Fig 26-CO All of these devices are capacitors, which store electric charge and energy. A capacitor is one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs) Fig 26-CO, p.795

Variable capacitors (typically 10 to 500 pF) usually consist of two interwoven sets of Figure 26.18 A variable capacitor. When one set of metal plates is rotated so as to lie between a fixed set of plates, the capacitance of the device changes. Fig 26-18, p.813

Figure 26. 17 Three commercial capacitor designs Figure 26.17 Three commercial capacitor designs. (a) A tubular capacitor, whose plates are separated by paper and then rolled into a cylinder. Fig 26-17a, p.813

Figure 26.5 (Quick Quiz 26.2) One type of computer keyboard button. Fig 26-5, p.800

Fig 26-CO All of these devices are capacitors, which store electric charge and energy. A capacitor is one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs) Fig 26-CO, p.795

Capacitors on a chip Fig 26-CO, p.795 Fig 26-CO All of these devices are capacitors, which store electric charge and energy. A capacitor is one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs) Fig 26-CO, p.795

Transmission Lines Fig 26-CO, p.795 Fig 26-CO All of these devices are capacitors, which store electric charge and energy. A capacitor is one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs) Fig 26-CO, p.795

MOS FET Fig 26-CO All of these devices are capacitors, which store electric charge and energy. A capacitor is one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs) Fig 26-CO, p.795

Figure 26.3 (b) Electric field pattern of two oppositely charged conducting parallel plates. Small pieces of thread on an oil surface align with the electric field. Fig 26-3b, p.799

Figure 25.6 (Example 25.2) A proton accelerates from A to B in the direction of the electric field. Fig 25-6, p.767

Figure 26. 17 Three commercial capacitor designs Figure 26.17 Three commercial capacitor designs. (b) A high-voltage capacitor consisting of many parallel plates separated by insulating oil. Fig 26-17b, p.813

Figure 26. 17 Three commercial capacitor designs Figure 26.17 Three commercial capacitor designs. (c) An electrolytic capacitor. Fig 26-17c, p.813

Figure 26. 17 Three commercial capacitor designs Figure 26.17 Three commercial capacitor designs. (a) A tubular capacitor, whose plates are separated by paper and then rolled into a cylinder. (b) A high-voltage capacitor consisting of many parallel plates separated by insulating oil. (c) An electrolytic capacitor. Fig 26-17, p.813

Figure 26. 1 A capacitor consists of two conductors Figure 26.1 A capacitor consists of two conductors. When the capacitor is charged, the conductors carry charges of equal magnitude and opposite sign. Fig 26-1, p.796

Figure 26.2 A parallel-plate capacitor consists of two parallel con-ducting plates, each of area A, separated by a distance d. When the capacitor is charged by connecting the plates to the terminals of a battery, the plates carry equal amounts of charge. One plate carries positive charge, and the other carries negative charge. Fig 26-2, p.797

Figure 26.3 (a) The electric field between the plates of a parallel-plate capacitor is uniform near the center but nonuniform near the edges. Fig 26-3a, p.799

Figure 26. 8 Circuit symbols for capacitors, batteries, and switches Figure 26.8 Circuit symbols for capacitors, batteries, and switches. Note that capacitors are in blue and batteries and switches are in red. Fig 26-8, p.802

Active Figure 26.9 (a) A parallel combination of two capacitors in an electric circuit in which the potential difference across the battery terminals is V. (b) The circuit diagram for the parallel combination. (c) The equivalent capacitance is Ceq C1=C2. Fig 26-9, p.803

Active Figure 26. 10 (a) A series combination of two capacitors Active Figure 26.10 (a) A series combination of two capacitors. The charges on the two capacitors are the same. (b) The circuit diagram for the series combination. (c) The equivalent capacitance can be calculated from the relationship 1 /Ceq =1 /C 1+ 1/ C 2 . Fig 26-10, p.804

Figure 26.11 (Example 26.4) To find the equivalent capacitance of the capacitors in part (a), we reduce the various combinations in steps as indicated in parts (b), (c), and (d), using the series and parallel rules described in the text. Fig 26-11, p.806

 Figure 26.12 A plot of potential difference versus charge for a capacitor is a straight line having a slope 1/C. The work required to move charge dq through the potential difference V existing at the time across the capacitor plates is given approximately by the area of the shaded rectangle. The total work required to charge the capacitor to a final charge Q is the triangular area under the straight line, W =1/2 Q V. (Don’t forget that 1 V J/C; hence, the unit for the triangular area is the joule.) Fig 26-12, p.807

Figure 26.25 (a) Polar molecules are randomly oriented in the absence of an external electric field. (b) When an external electric field is applied, the molecules partially align with the field. (c) The charged edges of the dielectric can be modeled as an additional pair of parallel plates establishing an electric field Eind in the direction opposite to that of E0. Fig 26-25, p.817

Figure 26.28 (Example 26.9) (a) A parallel-plate capacitor of plate separation d partially filled with a metallic slab of thickness a. Fig 26-28a, p.819

Table 26-1, p.812

Figure 26.6 (Example 26.2) (a) A cylindrical capacitor consists of a solid cylindrical conductor of radius a and length l surrounded by a coaxial cylindrical shell of radius b. (b) End view. The electric field lines are radial. The dashed line represents the end of the cylindrical gaussian surface of radius r and length l. Fig 26-6, p.801

