who is the Artist? A) B) C) D) E) Derek Trucks Band Trucks Band Robert Plant & Alison Kraus CCR Emmylou Harris & Gregg Allman Led Zeppelin Theme of the week Bluegrass fiddlers (Mark O’Connor, Alison Kraus) doing something different !! Also: From today’s Lecture Thoughts: “You should ALTERNATE your CURRENT music pattern and put up a song - sister rosetta walks before us, preferably - from Raising Sand - please and thanks!” P.S. Did you know this is Alison Kraus’ hometown? Physics 212 Lecture 20, Slide 2 Your Your Comments “I need more practice reading the phasor phasor diagrams, and please explain what exactly is meant by two elements being "in phase" or "out of phase." Think about what the voltage across each element is proportional to: Q, I, dI/dt C, R, L “This was rather confusing.... Can you please explain the phasor diagrams and a circuit with all 3 elements (capacitors, inductors, and resistors) in it?” “Where does Z come from? I don't understand how wL and wC could be related to each other... And the units are weird too...”.” Absolutely Absolutely Will Do ! Impedance Impedance Triangle fl Phases !! Rotation of Phasors fl Voltages at any time “explain the check points!! I seem to be LAGGING behind the prelecture by something greater than 90 degrees.” th 90 “I just finished the midterm 2 just in time for me to do more physics. Right now, I'm all "phased" out.” “Obvious Star Trek/phasor pun goes here” Trek/phasor 05 Physics 212 Lecture 20, Slide 3 Resistors = Vmaxsin(t) R I = VR/R = Vmax/R sin(t) Amplitude = Vmax/R Physics 212 Lecture 20, Slide 4 Capacitors Q = CV = CVmaxsin(t) CV CV I = dQ/dt = Vmaxsin(t) C I = VmaxC cos(t) Amplitude = Vmax/XC 90o where XC = 1/C is like the “resistance” of of the capacitor XC depends on Physics 212 Lecture 20, Slide 5 Inductors dI/dt = VL = Vmaxsin(t) = Vmaxsin(t) L I = - Vmax/L cos(t) Amplitude = Vmax/XL 90o where XL = L is like the “resistance” of of the inductor XL depends on Physics 212 Lecture 20, Slide 6 RL ACT An RL circuit is driven by an AC generator as shown in the figure. XL = L L R As Ø 0, so does XL As Ø 0, resistance of circuit Ø R current gets bigger For what driving frequency of the generator will the th current current through the resistor be largest A) large B) Current through R doesn’t depend on C) small Physics 212 Lecture 20, Slide 7 Summary Summary R Imax = Vmax/R VR in phase with I Because resistors are simple C Imax = Vmax/XC XC = 1/C VC 90o behind I Current comes first since it charges capacitor Like a wire at high L Imax = Vmax/XL XL = L VL 90o ahead of I Opposite of capacitor Like a wire at low Physics 212 Lecture 20, Slide 8 Makes sense to write everything in Makes terms of I since this is the same everywhere in a one-loop circuit: one- Phasors make this simple to see Imax XL Vmax = Imax XC V 90o behind I C max L R Imax R Vmax = Imax XL V 90o ahead of I Vmax = Imax R V in phase with I Simulation from the Prelecture Imax XC Always looks the same. Only the lengths will change change Physics Physics 212 Lecture 20, Slide 9 Imax XC The The voltages still add up C max But now we are adding vectors: Imax XL L R Imax R Imax XL Imax R max Imax R Imax R Imax XC Imax XC Imax XL Imax XC Imax XL max Physics 212 Lecture 20, Slide 10 Imax XC Making Making this simpler… C max Imax XL L Imax XL R Imax R Imax XL max Imax R Imax XC Imax R Imax XC Physics 212 Lecture 20, Slide 11 Imax XC Making Making this simpler… C max L Imax XL R Imax R Imax XL max = Imax Z max max Imax R Imax(XL-XC) Imax R Imax XC Physics 212 Lecture 20, Slide 12 Imax XC Making Making this simpler… C max L Imax XL R Imax R max = Imax Z max max Imax(XL-XC) Imax R Physics 212 Lecture 20, Slide 13 Imax XC Making Making this simpler… C max Imax XL R max = Imax Z Imax R Imax(XL-XC) L Imax R (XL-XC) Impedance Triangle R X L XC tan R Physics 212 Lecture 20, Slide 14 Imax XC Summary: Summary: C VCmax= Imax XC max VLmax= Imax XL L Imax XL R VRmax= Imax R Imax R max = Imax Z Imax = max / Z max Z R X L XC 2 X L XC tan R 2 XL-XC) R Physics 212 Lecture 20, Slide 15 Example: Example: RL Circuit Xc=0 max L Imax XL R Imax R Imax XL max Imax R Physics 212 Lecture 20, Slide 16 CheckPoint CheckPoint 1a Draw Voltage Phasors Imax XL max Imax R A B C 60 50 40 “I lags V for the inductor by 90-° and V(resistor) is IR, that means that the voltage across the resistor lags the generator voltage” 30 20 10 0 “The generator is always in phase with resistors.” Physics Physics 212 Lecture 20, Slide 17 CheckPoint 1b Draw Voltage Phasors Imax XL max Imax R A B C 60 50 40 30 “The voltages across the resistor and the inductor are always 90 degrees out of phase.” 