Lect08 - Physics 212 Lecture 8 Today's Concept Capacitors...

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Unformatted text preview: Physics 212 Lecture 8 Today's Concept: Capacitors Capacitors in a circuits, Dielectrics, Energy in capacitors Physics 212 Lecture 8, Slide 1 Music Who is the Artist? BB A) B) C) D) E) Michael McDonald Van Morrison Glenn Frey Robert Palmer David Bowie My favorite Van the Man album… Many of Many my friends agree that this one is on the list of 10 albums you must have on a desert island.. What does that say about my friends?? does Did you know he wrote “Gloria”.. He did! Did From Last time: Really.. Incredible “Send in the Clowns” By Van the Man A Classic, Of Course ! Physics 212 Lecture 8, Slide 2 Your Comments “The last parts of this preflight, and if you could post my comment it would be awesome! nt Shout out to Sam!!!!! Shout “Problem 8, 10, and 12 from the prelecture. ” Problem prelecture Will Do.. They were the hardest “I am confused about what things change when am dielectrics are added and what things stay the same.” dielectrics “Most concepts, but specifically, why capacitance and potential energy are inversely nergy proportional. That seems counterintuitive to me. ” Careful.. There are Three Variables U = ½ Q2/C = ½ CV2 /C “DO MORE HOMEWORK LIKE PROBLEMS! “ DO 35 “Dielectrics! especially when they do not cover the Dielectrics! 30 whole space between capacitor plates! you're blowing my mind! “ 25 WILL DO See Calculation at End 20 15 10 5 0 05 Confused Confident Physics 212 Lecture 8, Slide 3 Some Exam Stuff • Exam next Wednesday at 7:00 – – – – Covers material through lecture 8 Bring your ID Conflict exam at 5:15 – sign up in your gradebook if you need to If you have conflicts with both of these contact us immediately https://my.physics.illinois.edu/undergrad/examprep/index.asp Physics 212 Lecture 8, Slide 4 Simple Capacitor Circuit Q V C +Q -Q V C Q=VC Q This “Q” really means that the battery has This really moved charge Q from one plate to the other, moved so that one plate holds +Q and the other -Q. so 8 Physics 212 Lecture 8, Slide 5 Dielectrics V C0 Q0=VC0 V C1=κC0 Q1=VC1 By adding a dielectric you are just making a By new capacitor with larger capacitance (factor of κ) new 11 Physics 212 Lecture 8, Slide 6 Qtotal V Parallel Capacitor Circuit C2 C1 Q1 = C1V Q2 = C2V Qtotal Key point: V is the same for both capacitors Key Point: Qtotal = Q1 + Q2 = VC1 + VC2 = V(C1 + C2) Ctotal = C1 + C2 14 Physics 212 Lecture 8, Slide 7 Series Capacitor Circuit Q Q=VCtotal +Q -Q V V1 Q V +Q -Q V2 C1 C2 Q Q Q Key point: Q is the same for both capacitors Key point: Q = VCtotal = V1C1 = V2C2 VC Also: V = V1 + V2 17 Q/Ctotal = Q/C1 + Q/C2 1 1 1 = + C1 C2 Ctotal Physics 212 Lecture 8, Slide 8 Preflight 2 Which has lowest total capacitance: C C C C C Ctotal = C 1/Ctotal = 1/C + 1/C = 2/C 2/C Ctotal = C/2 Ctotal = 2C 70 60 50 40 30 20 10 18 0 Physics 212 Lecture 8, Slide 9 Preflight 4 Which has lowest total capacitance: C C C C C Cleft = C/2 Cright = C/2 Ctotal = C Ctotal = Cleft + Cright 70 Ctotal = C 50 40 30 20 Same 60 10 0 20 Physics 212 Lecture 8, Slide 10 10 Similar to Preflight 6 Q2 C2 V0 V1 C1 BB V2 Q1 V3 C3 Q3 Ctotal Which of the following is NOT necessarily true: A) B) C) D) E) 24 V0 = V1 Ctotal > C1 V2 = V3 Q2 = Q3 V1 = V2 + V3 Physics 212 Lecture 8, Slide 11 11 Preflight 6 BB To simplify, To Assume C1 = C2 = C3 Assume NO YES NO YES NO YES Q1 = Q2 V1 < V2 25 (A) V1 = V2 + V3 V1 > V2 Q2 = Q3 Q1 Q2 Q2 = + C1 C2 C3 Q2 = C2C3 Q1 C1 (C2 + C3 ) Q1 = Q2 V1 < V2 Q1 = Q2 V1 < V2 Q1 = Q2 V1 < V2 (B) (C) (D) Physics 212 Lecture 8, Slide 12 12 Energy in a Capacitor In Prelecture 7 we calculated the work done to move charge Q from In Prelecture we one plate to another: one C +Q V -Q U = 1/2QV = 1/2CV2 =1/2Q2/C Since Q = VC This is potential energy waiting to be used… 26 Physics 212 Lecture 8, Slide 13 13 Messing w/ Capacitors • If connected to a battery V stays constant V1 = V V κ C1 = κ C Q1 = C1V1 = κ CV = κQ • If isolated then total Q stays constant κ Q1 = Q C1 = κ C V1 = Q1/C1 = Q/κC = V /κ Physics 212 Lecture 8, Slide 14 14 Preflight 8 BB 60 “When a dielectric is added to a capacitor, the capacitance will increase. Because C=Q/V and Q is constant, this means that V has to decrease. “ 50 “C=Q/V; since C increases and Q increases proportionally with C, V is constant ” 20 “Capacitance lowers in case 2, meaning V increases in case 2. ” 33 40 30 10 0 Physics 212 Lecture 8, Slide 15 15 Messing w/ Capacitors ACT Two identical parallel plate capacitors are connected to identical batteries. Then a dielectric is inserted between the plates of capacitor C1. Compare the energy stored in the two capacitors. C0 V A) U1 < U0 V B) U0 = U1 C1 BB BB κ=2 C) U1 > U0 Compare using U = 1/2CV2 U1/U0 = κ 35 Potential Energy goes UP Potential UP Physics 212 Lecture 8, Slide 16 16 Preflight 10 BB A B C “U=(1/2)QV. The V decreases and the Q stays the U=(1/2)QV. same, since it has nowhere to go. Therefore, the potential energy decreases. ” potential “Potential energy depends on the charge and the radius, Potential since neither has changed, it remains the same. “ since “the addition of a dielectric increases the the capacitance, the charge, and the potential energy” capacitance, 33 40 30 20 10 0 Physics 212 Lecture 8, Slide 17 17 Preflight 12 BB V must be the same ! 