Last time. Resistors. Circuits. Question. Quick Quiz. Quick Quiz. ( V c. Which bulb is brighter? A. A B. B. C. Both the same

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1 Last tim Bgin circuits Rsistors Circuits Today Rsistor circuits Start rsistor-capacitor circuits Physical layout Schmatic layout Tu. Oct. 13, 2009 Physics 208 Lctur 12 1 Tu. Oct. 13, 2009 Physics 208 Lctur 12 2 Which bulb is brightr? Whn currnt flows, charg movs around th circuit. Suppos that positiv charg carrirs flow around th circuit. What is th chang in potntial nrgy of a positiv charg as movs from c to d? C. Both th sam A. qv d qv c B. qv c qv d Currnt through ach must b sam Consrvation of currnt (Kirchoff s currnt law) Charg that gos in must com out Tu. Oct. 13, 2009 Physics 208 Lctur 12 3 C. qv d + qv c D. zro Tu. Oct. 13, 2009 Physics 208 Lctur 12 4 What is th chang in kintic nrgy as it movs from c to d? A. qv d qv c B. qv c qv d C. qv d + qv c D. zro Tu. Oct. 13, 2009 Physics 208 Lctur 12 5 Powr dissipation (Joul hating) Charg loss nrgy from c to d. Ohm s law: ( V c V d ) = R E lost = ΔE = ( ΔKE + ΔU) = 0 q( V d V c ) E lost = qr Enrgy dissipatd in rsistor as Hat (& light) in bulb Powr dissipatd in rsistor = de lost = dq R = 2 R Jouls / s = Watts Tu. Oct. 13, 2009 Physics 208 Lctur

2 Light bulbs and powr Houshold voltag is 120V Cost 24 hours on rquirs 60W = 60J /s = 2 R = ( R) = V = 60W /120V = 0.5A R = V / =120V /0.5A = 240Ω ( 60J /s)( 24hour) ( 3600s/hour) = 5,184,000J MG&E ~ 13 / kwatt-hour 1kW hour = 1000J /s 60 Watt ( )( 3600s/hour) = 3,600,000J 19 / day Tu. Oct. 13, 2009 Physics 208 Lctur 12 7 Two diffrnt bulbs P 1 = 2 R 1 a P 2 = 2 R 2 R 1 R 2 Currnt sam through ach d Powr dissipatd diffrnt Brightnss diffrnt b Tu. Oct. 13, 2009 Physics 208 Lctur 12 8 c Kirchoff s junction law Charg consrvation out = in 1 in 1 1 = What happns to th brightnss of th bulb A whn th switch is closd? A. Gts dimmr B. Gts brightr C. Stays sam D. Somthing ls out = 3 Tu. Oct. 13, 2009 Physics 208 Lctur 12 9 Tu. Oct. 13, 2009 Physics 208 Lctur As mor and mor rsistors ar addd to th paralll rsistor circuit shown hr th total currnt flowing R 1 R 2 R 3 R 4. A. ncrass if ach R i gtting biggr B. ncrass if ach R i gtting smallr C. Always incrass D. Always dcrass E. Stays th sam Each rsistor addd adds ΔV/R i to th total currnt Tu. Oct. 13, 2009 Physics 208 Lctur You us on powr strip to plug in your toastr, coff pot, microwav. 10 A 5 A 12 A Toastr Coff Pot Microwav Evrything works grat until you plug in your spac hatr, thn you smll smok. This is bcaus A. Th rsistanc of th circuit is too high B. Th voltag in th circuit is too high C. Th currnt in th circuit is too high Tu. Oct. 13, 2009 Physics 208 Lctur

3 Mor complicatd circuits Both sris & paralll Dtrmin quivalnt rsistanc Rplac combinations with quivalnt rsistanc Th circuit blow contains thr 100W light bulbs. Th mf ε = 110 V. Which light bulb(s) is(ar) brightst? D. B and C E. All thr ar qually bright. Tu. Oct. 13, 2009 Physics 208 Lctur Tu. Oct. 13, 2009 Physics 208 Lctur Masurmnts in a circuit A multimtr can masur currnts (as an ammtr), potntial diffrnc (as a voltmtr) Elctrical masuring dvics must hav minimal impact in th circuit ΔV ΔV V Voltmtr V R V R A ε A Ammtr ΔV A R ε Th intrnal rsistanc of th ammtr must b vry small Th intrnal rsistanc of th = A voltmtr must b vry larg ε = ΔV+ΔV A = R + r A R = v + R for r A 0 ΔV V = ε = ε + ε r V ε Tu. Oct. 13, 2009 Physics 208 Lctur 12 r V R 15 Kirchoff s loop law Consrvation of nrgy R Tu. Oct. 13, 2009 Physics 208 Lctur ε 1 R 1 2 R 2 R3 3 Rsistorcapacitor circuit What happns to chargs on th capacitor aftr switch is closd? Why dos th charg flow through th rsistor? Why dos th charg on th capacitor chang in tim? Charging a capacitor Again Kirchoff s loop law: ε R /C = 0 =ε/r / Tim t = 0: Q c = 0 =ε /R t incrass: Q c > 0 <ε /R Looks lik rsistor & battry: unchargd cap acts lik short circuit V C incrass, so V R dcrass Tim t = : V C =ε V R = 0 = 0 Fully chargd capacitor acts lik opn circuit Thur. Oct. 16, 2008 Physics 208 Lctur Thur. Oct. 16, 2008 Physics 208 Lctur

4 Discharging th capacitor discharg Kirchoff s loop law ( V B V A ) + ( V D V C ) = 0 B C ΔV c = Q c /C R = Q c A D tim constant τ = Chargs in th currnt com from capacitor: = dq c Thur. Oct. 16, 2008 Physics 208 Lctur Q = Q o = o Thur. Oct. 16, 2008 Physics 208 Lctur Charging a capacitor Th circuit contains thr idntical light bulbs and a fully-chargd capacitor. Which is brightst? Q = Q max ( 1 ) D. A & B E. All qually bright Thur. Oct. 16, 2008 Physics 208 Lctur Thur. Oct. 16, 2008 Physics 208 Lctur Th circuit contains thr idntical light bulbs and an unchargd capacitor. Which is brightst? discharg tim constant τ = D. A & B E. All qually bright tim t Thur. Oct. 16, 2008 Physics 208 Lctur Tu. Oct. 13, 2009 Physics 208 Lctur

5 analysis Kirchoff loop law: ΔV C + ΔV R = 0 C R = 0 rlatd to = d C + R d d = 0 = Tu. Oct. 13, 2009 Physics 208 Lctur analysis d = d = 1 Q Q o d = 1 t Q( t) t ln Q = o t 0 ( ) = Q o xp( t /) Tu. Oct. 13, 2009 Physics 208 Lctur