Your omments I thin this was easier than normal. I felt really good about the capacitance characteristics, although not quite as much about charge and other factors. The most confusing part was the different capacitor configurations. The concept of capacitance is difficult. Does it mean the amount of charge that can be contained in the electric field? Does that mean there is a limit? I am a little confused about the electric potential energy between a capacitor, can u explain it more? I understand the different types of connections and calculating the capacitance, charge, etc. However, I don't thin I'm fully understanding the dielectric and what exactly happens when that is placed between a capacitor. Particularly the last checpoint question is what I'm confused on. I thought I understood it until I was ased those questions. If the dialectic capacitor has less potential energy, why do we use dielectrics in capacitors??? Isn't the point to store energy? Bring on the resistors! How come a battery isn't defined as a capacitor in a circuit diagram even though the prelecture says that a battery is a capacitor? Electricity & Magnetism Lecture 8, Slide 1
Electricity & Magnetism Lecture 8, Slide 2
Exam Logistics 1) EXAM 1: WED February 19 th at 7pm Sign Up in Gradeboo for onflict Exam at 5:15pm if desired MATERIAL: Lectures 1-8 2) EXAM 1 PREPARATION Old Exams are a good way to assess what you need to now Prelecture of Fall 2010 solutions available 3) Extra Office Hours (Tuesday/ Wednesday next wee chec room#) Who is ready for that test... ;_; Electricity & Magnetism Lecture 7, Slide 3
Physics 212 Lecture 8 Today s oncept: apacitors (apacitors in a circuits, Dielectrics, Energy in capacitors) Electricity & Magnetism Lecture 8, Slide 4
Simple apacitor ircuit Q Q = 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. Electricity & Magnetism Lecture 8, Slide 5
Parallel apacitor ircuit Q total 1 2 Q 1 = 1 Q 2 = 2 Q total Key point: is the same for both capacitors Key Point: Q total = Q 1 + Q 2 = 1 + 2 = ( 1 + 2 ) total = 1 + 2 Electricity & Magnetism Lecture 8, Slide 6
Series apacitor ircuit Q Q = total 1 Q 1 2 2 Q Key point: Q is the same for both capacitors Key point: Q = total = 1 1 = 2 2 Also: = 1 + 2 Q/ total = Q/ 1 + Q/ 2 1 1 1 = + total 1 2 Electricity & Magnetism Lecture 8, Slide 7
hecpoint 1 Which has lowest total capacitance: A B total = 1/ total = 1/ + 1/ = 2/ total = /2 total = 2 Electricity & Magnetism Lecture 8, Slide 8
hecpoint 2 Which has lowest total capacitance? A) Single apacitor B) 4 apacitors ) Same : total = left = /2 right = /2 total = left + right total = Electricity & Magnetism Lecture 8, Slide 9
Similar to hecpoint 3 2 Q 2 0 1 2 3 1 Q 1 3 Q 3 total Which of the following is NOT necessarily true: A) 0 = 1 B) total > 1 ) 2 = 3 D) Q 2 = Q 3 E) 1 = 2 + 3 Electricity & Magnetism Lecture 8, Slide 10
hecpoint 3 A circuit consists of three unequal capacitors 1, 2, and 3 which are connected to a battery of voltage 0. The capacitance of 2 is twice that of 1. The capacitance of 3 is three times that of 1. The capacitors obtain charges Q 1, Q 2, and Q 3. ompare Q 1, Q 2, and Q 3. A. Q 1 > Q 3 > Q 2 B. Q 1 > Q 2 > Q 3. Q 1 > Q 2 = Q 3 D. Q 1 = Q 2 = Q 3 E. Q 1 < Q 2 = Q 3 X X 1. See immediately: Q 2 = Q 3 (capacitors in series) 2. How about Q 1 vs. Q 2 and Q 3? alculate 23 first. 1 1 1 1 1 5 = + = + = 2 3 6 23 2 3 1 1 1 6 = 5 23 1 Q = 1 1 0 6 Q = Q = Q = = 5 23 2 3 23 0 1 0 25
Dielectrics 0 Q 0 = 0 1 = 0 Q 1 = 1 By adding a dielectric you are just maing a new capacitor with larger capacitance (factor of ) Electricity & Magnetism Lecture 8, Slide 15
Messing with apacitors If connected to a battery stays constant 1 = 1 = Q 1 = 1 1 = = Q If isolated then total Q stays constant Q 1 = Q 1 = 1 = Q 1 / 1 = Q/ = / Electricity & Magnetism Lecture 8, Slide 16
hecpoint 4a Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. Then, a dielectric is placed between the plates of 2 A B Both have the same charge but 2 has a bigger capacitance so it has a smaller voltage. oltage depends on charge not dielectric =Q/. Q stays the same while increases due to the dielectric, so in order to adjust for this increase, we need to decrease the. Electricity & Magnetism Lecture 8, Slide 17
