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 40 30 20 10 0 Confused Avg = 3.4 Confident Physics 212 Lecture 8, Slide 1 Physics IMPORTANT EXAM ANNOUNCEMENTS • Exam next Wednesday at 7:00PM – Covers material through lecture 8 – Read my email about “exam procedures” carefully. Also contained in “Exam Information” tab of course website. – FAMILIARIZE YOURSELF WITH YOUR EXAM ROOM. THERE WILL BE ASSIGNED SEATING. (Conflict exam people—you too.) – Conflict exam at 5:15 – sign up in “gradebook” if you need to. Conflict exam room is MSEB 100 – If you have conflicts with both regular and conflict exams, contact us immediately – Exam Review: Tuesday 5:00-6:15 PM in Loomis 141 & 151 – Announcement by Prof. Gladding, Associate Head of Physics Physics 212 Lecture 8, Slide 2 Physics Simple Capacitor Circuit Q V C +Q -Q V C Q=VC Q This “Q” really means that the battery has moved charge Q from one plate to the other, so that one plate holds +Q and the other -Q. 8 Physics 212 Lecture 8, Slide 3 Physics Dielectrics V C0 Q0=VC0 V C1=κC0 Q1=VC1 By adding a dielectric you are just making a new capacitor with larger capacitance (factor of κ) 11 Physics 212 Lecture 8, Slide 4 Physics Qtotal Parallel Capacitor Circuit V C1 Q1 = C1V Qtotal C2 Q2 = C2V 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 5 Physics Series Capacitor Circuit Q Q=VCtotal +Q -Q C1 V1 V Q +Q -Q V V2 Q C2 Q Q Key point: Q is the same for both capacitors Key point: Q = VCtotal = V1C1 = V2C2 Also: V = V1 + V2 Q/Ctotal = Q/C1 + Q/C2 Physics 212 Lecture 8, Slide 6 Physics 17 1 1 1 = + C2 Ctotal C1 Preflight 2 Which has lowest total capacitance: C C C C C Ctotal = C 1/Ctotal = 1/C + 1/C = 2/C Ctotal = C/2 70 60 50 40 30 20 10 Ctotal = 2C 18 0 Physics 212 Lecture 8, Slide 7 Physics Preflight 4 Which has lowest total capacitance: C C C C C Cleft = C/2 Ctotal = C Ctotal = Cleft + Cright 70 60 40 30 20 10 0 Cright = C/2 Same 50 Ctotal = C 20 Physics 212 Lecture 8, Slide 8 Physics Similar to Preflight 6 Q2 C2 BB V0 V1 V2 C1 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 9 Physics Preflight 6 BB NO YES NO YES NO YES V1 = V2 + V3 Q2 = Q3 V1 > V2 Q1 Q2 Q2 = + C1 C2 C3 Q1 = Q2 V1 < V2 Q2 = C2C3 Q1 C1 (C2 + C3 ) Q1 = Q2 V1 < V2 Q1 = Q2 V1 < V2 25 Q1 = Q2 V1 < V2 (A) (B) (C) (D) Physics 212 Lecture 8, Slide 10 Physics Energy in a Capacitor In pre-lecture 7 we calculated the work done to move charge Q from one plate to another: C V +Q U = 1/2QV = 1/2CV2 =1/2Q2/C -Q Since Q = VC This is potential energy waiting to be used… 26 Physics 212 Lecture 8, Slide 11 Physics Messing w/ Capacitors • If connected to a battery V stays constant V1 = V V κ C1 = κ C Q1 = C1 V1 = 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 12 Physics Preflight 8 BB 60 “q is constant. the capacitance is increased thus voltage must be reduced.” (DH) “Dielectrics do not effect voltage.” (EMB) “The capacitance decreases in C2 due to the dielectric thus the voltage must increase because the charge is the same for both. C = Q/V” (SAG) 50 40 30 20 10 0 33 Physics 212 Lecture 8, Slide 13 Physics 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. BB BB V C0 V κ=2 C1 A) U1 < U0 B) U0 = U1 Compare using U = 1/2CV2 C) U1 > U0 U1/U0 = κ 35 Potential Energy goes UP Physics 212 Lecture 8, Slide 14 Physics Preflight 10 BB A B C 40 30 20 10 0 “U = Q^2/(2C). In this situation, Q does not change, but capacitance for C2 is larger than