Lect20 - Physics 212 Le cture20 AC Circuits Maximum...

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Unformatted text preview: Physics 212 Le cture20 AC Circuits Maximum currents & voltages Phasors: A Simple Tool 35 30 25 20 15 10 5 0 Confused Avg = 2.6 Confident Physics 212 Le cture20, S 1 lide Music Who is the Artist? A) B) C) D) E) Professor Longhair Johnny Adams David Egan Dr. John Allen Toussaint classics classics The Theme of the week: New Orleans piano players New A great piano CD Physics 212 Le cture20, S 2 lide Physics 212 Le cture20 AC Circuits Maximum currents & voltages Phasors: A Simple Tool 35 30 25 20 15 10 5 0 Confused Avg = 2.6 Confident Physics 212 Le cture20, S 3 lide Re sistors ε = ε maxsin(ω t) R I = VR/R = Vmax/ R sin(ω t) sin( Am plitude= Vmax/ R Am Physics 212 Le cture20, S 4 lide Capacitors Q = VC= C maxsin(ω t) I = dQ/dt ε ε = ε maxsin(ω t) C I = Vmaxω Ccos(ω t) cos( Am plitude= Vmax/ X Am C whe X = 1/ω C re C is likethe“re sistance ” of thecapacitor of X de nds on ω pe C Physics 212 Le cture20, S 5 lide Inductors dI/dt = VL = ε maxsin(ω t) ε = ε maxsin(ω t) L I = - Vmax/ ω L cos(ω t) cos( Am plitude= Vmax/ X Am whe X = ω L re L L is likethe“re sistance ” of theinductor of X de nds on ω pe L Physics 212 Le cture20, S 6 lide RL ACT An RL circuit is drive by an ACge rator as shown in thefigure n ne . An BB L I max = Vmax/XL X = ωL L R For what driving fre ncy ω of thege rator will the que ne For curre through there nt sistor belarge st A) ω large B) Curre through R doe de nd on ω nt sn’t pe C ω sm ) all Physics 212 Le cture20, S 7 lide Sm um ary R I max = Vmax/R V in phasewith I Be causere sistors aresim ple C I max = Vmax/XC X = 1/ ω C C V 90o be hind I C nt com s first sinceit urre e charge capacitor s Likea wireat high ω L I max = Vmax/XL X =ωL L V 90o ahe of I ad Oppositeof capacitor Likea wireat low ω Like Physics 212 Le cture20, S 8 lide Make se to writee rything in s ve Make nse t e s of I sincethis is thesam rm e e rywhe in a one ve re -loop circuit: Vmax = I max XC V 90o be hind I Phasors m this Phasors ake sim to se ple e sim I m ax X L C I R m ax ε max R L Vmax = I max XL V 90o ahe of I ad I X Vmax = I max R V in phasewith I Always looks thesam . e Only thele ngths will change change Physics 212 Le cture20, S 9 lide Prelecture animation Thevoltage still add up s The C But now weareadding ve ctors: But I max XC ε max R I m ax L I max XL I m ax X L X L I max R ε max I m ax I m ax R I X R I m ax R I m ax X L I X I X ε max Physics 212 Le cture20, S 10 lide 10 Making this sim r… ple C I max XC ε max R I m ax L I max XL X L I m ax X L I max R ε max I m ax R I m ax R I X I X Physics 212 Le cture20, S 11 lide 11 Making this sim r… ple C I max XC ε max R I m ax L I max XL X L I max R ε max = I max Z max I m ax R I m ax R I X Physics 212 Le cture20, S 12 lide 12 Making this sim r… ple C I max XC ε max R I max R L I max XL ε max = I max Z max I m ax R Physics 212 Le cture20, S 13 lide 13 Making this sim r… ple C Imax XC ε max ε max = I max Z max φ L R Imax R Imax XL I m ax R φ R Impedance Triangle XL − XC tan ( φ ) = R Physics 212 Le cture20, S 14 lide 14 Sm um ary: VCmax= I max XC VLmax= I max XL VRmax= I max R C I max XC ε max R I max R L I max XL ε max = I max Z max I max = ε max / Z max Z = R2 + ( X L − X C ) XL − XC tan ( φ ) = R 2 φ R Physics 212 Le cture20, S 15 lide 15 Exam : RL C ple ircuit Xc=0 ε max I m ax L R I max R I max XL X L ε max I m ax R Physics 212 Le cture20, S 16 lide 16 Pre flight 2 BB Draw VoltagePhasors I m ax X L ε max I m ax R A B C 60 50 40 30 20 10 0 Physics 212 Le cture20, S 17 lide 17 Pre flight 