Physics 212 Lecture 8, Slide 1Physics 212Lecture 8Today's Concept:CapacitorsCapacitors in a circuits, Dielectrics, Energy in capacitorsPhysics 212 Lecture 8MusicWho is the Artist?A) Ricky SkaggsB) Jerry Garcia & David GrismanC) Tony RiceD) Steve EarleE) Mike Marshall & Darol AngerTheme of the Week: Mandolin Players ExtraordinaireYoung (Chris Thile) & Old (David Grisman)Physics 212 Lecture 8, Slide 3Some Exam Stuff• Exam next Wednesday at 7:00 (Sep. 21)– Covers material through lecture 8– Bring your ID – Conflict exam at 5:15 – sign up in your gradebook by 10:00 TONIGHT– If you have class conflicts with both of these, please email Dr. Park ([email protected]) by 10:00 tonight.• Where do I go? EXAM ROOMS (by discussion section)• Preparation: no in class review :(– Practice exams– Worked examples– Exam Preparation Exercises– Extra Office HoursPhysics 212 Lecture 8, Slide 4Your Comments05“i thought i understood till the 2nd and 3rd checkpoints”“Please, explain last checkpoint question (capacitors with and without a dielectric). Everything else was fine :) ”WILL DOSee Calculation at EndWill Do.. They were the hardest“It seems like a lot of variables are inverses of each other... Can you clarify on this? An overview would be very helpful.”“How do different situations (e.g. capacitors in series, parallel, presence of dielectric, etc.) affect the charge, voltage, and energy of the circuit. ” “It's hard to keep all of the symbols and letters separate, and even harder to remember the "special cases" when variables stay they same or are changed.”“I would like to go over some more examples with different types of capacitors set in circuits with both parallel and series connections.““Detail detail detail, and some worked calculations would be “We’ll summarize main points.“I worry that I have reached the capacity of my brain, I guess I can forget Chem to make some room.”Physics 212 Lecture 8, Slide 5CV+Q-QQQThis “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.CVQ=VCSimple Capacitor Circuit8Physics 212 Lecture 8, Slide 6By adding a dielectric you are just making a new capacitor with larger capacitance (factor of κ)DielectricsC0VQ0=VC0C1=κC0VQ1=VC111Physics 212 Lecture 8, Slide 7VQ1= C1VQ2= C2VC2C1Parallel Capacitor CircuitKey point: V is the same for both capacitorsKey Point: Qtotal= Q1+ Q2= VC1+ VC2= V(C1+ C2)Ctotal= C1+ C2QtotalQtotal14Physics 212 Lecture 8, Slide 8Series Capacitor CircuitQQQ+Q+Q-Q-QVC1C2V1V2QVQKey point: Q is the same for both capacitorsAlso: V = V1+ V2Q=VCtotalKey point: Q = VCtotal= V1C1= V2C2Q/Ctotal= Q/C1+ Q/C21Ctotal1C11C2+=17Physics 212 Lecture 8, Slide 9Checkpoint 1CCCCC1/Ctotal= 1/C + 1/C= 2/CCtotal= C/2Ctotal= CCtotal= 2CWhich has lowest total capacitance:18Physics 212 Lecture 8, Slide 10Checkpoint 2Ctotal= CWhich has lowest total capacitance:CCCCCCleft= C/2Cright= C/2Ctotal= Cleft+ CrightCtotal= C20SamePhysics 212 Lecture 8, Slide 11Similar to Checkpoint 3C1C2C3V0V1Q1V2Q2V3Q3CtotalWhich of the following is NOT necessarily true:A) V0= V1B) Ctotal> C1C) V2= V3D) Q2= Q3E) V1= V2+ V324Physics 212 Lecture 8, Slide 12Checkpoint 325A circuit consists of three unequal capacitors C1, C2, and C3which are connected to a battery of voltage V0. The capacitance of C2is twice that of C1. The capacitance of C3is three times that of C1. The capacitors obtain charges Q1, Q2, and Q3.Compare Q1, Q2, and Q3.A. Q1> Q3> Q2B. Q1> Q2> Q3C. Q1> Q2= Q3D. Q1= Q2= Q3E. Q1< Q2= Q3“Since Q1 has the lowest capacitance, it has the highest charge and Q3 has the lowest”“Q=VC, V for C1 is greatest, charge in series for Q2, Q3 is the same”“The total capacitance of the Capacitors in series is 6/5C1. Since this total and C1 have the same amount of voltage between them, the charge through C2 and C3 must be higher in order to increase the capacitance to 6/5C1. Q2=Q3 because they are in series.”(HW 3,4)Physics 212 Lecture 8, Slide 13Checkpoint 3251. See immediately: Q2= Q3 (capacitors in series)23 2 3 1 1 11 1 1 1 1 52 3 6C C C C C C= + = + =23 165C C=A circuit consists of three unequal capacitors C1, C2, and C3which are connected to a battery of voltage V0. The capacitance of C2is twice that of C1. The capacitance of C3is three times that of C1. The capacitors obtain charges Q1, Q2, and Q3.Compare Q1, Q2, and Q3.A. Q1> Q3> Q2B. Q1> Q2> Q3C. Q1> Q2= Q3D. Q1= Q2= Q3E. Q1< Q2= Q3X X2. How about Q1vs. Q2and Q3? Calculate C23first.1 1 023 2 3 23 0 1 065Q C VQ Q Q C V C V== = = =Physics 212 Lecture 8, Slide 14In Prelecture 7 we calculated the work done to move charge Q from one plate to another:This is potential energy waiting to be used… Energy in a Capacitor+QV-QU = 1/2QV= 1/2CV2Since Q = VC=1/2Q2/CC26Physics 212 Lecture 8, Slide 15Messing w/ Capacitors• If connected to a battery V stays constant• If isolated then total Q stays constantκVC1= κ CV1= VQ1= C1V1= κ CV = κQκC1= κ CQ1= QV1= Q1/C1= Q/κC = V /κPhysics 212 Lecture 8, Slide 16Checkpoint 4a“Electric field decreases asd well as the voltage when dialectic is present. ““voltage is constant when a dielectric is added” “AHHHHHHH DECREASED DISTANCE INCREASES POTENTIAL DIFFERENCE”33Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2has been charged and disconnected, it is filled with a dielectric. Compare the voltages of the two capacitors.A. V1> V2B. V1= V2C. V1< V2Consider first the effect on the capacitance, then, does Q or V stay constant?Physics 212 Lecture 8, Slide 17Messing w/ CapacitorsU1/U0= κκ=2C0VC1VU = 1/2CV2Compare usingPotential Energy goes UP35A) U1< U0B) U0 = U1C) U1> U0Two 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.Physics 212 Lecture 8, Slide 18Checkpoint 4b33“The energy is inverse to the capacitance”“dielectric does not effect potential energy”“U=1/2(q)(v), and C increases which increases Q ” Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After C2has been charged and disconnected, it is filled with a dielectric. Compare the potential energy stored by the two capacitors.A. U1> U2B. U1= U2C. U1< U2Consider