Electricity and Magnetism Isolated Conductors and Potential Capacitance

Transcription

1 Electricity and Magnetism Isolated Conductors and Potential Capacitance Lana Sheridan De Anza College Oct 15, 2015

2 Last time electric potential Electric potential from many charges

3 Overview Electric potential between charged plates Potential of charged conductor Conductor in a field Capacitance Capacitance of a parallel plate capacitor

4 Potential Difference across a pair of charged plates Earlier we found: V = E d cos θ If we have a pair of charged plates at a separation, d, there is a uniform E-field between them: E = σ ɛ 0. E = σ 1 E E = 0

5 Potential Difference across a pair of charged plates APTER 24 ELECTRIC POTENTIAL V = E d cos θ Equipotential surface Field line + (a) (b) The potential difference between the two plates, separation, d: V = E d +

6 d n ) d and perpendicular to the plates. (a) Rank the pairs according to the magnitude of the electric field between the plates, Question greatest Consider first. three (b) For pairs which of pair parallel is the plates with the same separation. electric field pointing rightward? (c) If an electron The electric is released field midway between between the plates is uniform and perpendicular third to the pair plates. of plates, does it remain there, move rightward at constant speed, move (a) Rank the pairs according to the magnitude of the electric field leftward at constant speed, accelerate between the plates, greatest first. rightward, or accelerate leftward? t s 0 ) e e 50 V +150 V 20 V +200 V (1) (2) 200 V 400 V (3) (A) 1, 2, 3 (B) (1 and 3), 2 (C) 2, (1 and 3) (D) 3, 2, 1

7 d n ) d and perpendicular to the plates. (a) Rank the pairs according to the magnitude of the electric field between the plates, Question greatest Consider first. three (b) For pairs which of pair parallel is the plates with the same separation. electric field pointing rightward? (c) If an electron The electric is released field midway between between the plates is uniform and perpendicular third to the pair plates. of plates, does it remain there, move rightward at constant speed, move (a) Rank the pairs according to the magnitude of the electric field leftward at constant speed, accelerate between the plates, greatest first. rightward, or accelerate leftward? t s 0 ) e e 50 V +150 V 20 V +200 V (1) (2) 200 V 400 V (3) (A) 1, 2, 3 (B) (1 and 3), 2 (C) 2, (1 and 3) (D) 3, 2, 1

8 n ) d the pairs according to the magnitude of the electric field between the plates, greatest first. (b) For which pair is the electric field pointing rightward? (c) If an Question electron Consider is released threemidway pairs between of parallel the plates with the same separation. third Thepair electric of plates, field does between it remain there, plates is uniform and perpendicular move rightward constant speed, move to the plates. leftward at constant speed, accelerate (b) For which pair is the electric field pointing rightward? rightward, or accelerate leftward? t s 0 ) e e 50 V +150 V 20 V +200 V (1) (2) 200 V 400 V (3) (A) 1 (B) 2 (C) 3

9 n ) d the pairs according to the magnitude of the electric field between the plates, greatest first. (b) For which pair is the electric field pointing rightward? (c) If an Question electron Consider is released threemidway pairs between of parallel the plates with the same separation. third Thepair electric of plates, field does between it remain there, plates is uniform and perpendicular move rightward constant speed, move to the plates. leftward at constant speed, accelerate (b) For which pair is the electric field pointing rightward? rightward, or accelerate leftward? t s 0 ) e e 50 V +150 V 20 V +200 V (1) (2) 200 V 400 V (3) (A) 1 (B) 2 (C) 3

10 Question Consider three pairs of parallel plates with the same separation. The electric field between the plates is uniform and perpendicular to the plates. 50 V +150 V 20 V +200 V (c) If an electron is released midway between the third pair of (1) plates, does it (2) 200 V 400 V (3) (A) remain there (B) move at constant speed (C) accelerate rightward, or (D) accelerate leftward?

11 Question Consider three pairs of parallel plates with the same separation. The electric field between the plates is uniform and perpendicular to the plates. 50 V +150 V 20 V +200 V (c) If an electron is released midway between the third pair of (1) plates, does it (2) 200 V 400 V (3) (A) remain there (B) move at constant speed (C) accelerate rightward, or (D) accelerate leftward?

12 From earlier: some Implications of Gauss s Law If an excess charge is placed on an isolated conductor, that amount of charge will move entirely to the surface of the conductor. None of the excess charge will be found within the body of the conductor. A shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell s charge were concentrated at the center of the shell. If a charged particle is located inside a shell of uniform charge, there is no electrostatic force on the particle from the shell.

