普通物理 General Physics 25 - Capacitors and Capacitance 郭艷光Yen-Kuang Kuo 國立彰化師大物理系暨光電科技研究所 電子郵件: ykuo@cc.ncue.edu.tw 網頁: http://ykuo.ncue.edu.tw

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Outline 25-1 What Is Physics? 25-2 Capacitance 25-3 Calculating the Capacitance 25-4 Capacitors in Parallel and in Series 25-5 Energy Stored in an Electric Field 25-6 Capacitor with a Dielectric 25-7 Dielectrics: An Atomic View 25-8 Dielectrics and Gauss’ Law 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 25-1 What Is Physics? The focus of this chapter is on one extremely common example—the capacitor, a device in which electrical energy can be stored. The physics of capacitors can be generalized to other devices and to any situation involving electric fields. 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 25-2 Capacitance V+ V- SI Unit: Farad (symbol F) 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 25-2 Capacitance V q O q = CV -q +q + -_ V Capacitance Batteries 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-3 Calculating the Capacitance V+ V- 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-3 Calculating the Capacitance S P N 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-3 Calculating the Capacitance Cylindrical Capacitor: S 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-3 Calculating the Capacitance Spherical Capacitor: S 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-1 Switch S is closed to connect the uncharged capacitor of capacitance C = 0.25μF to the battery of potential difference V = 12 V. The lower capacitor plate has thickness L = 0.5 cm and face area A = 2.0 × 10-4 m2, and it consists of copper, in which the density of conduction electrons is n = 8.49 × 1028 electrons/m3. From what depth d within the plate must electrons move to the plate face as the capacitor becomes charged? 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-1 Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-4 Capacitors in Parallel and in Series 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-4 Capacitors in Parallel and in Series 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-2 (a) Find the equivalent capacitance for the combination of capacitances shown below, across which potential difference V is applied. Assume C1 = 12.0 F, C2 = 5.30 F, and C3 = 4.50 F. 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-2 (a) Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-2 (b) The potential difference applied to the input terminals is V = 12.5 V. What is the charge on C1? 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-2 (b) Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-3 Capacitor 1, with C1 = 3.55 F, is charged to a potential difference V0 = 6.30 V, using a 6.30 V battery. The battery is then removed, and the capacitor is connected as in Fig. 25-10 to an uncharged capacitor 2, with C2 = 8.95 F. When switch S is closed, charge flows between the capacitors until they have the same potential difference V. Find the charge on each capacitor when equilibrium is reached. 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-3 Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-5 Energy Stored in an Electric Field + dq' q' -q' V' - + q -q d A q' q V' V Charge Voltage O A B 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-4 A gurney holding a burn victim caught fire as the gurney was withdrawn from an enclosed chamber filled with oxygen-enriched air (hyperbaric chamber). Investigators realized that charge separation occurred between the patient’s skin, the hospital gown on the patient, and the sheet on the gurney. They also found that the gurney and the part of the chamber’s metal framework below the gurney formed a parallel-plate capacitor of capacitance Ci = 250 pF. 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-4 If the gurney discharged its excess charge and the associated energy by sparking, could the spark ignite the gurney? Measurements revealed that a spark could occur only if the potential difference V on the gurney-framework capacitor exceeded 2000 V and that a fire could start only if the capacitor’s potential energy U exceeded 0.20 mJ. However, the potential difference on the gurney-framework capacitor was only Vi = 600 V, not enough to produce a spark. 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-4(a) As the gurney was withdrawn from the chamber, the area of the gurney-framework overlap decreased. Thus, the plate area of the capacitor decreased from its initial value Ai. What was the potential difference Vf when the overlap plate area was Af = 0.10Ai? 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-4 (a) Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-4 (b) What was the energy Uf of the gurney-framework capacitor when the plate area was 0.10Ai? 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-4 (b) Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-5 (a) An isolated conducting sphere whose radius R is 6.85 cm has a charge q = 1.25 nC. How much potential energy is stored in the electric field of this charged conductor? 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-5 (a) Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-5 (b) What is the energy density at the surface of the sphere? Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-6 Capacitor with a Dielectric 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-6 Capacitor with a Dielectric 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-6 A parallel-plate capacitor whose capacitance C is 13.5 pF is charged by a battery to a potential difference V = 12.5 V between its plates. The charging battery is now disconnected, and a porcelain slab (κ = 6.50) is slipped between the plates. What is the potential energy (1) of the capacitor before the slab is inserted and (2) of the capacitor–slab device after the slab is inserted? 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-6 Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-7 Dielectrics: An Atomic View 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

25-8 Dielectrics and Gauss’ Law 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-7 A parallel-plate capacitor of plate area A and plate separation d. A potential difference V0 is applied between the plates. The battery is then disconnected, and a dielectric slab of thickness b and dielectric constant is placed between the plates as shown. Assume A = 115 cm2, d = 1.24 cm, V0 = 85.5 V, b = 0.780 cm, and κ = 2.61. 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-7 (a) What is the capacitance C0 before the dielectric slab is inserted? (b) What free charge appears on the plates? (c) What is the electric field E0 in the gaps between the plates and the dielectric slab? (d) What is the electric field E1 in the dielectric slab? (e) What is the potential difference V between the plates after the slab has been introduced? (f ) What is the capacitance with the slab in place between the plates of the capacitor? 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-7 Solutions: 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 Example 25-7 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授

普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授 End of chapter 25! 2018/9/20 普通物理講義-25 / 國立彰化師範大學物理系/ 郭艷光教授