4 I m ax BB Draw VoltagePhasors X L ε max I m ax R A B C 60 50 40 30 20 10 0 Physics 212 Le cture20, S 18 lide 18 Pre flight 6 I m ax BB TheCURRENT is THE C URRENT X L ε max I m ax φ A B C D R φ is thephasebe e twe n ge rator and curre ne nt 50 40 30 20 10 0 Physics 212 Le cture20, S 19 lide 19 Pre flight 8 BB A B C What doe thevoltagephasor s diagramlook likewhe the n curre is a m um nt axim ? I XL I XL ε IR ε IR I Xc I Xc 50 40 30 20 10 0 Physics 212 Le cture20, S 20 lide 20 Pre flight 10 BB A B C I XL I Xc ε IR 50 40 30 What doe thevoltagephasor s diagramlook likewhe the n capacitor is fully charge d? IR ε I Xc 20 10 0 I XL Physics 212 Le cture20, S 21 lide 21 Pre flight 12 BB A B C I XL I Xc ε IR 50 40 30 What doe thevoltagephasor s diagramlook likewhe the n voltageacross capacitor is at its positivem um axim ? IR ε I Xc 20 10 0 I XL Physics 212 Le cture20, S 22 lide 22 C alculation C onside theharm r onically drive se s LC circuit shown. n rie R Vm = 100 V ax Im = 2m ax A VC ax = 113 V m Thecurre le ge rator voltageby 45o nt ads ne L and R areunknown. What is XL, there actanceof theinductor, at this fre ncy? que V~ C L R ptual Analysis • Conce axim ach pone late actanceand to them um axim – Them umvoltagefor e com nt is re d to its re curre nt. pe te ine lationship be e them umvoltage for the twe n axim s – Theim dancetrianglede rm s there com nts pone trate • S gic Analysis ax ax te ine – UseVm and I m t o de rm Z pe te ine – Useim dancetriangleto de rm R m pe te ine – UseVC ax and im dancetriangleto de rm XL Physics 212 Le cture20, S 23 lide 23 C alculation C onside theharm r onically drive se s LC circuit shown. n rie R Vm = 100 V ax Im = 2m ax A VC ax = 113 V m Thecurre le ge rator voltageby 45o nt ads ne L and R areunknown. What is XL, there actanceof theinductor, at this fre ncy? que V~ C L R C pareXL and XC at this fre ncy: om que (A) XL < XC (B) XL = XC (C) XL > XC BB (D) Not e nough inform ation • This information is determined fromthephase urre ads – C nt le voltage V L IR 45ο VL = I m XL ax VC= I m XC ax V V V (phaseof curre nt) R V le ads Physics 212 Le cture20, S 24 lide 24 C alculation C onside theharm r onically drive se s LC circuit shown. n rie R Vm = 100 V ax Im = 2m ax A VC ax = 113 V m Thecurre le ge rator voltageby 45o nt ads ne L and R areunknown. What is XL, there actanceof theinductor, at this fre ncy? que V~ C L R What is Z, thetotal im danceof thecircuit? pe 35.4 kΩ (A) 70.7 kΩ (B) (C ) (D) 50 kΩ BB 21.1 kΩ Vmax 100V Z= = = 50k Ω I max 2mA Physics 212 Le cture20, S 25 lide 25 C alculation C onside theharm r onically drive se s LC circuit shown. n rie R Vm = 100 V ax Im = 2m ax A VC ax = 113 V m Thecurre le ge rator voltageby 45o nt ads ne L and R areunknown. What is XL, there actanceof theinductor, at this fre ncy? que V~ C L R Z = 50kΩ sin(45)=.707 cos(45)=.707 What is R? (A) 70.7 kΩ (B) (C ) 50 kΩ 35.4 kΩ (D) 21.1 kΩ • Determined fromimpedancetriangle R 45ο R cos(45) = Z R = Z cos(45) = 50k Ω ( .707 ) = 35.4 kΩ BB 50k Ω Z= Physics 212 Le cture20, S 26 lide 26 C alculation C onside theharm r onically drive se s LC circuit shown. n rie R Vm = 100 V ax Im = 2m ax A VC ax = 113 V m Thecurre le ge rator voltageby 45o nt ads ne L and R areunknown. What is XL, there actanceof theinductor, at this fre ncy? que V~ C L R Z = 50kΩ R = 35.4kΩ (A) 70.7 kΩ (B) Westart with the im dancetriangle pe : (C ) 50 kΩ 35.4 kΩ (D) 21.1 kΩ R 45ο XC − X L = tan 45° = 1 R X L = XC − R What is XC? BB Z VC max = I max X C X L = 56.5kΩ − 35.4kΩ 113 XC = = 56.5kΩ 2 Physics 212 Le cture20, S 27 lide 27 ...
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