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Capacitance and Dielectrics in Electric Energy Storage

This chapter discusses capacitance, dielectrics, and electric energy storage. It explores concepts such as charge comparison in capacitors, molecular description of dielectrics, and the role of dielectric constant. Additionally, the chapter provides a summary of key concepts in capacitors and introduces electric currents and resistance.

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Capacitance and Dielectrics in Electric Energy Storage

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  1. Chapter 24Capacitance, Dielectrics, Electric Energy Storage

  2. Recap:

  3. C2 = 1.0 mF C3 = 1.0 mF C1 = 1.0 mF 10 V 1) Q1=Q2 2) Q1>Q2 3) Q1<Q2 4) all charges are zero ConcepTest 24.3c Capacitors III How does the charge Q1 on the first capacitor (C1) compare to the charge Q2 on the second capacitor (C2)?

  4. C2 = 1.0 mF C3 = 1.0 mF C1 = 1.0 mF 10 V 1) Q1=Q2 2) Q1>Q2 3) Q1<Q2 4) all charges are zero ConcepTest 24.3c Capacitors III How does the charge Q1 on the first capacitor (C1) compare to the charge Q2 on the second capacitor (C2)? We already know that the voltage across C1 is 10 V and the voltage across both C2 and C3 is 5 V each. Since Q = CV and C is the same for all the capacitors, we have V1 > V2 and therefore Q1 > Q2.

  5. 24-6 Molecular Description of Dielectrics The molecules in a dielectric, when in an external electric field, tend to become oriented in a way that reduces the external field.

  6. 24-6 Molecular Description of Dielectrics This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential. This reorientation of the molecules results in an induced charge – there is no net charge on the dielectric, but the charge is asymmetrically distributed. The magnitude of the induced charge depends on the dielectric constant:

  7. Summary of Chapter 24 • Capacitor: nontouching conductors carrying equal and opposite charge. • Capacitance: • Capacitance of a parallel-plate capacitor:

  8. Summary of Chapter 24 • Capacitors in parallel: • Capacitors in series:

  9. Summary of Chapter 24 • Energy density in electric field: • A dielectric is an insulator. • Dielectric constant gives ratio of total field to external field. • For a parallel-plate capacitor:

  10. Chapter 25Electric Currents and Resistance

  11. Units of Chapter 25 • The Electric Battery • Electric Current • Ohm’s Law: Resistance and Resistors • Resistivity • Electric Power

  12. Units of Chapter 25 • Power in Household Circuits • Alternating Current • Microscopic View of Electric Current: Current Density and Drift Velocity • Superconductivity • Electrical Conduction in the Nervous System

  13. 25-1 The Electric Battery Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte. This is a simple electric cell.

  14. 25-1 The Electric Battery A battery transforms chemical energy into electrical energy. Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them. This potential difference can be maintained even if a current is kept flowing, until one or the other terminal is completely dissolved.

  15. 25-1 The Electric Battery Several cells connected together make a battery, although now we refer to a single cell as a battery as well.

  16. 25-2 Electric Current Electric current is the rate of flow of charge through or past a point: The instantaneous current is given by: Unit of electric current: the ampere, A: 1 A = 1 C/s.

  17. 25-2 Electric Current A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn’t look much like the physical circuit!

  18. 25-2 Electric Current Example: Current is flow of charge. A steady current of 2.5 A exists in a wire for 4.0 min. (a) How much total charge passed by a given point in the circuit during those 4.0 min? (b) How many electrons would this be? In a hydrogen atom, an electron circles a nucleus. Given that it takes a minimum of 13.6 eV to remove an electron from a hydrogen atom, what current is circling the nucleus?

  19. Hydrogen atom

  20. ConcepTest 25.1 Connect the Battery 4) all are correct 5) none are correct Which is the correct way to light the lightbulb with the battery? 1) 2) 3)

  21. ConcepTest 25.1 Connect the Battery 4) all are correct 5) none are correct Which is the correct way to light the lightbulb with the battery? 1) 2) 3) Current can flow only if there is a continuous connection from the negative terminal through the bulb to the positive terminal. This is the case for only Fig. (3).

  22. 25-2 Electric Current By convention, current is defined as flowing from + to -. Electrons actually flow in the opposite direction, but not all currents consist of electrons. Thanks, Ben!

  23. 25-3 Ohm’s Law: Resistance and Resistors Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends:

  24. 25-3 Ohm’s Law: Resistance and Resistors The ratio of voltage to current is called the resistance (R):

  25. 25-3 Ohm’s Law: Resistance and Resistors In many conductors, the resistance is independent of the voltage; this relationship is called Ohm’s law. Materials that do not follow Ohm’s law are called nonohmic. Unit of resistance: the ohm, Ω: 1 Ω = 1 V/A. (Diode)

  26. 25-3 Ohm’s Law: Resistance and Resistors Conceptual Example 25-3: Current and potential. Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B? (b) Is the current greater at point A or at point B?