13 Conductor in an Electric field The E-field inside an isolated conductor at equilibrium is zero. eg. an isolated conductor with excess charge: E = 0 1 Figure from Openstax College Physics.

14 762 Chapter 25 Electric Potential Potential due to an Isolated Charged Conductor a R perpendicular to t Equation 25.3, we essarily zero: b c k e Q R V E R k e Q r k e Q r 2 1 Figure from Serway Figure & Jewett, th (a) ed. The excess r r This result applies where on the surfa the surface of a potential surfac librium is at th field is zero insi inside the cond Because of the con

15 ming a small hole exists e Potential no net electric dueforce to an actsisolated Charged Conductor PART otential at all points inside r (m) SOLATED g a Because shows. CONDUCTOR all excess charge flows to 645 the outside, in the interior, the electric field is zero. (a) with radial distance for the l.the curves 12 of Fig b entiating with respect to r, 12 tant is zero). The curve of b by integrating with 8 V (kv) 4 E (kv/m) r (m) r (m) (a) (b) Since V = E d cos θ the potential inside the conductor is Fig constant. (a) A plot of V(r) both 12 inside and outside a charged spherical shell of radius 1.0 m. (b) A plot of 1 Figure from Halliday, Resnick, Walker, 9th ed.

16 inside is zero. We now generate another property of a charged c The electric potential potential. is constant Consider everywhere two points on a conductor and on the surfa (including the surface!), shown but in Figure the charge distribution Along a surface may vary. path connect Charge distribution on a conductor Notice from the spacing of the positive signs that the surface charge density is nonuniform. S E Figure An arbitra positive charge. When the librium, all the charge res the conductor, and the dir the conductor is perpendi potential is constant inside potential at the surface.

17 Charge distribution on a conductor An illustrative example (25.8), electric field around conductor. At all points on the object V is constant. q 1 r 1 V 1 = V 2 k e q 1 = k eq 2 r 1 r 2 q 1 = r 1 q 2 r 2 Since r 2 < r 1, q 1 > q 2. q 2 r 2 And σ 1 σ 2 = r 2 r 1 sharper curvature of surface, higher charge density

18 Charge distribution on a conductor An illustrative example (25.8), electric field around conductor. r 1 At all points on the object V is constant. q 1 V 1 = V 2 E 1 r 1 = E 2 r 2 E 1 E 2 = r 2 r 1 Since r 2 < r 1, E 1 < E 2. q 2 r 2 sharper curvature of surface, stronger electric field

19 Corona Discharge A corona discharge occurs when a conductor at a very high potential ionizes a fluid (eg. air) that surrounds it. The fields that form around sharp edges of the conductor are high enough to form small plasma regions, but not full electric breakdown.

20 Corona Discharge A corona discharge occurs when a conductor at a very high potential ionizes a fluid (eg. air) that surrounds it. The fields that form around sharp edges of the conductor are high enough to form small plasma regions, but not full electric breakdown. responsible for significant power losses in high voltage lines useful for pool sanitation ozone manufacture ionizers air purifiers nitrogen lasers (TEA lasers)

21 Coronal Discharge 1 Photo Wartenburg Pinwheel by Giles Read kV

22 Corona Discharge Fork in a microwave. (Microwave ovens generate electric fields.)

23 Capacitance capacitor Any two isolated conductors separated by some distance that store charges of equal magnitude and opposite sign. (When the capacitor is discharged this stored charge is 0.) Area A V Electric field lines Bottom side of top plate has charge +q d Top side of bottom plate has charge q A +q q The capacitance of a capacitor relates the potential difference across the capacitor to its stored charge. (a) Fig (a) A parallel-plate capacitor, made up of two plates of area A adistance d.the charges on the facing plate surfaces have the same magnit opposite signs. (b) As the field lines show, the electric field due to the charge (b)

24 seen by nighttime skiers on dry snow). Capacitors our discussion of capacitors is to determine how much. This how much is called capacitance. ce Usually capacitors are diagrammed and thought of as parallel sheets of equal area, but paired, isolated conductors of any shape me of can the many act as sizes capacitors. and shapes of capacitors. Figure 25-2 ments of any capacitor two isolated conductors of any +q q Fig Two conductors, isolated electrically from each other and from their surroundings, form a capacitor. When the capacitor is charged, the charges on the conductors, or plates as

