May Term in Guatemala

1. GDS 3559/STS 3500: Engineering Public Health: An Interdisciplinary Exploration of Community Development in Guatemala Interested in Public Health? Global Health? Medicine? Want to Learn how engineering affects community health? May Term in Guatemala Contact Kent Wayland (kaw6r@virginia.edu), Eric Anderson (ewa3a@virginia.edu), or David R. Burt, MD, at drb5p@virginia.edu for more information!

2. Chapter 24Capacitance, Dielectrics, Electric Energy Storage

3. Recap:

4. ConcepTest 24.1Capacitors 1) C1 2) C2 3) both have the same charge 4) it depends on other factors Capacitor C1 is connected across a battery of 5 V. An identical capacitor C2 is connected across a battery of 10 V. Which one has more charge?

5. ConcepTest 24.1Capacitors 1) C1 2) C2 3) both have the same charge 4) it depends on other factors Capacitor C1 is connected across a battery of 5 V. An identical capacitor C2 is connected across a battery of 10 V. Which one has more charge? Since Q = CV and the two capacitors are identical, the one that is connected to the greater voltage has more charge, which is C2 in this case.

6. –Q +Q ConcepTest 24.2aVarying Capacitance I 1) increase the area of the plates 2) decrease separation between the plates 3) decrease the area of the plates 4) either (1) or (2) 5) either (2) or (3) What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)?

7. –Q +Q ConcepTest 24.2aVarying Capacitance I 1) increase the area of the plates 2) decrease separation between the plates 3) decrease the area of the plates 4) either (1) or (2) 5) either (2) or (3) What must be done to a capacitor in order to increase the amount of charge it can hold (for a constant voltage)? Since Q = CV, in order to increase the charge that a capacitor can hold at constant voltage, one has to increase its capacitance. Since the capacitance is given by , that can be done by either increasing A or decreasing d.

8. 24-3 Capacitors in Series and Parallel Capacitors in parallel have the same voltage across each one. The equivalent capacitor is one that stores the same charge when connected to the same battery:

9. 24-3 Capacitors in Series and Parallel Capacitors in series have the same charge. In this case, the equivalent capacitor has the same charge across the total voltage drop. Note that the formula is for the inverse of the capacitance and not the capacitance itself!

10. 24-3 Capacitors in Series and Parallel Example 24-5: Equivalent capacitance. Determine the capacitance of a single capacitor that will have the same effect as the combination shown.

11. 24-3 Capacitors in Series and Parallel Example 24-5: Equivalent capacitance. Determine the capacitance of a single capacitor that will have the same effect as the combination shown.

12. 24-3 Capacitors in Series and Parallel Example 24-6: Charge and voltage on capacitors. Determine the charge on each capacitor and the voltage across each, assuming C = 3.0 μF and the battery voltage is V = 4.0 V.

13. 24-3 Capacitors in Series and Parallel Example 24-6: Charge and voltage on capacitors. Determine the charge on each capacitor and the voltage across each, assuming C = 3.0 μF and the battery voltage is V = 4.0 V.

14. 24-3 Capacitors in Series and Parallel Example 24-6: Charge and voltage on capacitors. Determine the charge on each capacitor and the voltage across each, assuming C = 3.0 μF and the battery voltage is V = 4.0 V.

15. o C Ceq C C o ConcepTest 24.3aCapacitors I 1) Ceq = 3/2C 2) Ceq = 2/3C 3) Ceq = 3C 4) Ceq = 1/3C 5) Ceq = 1/2C What is the equivalent capacitance, Ceq , of the combination below?

16. o C Ceq C C o ConcepTest 24.3aCapacitors I 1) Ceq = 3/2C 2) Ceq = 2/3C 3) Ceq = 3C 4) Ceq = 1/3C 5) Ceq = 1/2C What is the equivalent capacitance, Ceq , of the combination below? The 2 equal capacitors in series add up as inverses, giving 1/2C. These are parallel to the first one, which add up directly. Thus, the total equivalent capacitance is 3/2C.