  27. 25-3 Ohm’s Law: Resistance and Resistors Example 25-4: Flashlight bulb resistance. A small flashlight bulb draws 300 mA from its 1.5-V battery. (a) What is the resistance of the bulb? (b) If the battery becomes weak and the voltage drops to 1.2 V, how would the current change?

  28. 25-3 Ohm’s Law: Resistance and Resistors Standard resistors are manufactured for use in electric circuits; they are color-coded to indicate their value and precision.

  29. 25-3 Ohm’s Law: Resistance and Resistors This is the standard resistor color code. Note that the colors from red to violet are in the order they appear in a rainbow.

  30. 25-3 Ohm’s Law: Resistance and Resistors • Some clarifications: • Batteries maintain a (nearly) constant potential difference; the current varies. • Resistance is a property of a material or device. • Current is not a vector but it does have a direction. • Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end.

  31. 25-4 Resistivity The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area: The constant ρ, the resistivity, is characteristic of the material.

  32. 25-4 Resistivity This table gives the resistivity and temperature coefficients of typical conductors, semiconductors, and insulators.

  33. 25-4 Resistivity Example 25-5: Speaker wires. Suppose you want to connect your stereo to remote speakers. (a) If each wire must be 20 m long, what diameter copper wire should you use to keep the resistance less than 0.10 Ω per wire? (b) If the current to each speaker is 4.0 A, what is the potential difference, or voltage drop, across each wire?

  34. ConcepTest 25.2Ohm’s Law 1) Ohm’s law is obeyed since the current still increases when V increases 2) Ohm’s law is not obeyed 3) this has nothing to do with Ohm’s law You double the voltage across a certain conductor and you observe the current increases three times. What can you conclude?

  35. ConcepTest 25.2Ohm’s Law 1) Ohm’s law is obeyed since the current still increases when V increases 2) Ohm’s law is not obeyed 3) this has nothing to do with Ohm’s law You double the voltage across a certain conductor and you observe the current increases three times. What can you conclude? Ohm’s law, V = IR, states that the relationship between voltage and current is linear. Thus, for a conductor that obeys Ohm’s law, the current must double when you double the voltage. Follow-up: Where could this situation occur?

  36. ConcepTest 25.3b Wires II 1) it decreasesby a factor of 4 2) it decreasesby a factor of 2 3) it stays the same 4) it increasesby a factor of 2 5) it increasesby a factor of 4 A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance?

  37. ConcepTest 25.3b Wires II 1) it decreasesby a factor of 4 2) it decreasesby a factor of 2 3) it stays the same 4) it increasesby a factor of 2 5) it increasesby a factor of 4 A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? Keeping the volume (= area x length) constant means that if the length is doubled, the area is halved. Since , this increases the resistance by a factor of 4.

  38. 25-5 Electric Power Power, as in kinematics, is the energy transformed by a device per unit time: or

  39. 25-5 Electric Power The unit of power is the watt, W. For ohmic devices, we can make the substitutions:

  40. 25-5 Electric Power Example 25-8: Headlights. Calculate the resistance of a 40-W automobile headlight designed for 12 V.

  41. 25-4 Resistivity For any given material, the resistivity increases with temperature: Semiconductors are complex materials, and may have resistivities that decrease with temperature.

  42. 25-4 Resistivity Example: Resistance thermometer. A nichrome heater dissipates 500 W when the applied potential difference is 110 V and the wire temperature is 800 oC. What would the dissipation rate be if the wire temperature were held at 200 oC by immersing the wire in a bath of oil while the applied potential difference remains the same?

  43. 25-5 Electric Power What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time. We have been measuring energy in joules, but the electric company measures it in kilowatt-hours, kWh: 1 kWh = (1000 W)(3600 s) = 3.60 x 106 J.

  44. 25-5 Electric Power Example: Electric light. A 100 W light bulb is plugged into a standard 120 V outlet. a) At $0.08/kW-hr, how much does it cost to have the bulb on 24 hrs/day for a 31-day month? b) What is the resistance of the bulb? c) What is the current in the bulb?

  45. Electric light

  46. 25-6 Power in Household Circuits The wires used in homes to carry electricity have very low resistance. However, if the current is high enough, the power will increase and the wires can become hot enough to start a fire. To avoid this, we use fuses or circuit breakers, which disconnect when the current goes above a predetermined value.

  47. 25-6 Power in Household Circuits Fuses are one-use items – if they blow, the fuse is destroyed and must be replaced.

  48. 25-6 Power in Household Circuits Circuit breakers, which are now much more common in homes than they once were, are switches that will open if the current is too high; they can then be reset.

  49. 25-7 Alternating Current Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC).

  50. 25-7 Alternating Current , The voltage varies sinusoidally with time: , as does the current:

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