Understanding Force and Energy in Electricity

1. Electrical Energy and Capacitance • Chapter 16

2. Review Review • What is potential energy? – Energy at rest or energy due to position

3. • What is a conservative force? – A conservative force is a force that does work in such a way that the work done depends only upon the initial and final positions.

4. • Frictional force is dissipative. • The Coulomb force is conservative.

5. • What is meant by the conservation of energy? – Energy cannot be created or destroyed, only transformed.

6. • Gravitational force is conservative. • Gravitational potential energy depends upon mass, gravity, and position.

7. Introduction Introduction • New concepts – Electric potential energy – Electric potential – Voltage between two points – Electric potential difference – Capacitance

8. Work Done on a Charge • Electrostatic force is conservative – Work may be done by a conservative force

9. • The equation for work done on a charge: Since F = qE W = (F) d = (qE) d

10. Electric Potential • Electric potential (V) is a scalar quantity – It is defined as the energy per unit charge (J/C) at a given point – The unit for electric potential is the volt (1 volt = 1 Joule/Coulomb)

11. Potential Difference • Definition of the potential difference (  V) between points A and B   V = V B - V A =  PE/q = -E . d The units are Volts or Joules /Coulomb

12. • Useful relationships: 1 V = 1 J/C 1 N/C = 1 V/m

13. Electrical PE and KE • A positive charge gains electrical PE when it moves against the field. • A positive charge gains KE when it moves in the same direction as the field. 166, 16.2

14. • A negative charge gains electrical PE when it moves in the same direction as the field. • A negative charge gains KE when it moves against the field. 167

15. Potential Difference And Electric Potential • A 12-volt automobile battery – Maintains a potential difference across its terminals • The positive terminal is at a higher potential. (+ 12 volts) • The negative terminal is at a lower potential (0 volts) and is connected to the car frame. • Charge moves around the circuit. 16.3

16. Zero Potential • A point of zero potential is usually defined by grounding some point in the circuit.

17. • A point at infinity may be considered to be at zero potential in relation to a positive charge.

18. Electric Potential at a Point • The electric potential, at a particular location, created by a point charge can be found by using: V = k e (q/r)

19. Electric Potential • The electric potential depends upon only two things:

20. • The electric potential depends upon only two things: – Charge – Location

21. • The electric potential exists at every point surrounding a given charge. – A second charge is not needed.

22. • Electric potential is a scalar quantity. – If there are two or more charges, the potentials add algebraically at a given point. – no vectors to worry about

23. Electric PE • Electric potential energy is the energy that a charge has due to its position in the electric field produced by another charge. It is measured in Joules. 133

24. • The electric potential (PE) energy of a pair of charges can be found by using: PE = q 2 V 1 = q 2 (k e q 1 /r) PE = k e (q 1 q 2 /r) 16.7

25. • The electric potential energy is positive if the charges are identical and negative if they are different.

26. Equipotentials • No work is required to move a charge between two points that are at the same potential. W = -q(V B – V A )

27. • All points on the surface of a charged conductor which is in electrostatic equilibrium are at the same potential.

28. • The electric potential is constant everywhere on the surface of a charged conductor in equilibrium.

29. • The electric potential is constant everywhere inside a conductor and equal to its value at the surface.

30. The Electron-Volt • The electron-volt is the energy of an electron after it has been accelerated across a potential difference of 1 volt. – It is a very small unit of energy. 1 eV = 1.6 x 10 -19 J

31. Equipotential Surfaces • What is an equipotential surface? – An equipotential surface is one where all points are at the same potential. 169

32. • No work is required to move a charge at a constant speed along an equipotential surface. 134

33. • The electric field at every point of an equipotential surface is perpendicular to the surface. 16.7

34. Equipotential Lines • Equipotential lines – Two - dimensional views – Equipotential lines are always perpendicular to electric field lines. 16.10, 170, 16.6