20 10 0 “As we saw from the pre-lecture, the voltage across the inductor is again always in phase with the generator.” Physics Physics 212 Lecture 20, Slide 18 CheckPoint 1c The CURRENT is THE CURRENT Imax XL A B C D “The same current passes through the resistor and the inductor.” “The current through the resistor and inductor will always be 90 degrees, since the voltage across the resistor and inductor is always in phase.” max Imax R is the phase between generator and current 40 30 20 10 0 Physics 212 Lecture 20, Slide 19 CheckPoint CheckPoint 2a A B C What does the voltage phasor diagram look lik like when the current th IXL is a maximum? IXL IR 40 IR IXc IXc 30 20 10 0 Physics 212 Lecture 20, Slide 20 IXL IR IR A B C IXc CheckPoint CheckPoint 2b 30 IXc 20 10 IXL What does the voltage phasor diagram look lik like when the capacitor th is fully charged? 40 0 Physics 212 Lecture 20, Slide 21 IXL IR IR A B C IXc CheckPoint CheckPoint 2c 40 IXc 30 20 10 IXL What does the voltage phasor diagram look lik like when the voltage th across capacitor is at its positive maximum? 50 0 Physics 212 Lecture 20, Slide 22 Calculation Calculation Consider the harmonically driven series LCR circuit shown. Vmax = 100 V Imax = 2 mA VCmax = 113 V The current leads generator voltage by 45o L and R are unknown. C V~ L R What is XL, the reactance of the inductor, at this frequency? • Conceptual Analysis – – The maximum voltage for each component is related to its reactance and to the maximum current. The impedance triangle determines the relationship between the maximum voltages for the components • Strategic Analysis – – – Use Vmax and Imax to determine Z Use impedance triangle to determine R Use Use VCmax and impedance triangle to determine XL Physics Physics 212 Lecture 20, Slide 23 Calculation Calculation Consider the harmonically driven series LCR circuit shown. Vmax = 100 V Imax = 2 mA VCmax = 113 V The current leads generator voltage by 45o L and R are unknown. C V~ L R What is XL, the reactance of the inductor, at this frequency? Compare XL and XC at this frequency: (A) XL < XC (B) XL = XC (C) XL > XC (D) Not enough information • This information is determined from the phase – Current leads voltage VL VL = ImaxXL VC = ImaxXC VR (phase of current) V VC IR V leads Physics 212 Lecture 20, Slide 24 Calculation Calculation Consider the harmonically driven series LCR circuit shown. Vmax = 100 V Imax = 2 mA VCmax = 113 V The current leads generator voltage by 45o L and R are unknown. C V~ L R What is XL, the reactance of the inductor, at this frequency? What is Z, the total impedance of the circuit? (A) 70.7 k (B) 50 k (C) 35.4 k (D) 21.1 k Vmax 100V 50k Z I max 2mA Physics 212 Lecture 20, Slide 25 Calculation Calculation Consider the harmonically driven series LCR circuit shown. Vmax = 100 V Imax = 2 mA VCmax = 113 V The current leads generator voltage by 45o L and R are unknown. C V~ L R Z = 50k What is XL, the reactance of the inductor, at this frequency? sin(45)=.707 What is R? (A) 70.7 k cos(45)=.707 (B) 50 k (C) 35.4 k (D) 21.1 k • Determined from impedance triangle R Z=50k (XC-XL) R cos(45) Z R = Z cos(45o) = 50 kx 0.707 = 35.4 k Physics 212 Lecture 20, Slide 26 Calculation Calculation C Consider the harmonically driven series LCR circuit shown. Vmax = 100 V Imax = 2 mA VCmax = 113 V The current leads generator voltage by 45o L and R are unknown. V~ R Z = 50k What is XL, the reactance of the inductor, at this frequency? (A) 70.7 k (B) 50 k We start with the impedance triangle: R Z (C) 35.4 k XC X L tan 45 1 R L R = 35.4k 35.4k (D) 21.1 k XL = XC - R What is XC ? (XC-XL) VCmax = ImaxXC XL = 56.5 k – 35.4 k 113 XC 56.5k 2 Physics 212 Lecture 20, Slide 27 ...
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This note was uploaded on 03/12/2012 for the course PHYS 212 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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