50 40 Q: Q1 Q2 = C1 C2 U1 = 1 C1V 2 2 U: U 2 = 1 C2V 2 2 C Q1 = 1 Q2 C2 U1 = C1 U2 C2 30 20 10 0 Physics 212 Lecture 8, Slide 18 18 Calculation C0 V x0 An air-gap capacitor, V κ x0/4 BB having capacitance C 0 and width x0 is connected to a battery of voltage V. A dielectric (κ) of width x0/4 is inserted into the gap as shown. What is Qf, the final • Conceptual Analysis: charge on the Q capacitor? C≡ V What changes when the dielectric added? (A) Only C (B) only Q (B) (C) only V (C) (D) C and Q Adding dielectric changes the physical capacitor V does not change and C changes 38 (E) V and Q C changes Q changes Physics 212 Lecture 8, Slide 19 19 Calculation C0 V V x0 κ BB An air-gap capacitor, x0/4 • Strategic Analysis: – – Calculate new capacitance C Apply definition of capacitance to determine Q To calculate C, let’s first look at: Vleft (A) Vleft < Vright (A) κ A dielectric (κ) of width x0/4 is inserted into the gap as shown. What is Qf, the final charge on the capacitor? Vright (B) Vleft = Vright (B) (C) Vleft > Vright (C) The conducting plate is an equipotential !! 40 having capacitance C0 and width x0 is connected to a battery of voltage V. Physics 212 Lecture 8, Slide 20 20 An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. Calculation C0 V V x0 BB κ x0/4 A dielectric (κ) of width x0/4 is inserted into the gap as shown. What is Qf, the final charge on the capacitor? Can consider capacitor to be two capacitances, C1 and C2, in parallel κ = C1 κ C2 What is C1 ? (A) C1 = C0 (B) C1 = 3/4C0 (A) (B) (C) C1 = 4/3C0 (C) In general. For parallel plate capacitor: C = ε0A/d In A = 3/4A0 C1 = 3/4 (ε0A0/d0) d = d0 43 (D) C1 = 1/4C0 (D) C1 = 3/4C0 Physics 212 Lecture 8, Slide 21 21 Calculation C0 V x0 V An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. κ x0/4 κ = C1 κ C2 C1 = 3/4C0 BB A dielectric (κ) of width x0/4 is inserted into the gap as shown. What is Qf, the final charge on the capacitor? What is C2 ? (A)C2 = κC0 (B) C2 = 3/4 κC0 (B) (C) C2 = 4/3 κC0 (C) (D) C2 = 1/4 κC0 (D) In general. For parallel plate capacitor filled with dielectric: C = κε0A/d A = 1/4A0 d = d0 45 C = ¼(κε0A0/d0) C2 = 1/4 κC0 Physics 212 Lecture 8, Slide 22 22 An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. Calculation C0 V x0 V κ BB A dielectric (κ) of width x0/4 is inserted into the gap as shown. x0/4 κ C = C1 κ What is Qf, the final charge on the capacitor? C2 C2 = 1/4 κC0 C1 = 3/4C0 What is C? What (A) C = C1 + C2 (B) C = C1 + κ C2 (C) C = 1 + 1 (B) C C 1 2 C = parallel combination of C1 and C2: −1 C = C1 + C2 C = C0 (3/4 + 1/4 κ) 46 Physics 212 Lecture 8, Slide 23 23 An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. Calculation C0 V V x0 κ x0/4 κ C C1 = κ A dielectric (κ) of width x0/4 is inserted into the gap as shown. What is Qf, the final charge on the capacitor? C2 C1 = 3/4C0 C2 = 1/4 κC0 C = C0 (3/4 + 1/4 κ) What is Q? C≡ Q V Q = VC 3 1 Q f = VC0 + κ 4 4 50 Physics 212 Lecture 8, Slide 24 24 Different Problem V Q0 C0 x0 V κ BB BB 1/4x0 (A) Vf < V (B) Vf = V (B) Q stays same: no way to add or subtract stays We know C: (property of capacitor) We (C) Vf > V (C) An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V and then battery is disconnected. A dielectric (κ) of width 1/4x0 is inserted into the gap as shown. What is Vf, the final voltage on the capacitor? Q = Q0 = C0V C = C0 (3/4 + 1/4 κ) Vf = Q/C = V/(3/4 + 1/4 κ) Physics 212 Lecture 8, Slide 25 25 Different Problem V Q0 C0 x0 BB V κ 1/4x0 An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V and then battery is disconnected. A dielectric (κ) of width 1/4x0 is inserted into the gap as shown. What is Vf, the final voltage on the capacitor? Vf = Q/C = V/(3/4 + 1/4 κ) How did energy stored in capacitor How change when dielectric inserted? change (A) U increased (B) U stayed same (C) U decreased (B) (C) U = ½ Q2/C Q remained same C increased U decreased Physics 212 Lecture 8, Slide 26 26 ...
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