Agenda for Today. Elements of Physics II. Capacitors Parallel-plate. Charging of capacitors
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1 Capacitors Parallel-plate Physics 132: Lecture e 7 Elements of Physics II Charging of capacitors Agenda for Today Combinations of capacitors Energy stored in a capacitor Dielectrics in capacitors Physics 201: Lecture 1, Pg 1
2 How Capacitor works When a voltage is applied over a capacitor it will become charged. Circuit is open, and there is no charge on capacitor Battery Physics 201: Lecture 1, Pg 2
3 How Capacitor works When circuit is close and a voltage is applied over a capacitor it quickly becomes charged. -Q V C = 12 V +Q Battery V B = 12 V Potential difference is same as battery!! Electrons travel from y one oepaeo plate to the eother plate! Physics 201: Lecture 1, Pg 3
4 How Capacitor works What happens after capacitor is fully charged? No more charges flowing!!!! -Q +Q Battery Charge is ready to be used Physics 201: Lecture 1, Pg 4
5 How Capacitor works -Q +Q Battery Physics 201: Lecture 1, Pg 5
6 Definition of Capacitance Capacitance: The ratio of the charge on one conductor to the potential difference between conductors C Q V Units: Farad (F) The larger the capacitance, the more charge can be stored with a certain potential difference. Physics 201: Lecture 1, Pg 6
7 Parallel Plate Capacitor Capacitance of PP can be found: ε C Nm 2 A is area of plate 0 is permittivity of free space d is distance of separation Closer plates have bigger C!! C ε0 A d Physics 201: Lecture 1, Pg 7
8 How Capacitor works -Q +Q Battery Physics 201: Lecture 1, Pg 8
9 How Capacitor works -Q +Q Battery Physics 201: Lecture 1, Pg 9
10 How Capacitor works -Q +Q Battery Physics 201: Lecture 1, Pg 10
11 How Capacitor works -Q - +Q Battery Physics 201: Lecture 1, Pg 11
12 Capacitors Capacitors are important elements in electric circuits. They come in a variety of sizes and shapes. The keys on most computer keyboards are capacitor switches. Pressing the key pushes two capacitor plates closer together, increasing their capacitance. Physics 201: Lecture 1, Pg 12
13 Capacitors A capacitor can be charged slowly but then can release the energy very quickly. An important t medical application of capacitors is the defibrillator. A heart attack or a serious injury can cause the heart to enter a state known as fibrillation in which the heart muscles twitch randomly and cannot pump blood. A strong electric shock through the chest completely stops the heart,,giving gthe cells that control the heart s rhythm a chance to restore the proper heartbeat. Physics 201: Lecture 1, Pg 13
14 E-field of Capacitor We will approximate as constant: E 0 Q / A 0 Q A 0 Physics 201: Lecture 1, Pg 14
15 Dielectrics in Capacitors Insulating sheets called dielectrics are sometimes placed between the plates of a capacitor This allows for the plates to be closer together thus having a larger capacitance (without electrons flowing between) So we get a new relation for the capacitance of PP when a dielectric is between the plates: C κε 0 A d is dielectric constant Physics 201: Lecture 1, Pg 15
16 Dielectrics in Capacitors Electric field when capacitor is charged When a dielectric is added it polarizes Thi k E fi ld This makes an E-field that partially cancels the original E-field. Allows more charge to be held on the capacitor, thus capacitance is increased Physics 201: Lecture 1, Pg 16
17 Capacitors The production of a practical capacitor, as shown, almost always involves the use of a solid or liquid dielectric. All materials have a maximum electric field they can sustain without breakdown the production of a spark. The breakdown electric field of air is about V/m. A material s maximum sustainable electric field is called its dielectric strength. Physics 201: Lecture 1, Pg 17
18 Capacitors Physics 201: Lecture 1, Pg 18
19 Stored energy in a capacitor First electron: W = q V = q (0) Last electron: W = q V q V Average: W = 1/2 q V -Q +Q Battery U 1 2 QV Using Q = CV U = ½QV = ½CV 2 = ½Q 2 /C Physics 201: Lecture 1, Pg 19
20 Capacitors in Parallel -Q +Q 2 2 Total charge is increased! Potential difference is same for both! -Q 1 +Q 1 Battery Two capacitors don t y effect ec each other Physics 201: Lecture 1, Pg 20
21 Capacitors in Parallel C eq =C 1 +C 2 + The equivalent capacitance of a parallel combination of capacitors is greater than any of the individual capacitors Physics 201: Lecture 1, Pg 21
22 Capacitors in Series This time the capacitors will effect each other Potential difference of capacitors adds up to that of battery V B = V C1 + V C2 -Q +Q -Q V C1 V C2 +Q V B Battery Charge must be equal Physics 201: Lecture 1, Pg 22
23 Capacitors in Series V Q C C eq 1 C C eq V 1 V 2 Q Q C C C 1 C 2 The equivalent capacitance of a series combination i is always less than any individual id capacitor in the combination Physics 201: Lecture 1, Pg 23
24 Give it a try: Two configurations of capacitors are shown below. The capacitors are all identical. What is the ratio of the equivalent capacitance C B of configuration B to the equivalent capacitance C A configuration A? (a) C B / C A = 1/4 (b) C B / C A = 1/2 (c) C B / C A = 1 (d) C B / C A = 2 (e) C B / C A = 4 Physics 201: Lecture 1, Pg 24
25 Give it a try: Two configurations of capacitors are shown below. The capacitors are all identical. What is the ratio of the equivalent capacitance C B of configuration B to the equivalent capacitance C A configuration A? Physics 201: Lecture 1, Pg 25
26 Summary: Parallel and Series Parallel: Capacitors in parallel have the same potential difference V Q = Q 1 +Q 2 C 1 C 2 C eq C eq = C 1 + C 2 + Series: Capacitors in series have the same charge Q V= V 1 + V 2 1 C eq 1 1 C 1 C 2 C1 1 C 2 C eq Physics 201: Lecture 1, Pg 26
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