17. C2 = 1.0 mF C3 = 1.0 mF C1 = 1.0 mF 10 V ConcepTest 24.3b Capacitors II 1) V1=V2 2) V1>V2 3) V1<V2 4) all voltages are zero How does the voltage V1 across the first capacitor (C1) compare to the voltage V2 across the second capacitor (C2)?

18. C2 = 1.0 mF C3 = 1.0 mF C1 = 1.0 mF 10 V ConcepTest 24.3b Capacitors II 1) V1=V2 2) V1>V2 3) V1<V2 4) all voltages are zero How does the voltage V1 across the first capacitor (C1) compare to the voltage V2 across the second capacitor (C2)? The voltage across C1 is 10 V. The combined capacitors C2+ C3 are parallel to C1. The voltage across C2 + C3 is also 10 V. Since C2 and C3 are in series, their voltages add. Thus the voltage across C2 and C3 each has to be 5 V, which is less than V1. Follow-up:What is the current in this circuit?

19. 24-4 Electric Energy Storage A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor. Consider two sheets of charge, one positive and one negative on the surface of conductor b. Work required to pull the negatively charged sheet to conductor a is:

20. 24-4 Electric Energy Storage National Ignition Facility (NIF) Lawrence Livermore National Laboratory

21. NIF • Laser system driven by 4000 300 μF capacitors • which store a total of 422 MJ. They take 60 s to • charge and are discharged in 400 μs. • What is the potential difference across each • capacitor? • What is the power delivered during the • discharge?

22. NIF • Laser system driven by 4000 300 μF capacitors • which store a total of 422 MJ. They take 60 s to • charge and are discharged in 400 μs. • What is the potential difference across each • capacitor? • What is the power delivered during the • discharge? • Solution: • U = CV2/2 →V = (2U/C)1/2 • →V = [2(422x106)/4000/300x10-6] ½ = 26.5 kV • P = W/t = U/t = 422x106 /400x10-6 ~ 1012 W • = 1000 GW! cf. 1.0-1.5 GW for power plant

23. 24-4 Electric Energy Storage Conceptual Example: Capacitor plate separation increased. A parallel-plate capacitor carries charge Q and is then disconnected from a battery. The two plates are initially separated by a distance d. Suppose the plates are pulled apart until the separation is 2d. a) How has the energy stored in this capacitor changed? b) Would the answer change if the battery were not disconnected?

24. 24-4 Electric Energy Storage

25. 24-4 Electric Energy Storage Heart defibrillators use electric discharge to “jump-start” the heart, and can save lives.

26. 24-4 Electric Energy Storage The energy density, u, defined as the energy per unit volume, is the same no matter the origin of the electric field: The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source – be careful!

27. 24-5 Dielectrics A dielectric is an insulator, and is characterized by a dielectric constant K. Capacitance of a parallel-plate capacitor filled with dielectric: Using the dielectric constant, we define the permittivity:

28. 24-5 Dielectrics Dielectric strength is the maximum field a dielectric can experience without breaking down.

29. 24-5 Dielectrics Here are two experiments where we insert and remove a dielectric from a capacitor. In the first, the capacitor is connected to a battery, so the voltage remains constant. The capacitance increases, and therefore the charge on the plates increases as well.

30. 24-5 Dielectrics In this second experiment, we charge a capacitor, disconnect it, and then insert the dielectric. In this case, the charge remains constant. Since the dielectric increases the capacitance, the potential across the capacitor drops.

31. 24-5 Dielectrics Example 24-11: Dielectric removal. A parallel-plate capacitor, filled with a dielectric with K= 3.4, is connected to a 100-V battery. After the capacitor is fully charged, the battery is disconnected. The plates have area A= 4.0 m2 and are separated by d = 4.0 mm. (a) Find the capacitance, the charge on the capacitor, the electric field strength, and the energy stored in the capacitor. (b) The dielectric is carefully removed, without changing the plate separation nor does any charge leave the capacitor. Find the new values of capacitance, electric field strength, voltage between the plates, and the energy stored in the capacitor.

32. 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.

33. 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:

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

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

36. 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:

37. Questions?