25 Capacitors When a capacitor is charged is has a net charge +q on one plate and a net charge q on the other plate. An electric field exists between the plates. For the case of parallel sheet plates, the field is uniform, except at the edges of the plates. 2 Area A V Electric field lines Bottom side of top plate has charge +q d Top side of bottom plate has charge q A +q q (a) (b) Fig (a) A parallel-plate capacitor, made up of two plates of area A separated by adistance d.the charges on the facing plate surfaces have the same magnitude q but

26 Charge of a Capacitor The net charge on a capacitor is zero: (+q) + ( q) = 0. However, when we speak of the charge of a capacitor, q, we mean that the absolute value of the charge on either plate is q.

27 ia lightning. The charge that skis collect as they slide along d as Charge being stored ofin a capacitor Capacitor that frequently discharges as seen by nighttime skiers on dry snow). our discussion of capacitors is determine how much The net charge on a capacitor is zero: (+q) + ( q) = 0.. This how much is called capacitance. ce However, when we speak of the charge of a capacitor, q, we mean that the absolute value of the charge on either plate is q. me of The the many charge sizes onand this shapes capacitor of capacitors. is q: Figure 25-2 ments of any capacitor two isolated conductors of any +q q Fig Two conductors, isolated electrically from each other and from their surroundings, form a capacitor.

28 Potential Difference The potential difference between two points a and b is the difference between the electric potential at a and the potential at b. V = V b V a This can be positive or negative, but very, very often, people also just are interested in the magnitude of it, so quote it as: V = V b V a The book uses V instead of V for the potential difference from here on out. We will stick with V. What the book does can be a bit confusing, but unfortunately it is almost universally done when talking about circuits.

29 Capacitance When the capacitor is connected By definition capacitance is alwa potential difference DV are alw From Equation 26.1, we see Named in honor of Michael F When a battery is connected to the terminals to a of paira battery, of plates so that one plate is electrons transfer between the connected to the positive terminal of the battery and the other is plates and the wires so that the connected to the negative plates terminal, become charged. the plates become charged. Q d Q Area A The farad is a very large unit o itances ranging from microfar symbol mf to represent micro physical capacitors are often la crofarads or, equivalently, pf Let s consider a capacitor fo Each plate is connected potential difference. If the ca an electric field in the connec on the plate connected to the the wire applies a force on ele force causes the electrons to the plate, the wire, and the ter equilibrium situation is attain the terminal and the plate; as Figure 26.2 A parallel-plate 1 capacitor consists of two parallel Diagram from Serway conducting & Jewett, plates, 9theach ed, of page area 778. A, 1 Although the total charge on the capacit tor as there is excess negative charge on th either conductor as the charge on the cap

30 Capacitance capacitance, C The constant of proportionality relating the charge of the capacitor to the potential difference across it: q = C V ; C = Q V Capacitance is always positive by convention. where V is the potential difference between one plate of the capacitor and the other. Capacitance is measured in Farads. 1 F = 1 C/V. C is a property of the geometry of the capacitor.

31 Capacitance Questions A capacitor is altered so that the charge q is doubled on the plates, while the potential difference V is held constant. Capacitance: (A) increases (B) decreases (C) remains the same

32 Capacitance Questions A capacitor is altered so that the charge q is doubled on the plates, while the potential difference V is held constant. Capacitance: (A) increases (B) decreases (C) remains the same

33 Capacitance Questions A capacitor is altered so that the potential difference V is tripled across the plates, while the charge q is held constant. Capacitance: (A) increases (B) decreases (C) remains the same 1 Halliday, Resnick, Walker, page 658.

34 Capacitance Questions A capacitor is altered so that the potential difference V is tripled across the plates, while the charge q is held constant. Capacitance: (A) increases (B) decreases (C) remains the same 1 Halliday, Resnick, Walker, page 658.

35 Capacitance Questions If the potential difference is fixed, eg. the capacitor plates are charged by a constant 9 V battery, does capacitance (A) increase (B) decrease (C) remain the same when the separation of the plates d is doubled? 1 Halliday, Resnick, Walker, page 661.

36 Capacitance Questions If the potential difference is fixed, eg. the capacitor plates are charged by a constant 9 V battery, does capacitance (A) increase (B) decrease (C) remain the same when the separation of the plates d is doubled? 1 Halliday, Resnick, Walker, page 661.

37 Capacitance Questions If the potential difference is fixed, eg. the capacitor plate are charged by a constant 9 V battery, does capacitance (A) increase (B) decrease (C) remain the same when the area of the plates A is doubled?

