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Week # 12
Capacitance and Dielectric: Capacitors & capacitances, capacitors in
series & parallel, dielectrics, molecular model of induced charges
Book: “University Physics” by Young & Freedman 13th edition, page: P-725”
Physics-II (Ph-1002), 4 (3, 3)
1
24.1: Capacitors and Capacitance, p-789
24.1 Any two conductors and
insulated from each other form a
capacitor.
In circuit diagrams a capacitor is
represented by either of these symbols
2
Calculating Capacitance: Capacitors in Vacuum
The simplest form of capacitor consists of two parallel conducting
plates, each with area A separated by a distance d that is small in
comparison with their dimensions (Fig. 24.2a). When the plates are
charged, the electric field is almost completely localized in the region
between the plates (Fig. 24.2b). As we discussed in Example 22.8
(Section 22.4), the field between such plates is essentially uniform, and
the charges on the plates are uniformly distributed over their opposing
surfaces. We call this arrangement a parallel-plate capacitor.
3
4
5
6
Application of Capacitor: 24.3 p-790, Inside a condenser
microphone is a capacitor with one rigid plate and one
flexible plate. The two plates are kept at a constant
potential difference Vab. Sound waves cause the flexible
plate to move back and forth, varying the capacitance C
and causing charge to flow to and from the capacitor in
accordance with the relationship C=Q/Vab . Thus a sound
wave is converted to a charge flow that can be amplified
and recorded digitally.
Front plate Back plate

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Week-12(ph-1002).pptx

  • 1. Week # 12 Capacitance and Dielectric: Capacitors & capacitances, capacitors in series & parallel, dielectrics, molecular model of induced charges Book: “University Physics” by Young & Freedman 13th edition, page: P-725” Physics-II (Ph-1002), 4 (3, 3) 1
  • 2. 24.1: Capacitors and Capacitance, p-789 24.1 Any two conductors and insulated from each other form a capacitor. In circuit diagrams a capacitor is represented by either of these symbols 2
  • 3. Calculating Capacitance: Capacitors in Vacuum The simplest form of capacitor consists of two parallel conducting plates, each with area A separated by a distance d that is small in comparison with their dimensions (Fig. 24.2a). When the plates are charged, the electric field is almost completely localized in the region between the plates (Fig. 24.2b). As we discussed in Example 22.8 (Section 22.4), the field between such plates is essentially uniform, and the charges on the plates are uniformly distributed over their opposing surfaces. We call this arrangement a parallel-plate capacitor. 3
  • 4. 4
  • 5. 5
  • 6. 6 Application of Capacitor: 24.3 p-790, Inside a condenser microphone is a capacitor with one rigid plate and one flexible plate. The two plates are kept at a constant potential difference Vab. Sound waves cause the flexible plate to move back and forth, varying the capacitance C and causing charge to flow to and from the capacitor in accordance with the relationship C=Q/Vab . Thus a sound wave is converted to a charge flow that can be amplified and recorded digitally. Front plate Back plate
  • 7. 7
  • 8. 8
  • 9. 9
  • 10. 10
  • 11. 11
  • 12. 12
  • 13. 13
  • 14. 14
  • 15. 15
  • 16. 16
  • 17. 17
  • 18. 24.2: Capacitors in Series and Parallel, p-793 Capacitors in Series 18
  • 19. 19
  • 20. 20
  • 21. 21
  • 22. 22
  • 23. 23
  • 24. 24 Application Touch Screens and Capacitance The touch screen on a mobile phone, an MP3 player, or (as shown here) a medical device uses the physics of capacitors. Behind the screen are two parallel layers, one behind the other, of thin strips of a transparent conductor such as indium tin oxide. A voltage is maintained between the two layers. The strips in one layer are oriented perpendicular to those in the other layer; the points where two strips overlap act as a grid of capacitors. When you bring your finger (a conductor) up to a point on the screen, your finger and the front conducting layer act like a second capacitor in series at that point. The circuitry attached to the conducting layers detects the location of the capacitance change, and so detects where you touched the screen.
  • 25. 25 The physics of a computer keyboard. One common kind of computer keyboard is based on idea of capacitance. Each key is mounted on one end of a plunger, the other end being attached to a movable metal plate . The movable plate is separated from a fixed plate, two plates forming a capacitor. When the key is pressed, movable plate is pushed closer to the fixed plate, and the capacitance increases. Electronic circuitry enables the computer to detect the change in capacitance, thereby recognizing which key has been pressed. The separation of the plates is normally but decreases to when a key is pressed. The plate area is , and the capacitor is filled with a material whose dielectric constant is 3.50 . In one kind of computer keyboard, each key, when pressed, changes the separation between the plates of a capacitor
  • 27. 27
  • 29. 29
  • 30. 30 The physics of an electronic flash attachment for a camera. The energy-storing capability of a capacitor is often put to good use in electronic circuits. For example, in an electronic flash attachment for a camera, energy from the battery pack is stored in a capacitor. The capacitor is then discharged between the electrodes of the flash tube, which converts the energy into light. Flash duration times range from 1/200 to 1/1 000 000 second or less, with the shortest flashes being used in high-speed photography. Some flash attachments automatically control the flash duration by monitoring the light reflected from the photographic subject and quickly stopping or quenching the capacitor discharge when the reflected light reaches a predetermined level.