C1; therefore U1>U2.” (BLF) “It should be the same due to the same amount of charge.” (TRCK) “Higher V means higher energy” (MCA) “lady gaga” (KA); “duuuuhhhhh... i don know ” (JSD) 33 Physics 212 Lecture 8, Slide 15 Physics Preflight 12 BB V must be the same ! Q: 60 50 40 30 20 Q1 Q2 = C1 C2 C1 Q1 = Q2 C2 C U1 = 1 U 2 C2 U1 = 1 C1V 2 2 U: U 2 = 1 C2V 2 2 10 0 Physics 212 Lecture 8, Slide 16 Physics Calculation V x0 C0 V κ BB having capacitance C 0 An air-gap capacitor, x0/4 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 (C) only V (D) C and Q (E) V and Q C changes Q changes Adding dielectric changes the physical capacitor V does not change and C changes 38 Physics 212 Lecture 8, Slide 17 Physics Calculation V x0 C0 V κ x0/4 BB An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. • Strategic Analysis: – – Calculate new capacitance C Apply definition of capacitance to determine Qf A dielectric (κ) of width x0/4 is inserted into the gap as shown. What is Qf, the final charge on the capacitor? To calculate C, let’s first look at: Vleft κ Vright (A) Vleft < Vright 40 (B) Vleft = Vright (C) Vleft > Vright Physics 212 Lecture 8, Slide 18 Physics The conducting plate is an equipotential !! Calculation V x0 C0 V An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. κ x0/4 BB 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 What is C1 ? = C1 κ C2 (A) C1 = C0 (B) C1 = 3/4C0 (C) C1 = 4/3C0 (D) C1 = 1/4C0 43 In general. For parallel plate capacitor: C = ε0A/d A = 3/4A0 C1 = 3/4 (ε0A0/d0) d = d0 C1 = 3/4C0 Physics 212 Lecture 8, Slide 19 Physics Calculation V x0 C0 V An air-gap capacitor, having capacitance C0 and width x0 is connected to a batter of voltage V. κ x0/4 BB A dielectric (κ) of width x0/4 is inserted into the gap as shown What is Qf, the final charge on the capacitor? κ What is C2 ? = C1 κ C2 C1 = 3/4C0 (A)C2 = κC0 (B) C2 = 3/4 κC0 (C) C2 = 4/3 κC0 (D) C2 = 1/4 κC0 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 20 Physics Calculation V x0 C0 V An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. κ BB 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? κ What is C? What C = C1 κ C2 C1 = 3/4C0 C2 = 1/4 κC0 (A) C = C1 + C2 (B) C = C1 + κ C2 (C) C = ⎛ 1 + 1 ⎞ ⎜C C ⎟ ⎝1 2⎠ C = parallel combination of C1 and C2: C = C1 + C2 −1 C = C0 (3/4 + 1/4 κ) 46 Physics 212 Lecture 8, Slide 21 Physics Calculation V x0 C0 V An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V. κ BB 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? κ C = C1 κ 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 22 Physics Different Problem V Q0 x0 C0 V κ BB BB 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? 1/4x0 (A) Vf < V (B) Vf = V (C) Vf > V Q stays same: no way to add or subtract We know C: (property of capacitor) Q = Q0 = C0V C = C0 (3/4 + 1/4 κ) Vf = Q/C = V/(C0 (3/4 + 1/4 κ)) Physics 212 Lecture 8, Slide 23 Physics Different Problem V Q0 x0 C0 V BB 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? κ 1/4x0 Vf = Q/C = V/(C0 (3/4 + 1/4 κ)) How did energy stored in capacitor change when dielectric inserted? (A) U increased (B) U stayed same (C) U decreased U = ½ Q2/C Q remained same C increased U decreased Physics 212 Lecture 8, Slide 24 Physics ...
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This note was uploaded on 02/21/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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