38 Capacitance Questions If the potential difference is fixed, eg. the capacitor plate are charged by a constant 9 V battery, does capacitance (A) increase (B) decrease (C) remain the same when the area of the plates A is doubled?

39 Capacitance q = C V C = q V C is a property of the geometry of the capacitor. A particular capacitor will have a particular fixed value of C, just like a given resistor will have a constant value of resistance R. For a parallel plate capacitor: C = ɛ 0A d where d is the separation distance of the plates and A is the area of each plate

40 Capacitance Capacitors with different construction will have different values of C. For example, for a cylinderical capacitor of length L, inner radius a and outer radius b: L C = 2πɛ 0 ln(b/a)

41 Capacitance Capacitors with different construction will have different values of C. For example, for a cylinderical capacitor of length L, inner radius a and outer radius b: L C = 2πɛ 0 ln(b/a) for a spherical capacitor of inner radius a and outer radius b: C = 4πɛ 0 ab b a

42 Capacitance Capacitors with different construction will have different values of C. For example, for a cylinderical capacitor of length L, inner radius a and outer radius b: L C = 2πɛ 0 ln(b/a) for a spherical capacitor of inner radius a and outer radius b: C = 4πɛ 0 ab b a for an isolated charged sphere of radius R: C = 4πɛ 0 R

43 Parallel Plate Capacitor Back to the parallel plate capacitor: C = ɛ 0A d Let s justify why this expression should hold.

44 Parallel Plate Capacitor Back to the parallel plate capacitor: C = ɛ 0A d Let s justify why this expression should hold. From Guass s law: Q = ɛ 0 Φ E Q = ɛ 0 EA

45 Parallel Plate Capacitor Also: V = Ed Taking the ratio gives: Confirming that since C = Q/( V ). Q V = ɛ 0A d C = ɛ 0A d

46 Parallel Plate Capacitor In particular, notice that we used expressions for the charge on a parallel plate capacitor: q = ɛ 0 EA and the potential difference across the plates of a parallel plate capacitor: V = Ed

47 Circuits Circuits consist of electrical components connected by wires. Some types of components: batteries, resistors, capacitors, lightbulbs, LEDs, diodes, inductors, transistors, chips, etc. The wires in circuits can be thought of as channels for an electric field that distributes charge to (or charge flow through) the components.

48 Circuit substitution problem. of is superconducting magne Notice that this the as Equation 26.2 Notice that thisexpression expression is the samesame asthis Equation 26.2, the capa Capacitor section. Th approximately ten times g component symbols symbol initially unchar Use Equation to express the magnetic field in the tromagnets. Such superco In Supercond studying e storing energy. interior of the base solenoid: 26.3circuit Combinations resonance imaging, or MR diagram " Battery 26.3 Combin Find the mutual inductance, noting that magnetic Twothe or more capacitors oftenfo a organs without the need elements. The symbol battery V the equivalent capacitance of c! coil caused flux F BH through the handle s by the magful radiation. orthroughout more capacito Capacitor this Two section. this se wires between symbol initially theuncharged. equivalent capac netic field the base coil is BA: The of direction of the effective flowcapacitor of positive and switches asw In studying electric circuits, this section. Through diagram. Such The a diagra "a number circuit Switch Wireless charging is used ofinitially other cordless ds Battery in ure Open charge is clockwise. capacitor Csymbol 27.6 Electrical elements. Theuncharged. circuit symbolsp symbol! symbol used by some manufacturers of electricwires cars that avoids model for a dire cap In studying electric between the circuit elem I andcircuit switches as wellcircuits, as thesuch colo diagram. In typical electric ing apparatus. Closed is at the higher " Battery Switch ure The symbol for the ca Open elements. The circuit a source such as a battery symbol model for a capacitor, a pair of! switch Figure 26.6 Ssymbol CircuitClosed symbols forisdetermine between the atwires the higher potential and ci is r Let s an express batteries, and switches. Parallel Com and switches as well b capacitors, c symbols Figure 26.6 Circuit for transfer. First, consider thea capacitors, batteries, and Parallel Combination Notice that capacitors areswitches. in Switch uretwo The symbol # Open capacitors to a resistor. (Resistors are Notice that capacitors are in Rin green, Two capacitors as sho!v batteries blue, are and symbol model forconnected a capacitor blue, resistor R batteries are in green, andconnecting " wires also have nation of capacitors. Figure 26. nation of capac switches are in red. The closed switches are in red. The closed Closed is at the higher poten a d whereas capacitors. The left plates of the switch can carry current, some to the resistor. Unles capacitors. The switch can whereas the battery by a conducting wire thecarry open onecurrent, cannot.! Figure 26.6 Circuit symbols for ais capacitor When is conn wires small the open one batteries, cannot. the compared battery bywit a C L capacitors, and switches. Parallel Combinat " inductor L delivered to the wires is ne combination is an LC circu Q max Notice that capacitors are in Two capacitors following acurr pos blue, batteries are in green,then and Imagine closed, both theconne Figure A circuit consistnation of capacitors. switches are in red. The closedcircuit in Figure from late between maximum p ing of a resistor of can resistance R capacitors. The left pl switch carry current, whereas We identify the entire circu S and a battery having a potential cuit is zero, no energy is tr the open one cannot Oscillations the battery by a condu