35. Applications • Electrostatic precipitator – Power company smokestacks • Electrostatic air cleaners – Furnace filters – Smoke eaters at party halls

36. • How does a copy machine work? – Corotron – Selenium drum – Heated pressure rollers 165

37. • How does laser printer work? 16.12

38. QUESTIONS 1, 4 – 7, 11 Pg. 564

39. Capacitors • What is a capacitor? – A capacitor is made up of two parallel metal plates with a surface area (A) separated by a dielectric with thickness (d) 171

40. • How it works: – Each plate is connected to one side of a battery – Charge flows until the plates have the same potential difference as the battery • One is positive while the other is negative (+ Q and –Q) 68

41. The Definition Of Capacitance • What is capacitance ? – Capacitance is the ratio of the magnitude of the charge on either conducting surface to the potential difference between the two conducting surfaces. C = Q/  V Therefore: Q =  V . C

42. • What is the unit of capacitance ? – Farad (F) • Named after Michael Faraday • 1 farad = 1 Coulomb/volt • Microfarads (  F) and picofarads (pF) are more commonly used

43. Capacitance Applications • Tuning stations on radio and television receivers • Storing charge in electronic flash units • Computer keyboards

44. The Parallel Plate Capacitor • Factors affecting capacitance: – Area (A) – Separation (d) – Permittivity of free space (  o ) C =  o A/d (in air) Also: k e = 1/4  o

45.  o = 8.85 x 10 -12 C 2 /N . m 2

46. • How things work: – Flash attachment

47. • How things work: – Computer keyboard 173

48. Circuit Symbols • Symbols for circuit elements – Battery – Capacitor – Resistor – Wires

49. Types of Electrical Circuits • Complete Circuits – Series – Parallel – Combination 7, 16.15

50. Capacitors in Parallel • In Parallel: – The potential differences across each of the capacitors is equal to the battery voltage 16.17

51. • In Parallel: – The equivalent capacitance of the circuit is equal to the sum of the individual capacitors C eq = C 1 + C 2 + …

52. • In Parallel: – The total charge stored by the capacitors is: Q = Q 1 + Q 2 + …

53. • In Parallel: – The equivalent capacitance of a parallel combination is always greater than any of the individual capacitances

54. Capacitors in Series • In Series: – The potential differences across each of the capacitors add up to the battery voltage 16.19

55. • In Series: – The equivalent capacitance of the circuit can be found by using: 1/C eq = 1/C 1 +1/C 2 + … There is a Shortcut!

56. • The equivalent capacitance of two capacitors in series can be found by using:

57. • In Series: – All of the capacitors must have the same charge: Q T = Q 1 = Q 2 = …

58. • In Series: – The equivalent capacitance of a series combination is always less than any individual capacitance in the combination 187, 188

59. Combinations Of Capacitors • Some circuits involve combinations of series and parallel capacitors

60. Energy Stored In A Charged Capacitor • A capacitor stores electrical energy in its field – Discharges can be dangerous if high voltages are present.

61. • Work is done in charging a capacitor W = 0.5 Q  V 50

62. • The energy stored in a capacitor is given by: E = 0.5 C  V 2

63. • Electrical breakdown limits the amount of energy that can be stored in a capacitor

64. Medical Applications • Defibrillators – Paddles – Capacitors charge to a high voltage – Charging takes time

65. Capacitors With Dielectrics • A dielectric is an insulating material – Examples of dielectrics • Rubber • Glass • Plastic • Waxed paper

66. • Dielectrics can increase capacitance – The dielectric constant (  ) • See Table 16.1 (Pg. 557) – Air has a dielectric constant of 1 C =  o A/d 172, 16.23

67. Types of Capacitors • Tubular • High voltage • Electrolytic (polarized) • Variable

68. Application: DNA And Forensic Science • DNA fragments are separated by mass and by charge

69. QUESTIONS 8, 9, 10, 12 - 14 Pg. 564