Messing with apacitors licer Question Two identical parallel plate capacitors are connected to identical batteries. Then a dielectric is inserted between the plates of capacitor 1. ompare the energy stored in the two capacitors. 0 1 A) U 1 < U 0 B) U 0 = U 1 ) U 1 > U 0 ompare using U = 1 / 2 2 U 1 /U 0 = Potential Energy goes UP Electricity & Magnetism Lecture 8, Slide 18
hecpoint 4b Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. Then, a dielectric is placed between the plates of 2 A) B) ) The potential energy is directly related to the electric field. The lower the field, the lower the potential energy. The potential energy depends on the charge only =Q/ Q remains the same while reduced, so increase. since U=0.5^2, U is increased. Electricity & Magnetism Lecture 8, Slide 19
hecpoint 4c Two identical parallel plate capacitors are given the same charge Q, after which they are disconnected from the battery. After 2 has been charged and disconnected, it is filled with a dielectric. The two capacitors are now connected to each other by wires as shown. How will the charge redistribute itself, if at all? A. The charges will flow so that the charge on 1 will become equal to the charge on 2. B. The charges will flow so that the energy stored in 1 will become equal to the energy stored in 2.. The charges will flow so that the potential difference across 1 will become the same as the potential difference across 2. D. No charges will flow. The charge on the capacitors will remain what it was before they were connected. must be the same!! Q: U: Q 1 Q2 = Q 1 1 = Q 1 2 2 2 1 2 1 2 1 1 2 2 2 2 U = U = U = 1 1 U2 2
alculation x 0 0 x 0 /4 An air-gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. onceptual Analysis: Q What changes when the dielectric added? What is Q f, the final charge on the capacitor? A) Only B) only Q ) only D) and Q E) and Q Adding dielectric changes the physical capacitor does not change and changes changes Q changes Electricity & Magnetism Lecture 8, Slide 21
alculation x 0 0 Strategic Analysis: alculate new capacitance Apply definition of capacitance to determine Q x 0 /4 An air-gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. What is Q f, the final charge on the capacitor? To calculate, let s first loo at: left right A) left < right B) left = right ) left > right The conducting plate is an equipotential! Electricity & Magnetism Lecture 8, Slide 22
alculation x 0 0 An air-gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. x 0 /4 A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. What is Q f, the final charge on the capacitor? an consider capacitor to be two capacitances, 1 and 2, in parallel = 1 2 What is 1? A) 1 = 0 B) 1 = 3 / 4 0 ) 1 = 4 / 3 0 D) 1 = 1 / 4 0 In general. For parallel plate capacitor: = e 0 A/d A = 3 / 4 A 0 d = d 0 1 = 3 / 4 (e 0 A 0 /d 0 ) 1 = 3 / 4 0 Electricity & Magnetism Lecture 8, Slide 23
alculation x 0 0 An air-gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. x 0 /4 A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. = 1 2 1 = 3 / 4 0 What is Q f, the final charge on the capacitor? What is 2? A) 2 = 0 B) 2 = 3 / 4 0 ) 2 = 4 / 3 0 D) 2 = 1 / 4 0 In general. For parallel plate capacitor filled with dielectric: = e 0 A/d A = 1 / 4 A 0 d = d 0 = ¼(e 0 A 0 /d 0 ) 2 = 1 / 4 0 Electricity & Magnetism Lecture 8, Slide 24
alculation x 0 0 An air-gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. x 0 /4 A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. = What is Q f, the final charge 1 2 on the capacitor? 2 = 1 1 = 3 / 4 0 / 4 0 What is? -1 1 1 A) = 1 + 2 B) = 1 + 2 ) = + 1 2 = parallel combination of 1 and 2 : = 1 + 2 = 0 ( 3 / 4 + 1 / 4 ) Electricity & Magnetism Lecture 8, Slide 25
alculation x 0 0 An air-gap capacitor, having capacitance 0 and width x 0 is connected to a battery of voltage. x 0 /4 A dielectric ( ) of width x 0 /4 is inserted into the gap as shown. = 1 2 1 = 3 / 4 0 What is Q f, the final charge on the capacitor? 2 = 1 / 4 0 = 0 ( 3 / 4 + 1 / 4 ) What is Q? Q Q f Q = 3 1 = 0 + 4 4 Electricity & Magnetism Lecture 8, Slide 26