  • 31. 31 The physics of a defibrillator: During a heart attack, the heart produces a rapid, unregulated pattern of beats, a condition known as cardiac fibrillation. Cardiac fibrillation can often be stopped by sending a very fast discharge of electrical energy through the heart. Emergency medical personnel use defibrillators. A paddle is connected to each plate of a large capacitor, and the paddles are placed on the chest near the heart. The capacitor is charged to a potential difference of about a thousand volts. The capacitor is then discharged in a few thousandths of a second; the discharge current passes through a paddle, the heart, and the other paddle. Within a few seconds, the heart often returns to its normal beating pattern.
  • 32. 32
  • 33. 33
  • 34. 34
  • 35. 35
  • 36. 36
  • 37. 37
  • 38. 38
  • 39. 39 Most capacitors have a non-conducting material, or dielectric, between their conducting plates. A common type of capacitor uses long strips of metal foil for the plates, separated by strips of plastic sheet such as Mylar. A sandwich of these materials is rolled up, forming a unit that can provide a capacitance of several microfarads in a compact package. First, it solves the mechanical problem of maintaining two large metal sheets at a very small separation without actual contact. Second, using a dielectric increases the maximum possible potential difference between the capacitor plates. Any insulating material, when subjected to a sufficiently large electric field, experiences a partial ionization that permits conduction through it. This is called dielectric breakdown. Many dielectric materials can tolerate stronger electric fields without breakdown than can air. Thus using a dielectric allows a capacitor to sustain a higher potential difference (V) and so store greater amounts of charge and energy. Placing a solid dielectric between the plates of a capacitor serves three functions.
  • 40. 40 Third, the capacitance of a capacitor of given dimensions is greater when there is a dielectric material between the plates than when there is vacuum. We can demonstrate this effect with the aid of a sensitive electrometer (a device that measures the potential difference between two conductors without letting any appreciable charge flow from one to the other). Figure 24.14a next slide shows an electrometer connected across a charged capacitor, with magnitude of charge (Q) on each plate and potential difference (V) When we insert an uncharged sheet of dielectric, such as glass, paraffin, or polystyrene, between the plates, experiment shows that the potential difference decreases to a smaller value (Fig. 24.14b, next slide). When we remove the dielectric, the potential difference returns to its original value showing that the original charges on the plates have not changed.
  • 41. 41
  • 42. 42
  • 43. The charge Q is the same in both cases, and V is less than Vo so we conclude that the capacitance C with the dielectric present is greater Co than When the space between plates is completely filled by the dielectric, the ratio of C to Co (equal to the ratio of Vo to V) is called the dielectric constant of the material, K = C/C0 (definition of dielectric constant) ……….. (eq. 24.12) When the charge is constant Q = C0/V0 (without dielectric)— (i ) and Q=C/V (with dielectric) -----------(ii) So from i &ii C/C0 = V0/V eq 24.12 can be written as K=V0/V ►V=Vo / K With the dielectric present, the potential difference for a given charge Q is reduced by a factor K
  • 44. 44
  • 45. 45
  • 46. 46
  • 47. 47 Application: Dielectric Cell Membrane The membrane of a living cell behaves like a dielectric between the plates of a capacitor. The membrane is made of two sheets of lipid molecules, with their water-insoluble ends in the middle and their water-soluble ends (shown in red) on the surfaces of the membrane. The conductive fluids on either side of the membrane (water with negative ions inside the cell, water with positive ions outside) act as charged capacitor plates, and the non-conducting membrane acts as a dielectric with K of about 10. The potential difference V across the membrane is about 0.07 V and the membrane thickness d is about 7×10-9 m, so the electric field E = V/d in the membrane is about 10-7 V/m—close to the dielectric strength of the membrane. If the membrane were made of air, V and E would be larger by a factor of K≈10 and dielectric breakdown would occur.
  • 48. 24.5: Molecular Model of Induced Charge See book p-805, Uni Phy. 13th ed. 48
  • 49. 49 24.19 Polarization of a dielectric in an electric field E gives rise to thin layers of bound charges on the surfaces, creating surface charge densities σi and -σi . The sizes of the molecules are greatly exaggerated for clarity.
  • 50. 50