49 Capacitor symbol Circuits: Batteries Battery symbol Switch symbol Batteries cause a potential difference between two parts of the circuit. Open This drives a charge flow. Closed this sectio initially u In stud circuit di elements. wires bet and switc ure model for is at the h

50 Circuits The different elements can be combined together in various ways to make complete circuits: paths for current to flow from one terminal of a battery or power supply to the other. l Terminal C h h l C + B V + B S Terminal S (a) (b) This 25-4 (a) Battery circuit is B, said switch to S, be and incomplete plates h and while l of capacitor the switch C, is connected open. in a cirb) A schematic diagram with the circuit elements represented by their symbols.

51 negative charges moving horizontally Flow of charge in a circuit ure Rank the current in these four Conventional current is said to flow from the positive terminal to the negative terminal. However, actually it is negatively charged electrons that flow through metal wires: c current, i d + 1 Figure from Serway and Jewett, 9th ed.

52 Series and Parallel Series When components are connected one after the other along a single path, they are connected in series. Parallel When components are connected side-by-side on different paths, they are connected in parallel. V R1 V R1 R 2 R 2

53 s stored on all the capacitors. Capacitors in Parallel + B V V q 3 q 2 C C 3 Capacitors in parallel all have the same potential (a) PART difference Terminal 3 across them. PARALLEL AND IN SERIES 663 Three capacitors in parallel: Equivalent circuit: with an equivalent Terminal capacitor that difference V as the actual +q + 3 +q 2 +q 1 +q + B V V V V B V q 3 q 2 C 2 q 1 C q 1 in parallel, we can simplify it with + +q C 3 sense word par-v, which is close (a) Terminal the same V. ) Figure 25-8b shows Parallel capacitors and Fig (a) Three capa citance We could C eq ) replace that has all three replaced capacitors thein the circuit with one their equivalent have in parallel to battery B.The equivalent 2,and C 3 ) of Fig. capacitance. 25-8a. The current and potential difference in the the same V ( par-v ). tains potential difference V rest of the circuit is unchanged by this. 8b,we first use Eq.25-1 to find the nals and thus across each ca equivalent capacitor, with c (b) Parallel c their equi the same C eq

54 s stored on all the capacitors. Capacitors in Parallel + B V V q 3 q 2 C C 3 Capacitors in parallel all have the same potential (a) PART difference Terminal 3 across them. PARALLEL AND IN SERIES 663 Parallel c Three capacitors in parallel: their equi Equivalent circuit: the same with an equivalent Terminal capacitor that difference V as the actual +q + 3 +q 2 +q 1 +q + B V V V V B V q 3 C 3 q 2 C 2 q 1 C q 1 C eq (b) sense word par-v, which is close (a) Terminal the same V. ) Figure 25-8b shows Parallel capacitors and Fig (a) Three capa citance We could C eq ) replace that has all three replaced capacitors thein the circuit with one their equivalent have in parallel to battery B.The equivalent 2,and C 3 ) of Fig. capacitance. 25-8a. The current and potential difference in the the same V ( par-v ). tains potential difference V rest of the circuit is unchanged by this. nals and thus across each ca What would be the capacitance of this equivalent equivalent capacitor? capacitor, with c +q + in parallel, we can simplify it with 8b,we first use Eq.25-1 to find the

55 Capacitors in Parallel Capacitors in parallel all have the same potential difference across them. V 1 = V 2 = V 3 = V The total charge on the three capacitors is the sum of the charge on each. where q 1 = C 1 V. Capacitance is C = q/( V ): q net = q 1 + q 2 + q 3 C eq = q net V

56 Capacitors in Parallel Equivalent capacitance: C eq = q net V = q 1 V + q 2 V + q 3 V = C 1 + C 2 + C 3

57 Capacitors in Parallel Equivalent capacitance: C eq = q net V = q 1 V + q 2 V + q 3 V = C 1 + C 2 + C 3 So in general, for any number n of capacitors in parallel, the effective capacitance of them all together is: C eq = C 1 + C C n = n i=1 C i

58 +q + B V V 2 q C 2 Capacitors in series all store the same charge. 664 CHAPTER 25 CAPACITANCE +q Three capacitors in series: V 3 q C 3 Terminal produces charge Terminal negative charge fr +q Series c Equivalent circuit: repelled negative V (a) 1 charge q). their That equ q C 1 charge from the the same to +q + plate +q + of capacitor B V V 2 B q of capacitor 1 help C V 2 q C battery, eq leaving th +q Here are two V 3 (b) q C 3 1. When charge is Fig (a) it can Three move capac alo Terminal nected in series Series capacitors and Fig. to 25-9a.If battery the B. (a) maintains their equivalent have 2. potential The battery differenc di Capacitors in Series

59 Capacitors in Series Again, we could replace all three capacitors in the circuit with one equivalent capacitance and we can find the capacitance of this equivalent capacitor. The sum of the potential differences across capacitors in series is V, the battery s supplied potential difference. V = V 1 + V 2 + V 3 where V 1 = q/c 1, etc. Then, C eq = q V

60 Capacitors in Series Equivalent capacitance: C eq = = = = = q V q V 1 + V 2 + V 3 [ ] V1 + V 2 + V 1 3 q [ V1 q + V 2 q + V 3 q [ ] 1 C 1 C 2 C 3 ] 1

61 Capacitors in Series In general, for any number n of capacitors in series, we can always relate the effective capacitance of them all together to the individual capacitances by: 1 C eq = 1 C C C n = n 1 C i i=1 The equivalent capacitance of capacitors in series is always less than the smallest capacitance in the series.

62 Practice A 5.0 µf capacitor is connected in parallel with a 10 µf capacitor. What is the equivalent capacitance of this arrangement?

63 Practice A 5.0 µf capacitor is connected in parallel with a 10 µf capacitor. What is the equivalent capacitance of this arrangement? C eq = 15 µf

64 Practice A 5.0 µf capacitor is connected in parallel with a 10 µf capacitor. What is the equivalent capacitance of this arrangement? C eq = 15 µf A 5.0 µf capacitor is connected in series with a 10 µf capacitor. What is the equivalent capacitance of this arrangement?

65 Practice A 5.0 µf capacitor is connected in parallel with a 10 µf capacitor. What is the equivalent capacitance of this arrangement? C eq = 15 µf A 5.0 µf capacitor is connected in series with a 10 µf capacitor. What is the equivalent capacitance of this arrangement? C eq = 3.3 µf

66 More Practice We first reduce the circuit to a single capacitor. What is the equivalent capacitance of this arrangement? A The equival parallel cap is larger. A C 1 = 12.0 µf V C 3 = 4.50 µf (a) C 2 = 5.30 µf B V C C (b)

67 itance More Practice When solving this type of problem, take an iterative approach. itance Identify sets of capacitors that are in parallel, then series, then parallel, etc. and at each step replace with the equivalent capacitance: and b for the re 26.9a. All ly and make e connected. llel connec- a a b a b b

68 y More can be Practice connected in series or pacitance for the combination, parallel When(c) solving either this way type because of problem, take an iterative approach. Identify sets of capacitors that are in parallel, then series, then parallel, etc. and at each step replace with the equivalent capacitance: the All ake ted. ecins 6.0 a b a b a b a 6.0 b a b c d Figure 26.9 (Example 26.3) To find the equivalent capacitance

69 More Practice We first reduce the circuit to a single capacitor. What is the equivalent capacitance of this arrangement: A The equival parallel cap is larger. A C 1 = 12.0 µf V C 3 = 4.50 µf (a) C 2 = 5.30 µf B V C C (b)

70 Summary Electric potential difference of charged plates electric potential and conductors capacitance Homework worksheet Halliday, Resnick, Walker: Ch 24, onward from page 651. Problems: 47, 59, 65, 73 Ch 25, onward from page 675. Questions: 1; Problems: 1, 3, 5