Figure 26.7 (Example 26.3) A spherical capacitor consists of an inner sphere of radius a surrounded by a concentric spherical shell of radius b. The electric field between the spheres is directed radially outward when the inner sphere is positively charged. Fig 26-7, p.802

Table 26-2, p.821

Figure 26. 16 Dielectric breakdown in air Figure 26.16 Dielectric breakdown in air. Sparks are produced when the high voltage between the wires causes the electric field to exceed the dielectric strength of air. Fig 26-16, p.812

Active Figure 26.4 (a) A circuit consisting of a capacitor, a battery, and a switch. (b) When the switch is closed, the battery establishes an electric field in the wire that causes electrons to move from the left plate into the wire and into the right plate from the wire. As a result, a separation of charge exists on the plates, which represents an increase in electric potential energy of the system of the circuit. This energy in the system has been transformed from chemical energy in the battery. Fig 26-4, p.800

Active Figure 26.4 (a) A circuit consisting of a capacitor, a battery, and a switch. Fig 26-4a, p.800

Active Figure 26.4 (b) When the switch is closed, the battery establishes an electric field in the wire that causes electrons to move from the left plate into the wire and into the right plate from the wire. As a result, a separation of charge exists on the plates, which represents an increase in electric potential energy of the system of the circuit. This energy in the system has been transformed from chemical energy in the battery. Fig 26-4b, p.800

Figure 26.6 (Example 26.2) (a) A cylindrical capacitor consists of a solid cylindrical conductor of radius a and length l surrounded by a coaxial cylindrical shell of radius b. Fig 26-6a, p.801

Figure 26. 6 (Example 26. 2) (b) End view Figure 26.6 (Example 26.2) (b) End view. The electric field lines are radial. The dashed line represents the end of the cylindrical gaussian surface of radius r and length l. Fig 26-6b, p.801

Active Figure 26.9 (a) A parallel combination of two capacitors in an electric circuit in which the potential difference across the battery terminals is V. Fig 26-9a, p.803

Active Figure 26.9 (b) The circuit diagram for the parallel combination. Fig 26-9b, p.803

Active Figure 26.9 (c) The equivalent capacitance is Ceq C1=C2. Fig 26-9c, p.803

Active Figure 26. 10 (a) A series combination of two capacitors Active Figure 26.10 (a) A series combination of two capacitors. The charges on the two capacitors are the same. Fig 26-10a, p.804

Active Figure 26.10 (b) The circuit diagram for the series combination. Fig 26-10b, p.804

Active Figure 26.10 (c) The equivalent capacitance can be calculated from the relationship 1 /Ceq =1 /C 1+ 1/ C 2 . Fig 26-10c, p.804

Figure 26.11 (Example 26.4) To find the equivalent capacitance of the capacitors in part (a), we reduce the various combinations in stepsas indicated in parts (b), (c), and (d), using the series and parallel rules described in the text. Fig 26-11, p.806

Figure 26.13 (Example 26.5) (a) Two capacitors are charged to the same initial potential difference and connected together with plates of opposite sign to be in contact when the switches are closed. Fig 26-13a, p.808

Figure 26.13 (Example 26.5) (b) When the switches are closed, the charges redistribute. Fig 26-13b, p.808

Figure 26.15 A charged capacitor (a) before and (b) after insertion of a dielectric between the plates. The charge on the plates remains unchanged, but the potential difference decreases from V0 to V= V0/k . Thus, the capacitance increases from C0 to C0. Fig 26-15, p.811

Figure 26.25 (a) Polar molecules are randomly oriented in the absence of an external electric field. Fig 26-25a, p.817

Figure 26.25 (b) When an external electric field is applied, the molecules partially align with the field. Fig 26-25b, p.817

that the induced charge density is two-thirds the charge density on the plates. If no dielectric is present, then 1 and ind 0 as expected. However, if the dielectric is replaced by an electrical conductor, for which E 0, then Equation 26.22 indicates Figure 26.26 Induced charge on a dielectric placed between the plates of a charged capacitor. Note that the induced charge density on the dielectric is less than the charge density on the plates. Fig 26-26, p.818

Figure 26.25 (c) The charged edges of the dielectric can be modeled as an additional pair of parallel plates establishing an electric field Eind in the direction opposite to that of E0. Fig 26-25c, p.817

Figure 26. 19 (Quick Quiz 26. 8) A stud-finder Figure 26.19 (Quick Quiz 26.8) A stud-finder. (a) The materials between the plates of the capacitor are the wallboard and air. (b) When the capacitor moves across a stud in the wall, the materials between the plates are the wallboard and the wood. The change in the dielectric constant causes a signal light to illuminate. Fig 26-19, p.813

Figure 26.14 In a hospital or at an emergency scene, you might see a patient being revived with a defibrillator. The defibrillator’s paddles are applied to the patient’s chest, and an electric shock is sent through the chest cavity. The aim of this technique is to restore the heart’s normal rhythm pattern. Adam Hart- Davis/ SPL/ Custom Medical Stock Fig 26-14, p.810

Figure 26.20 (Example 26.7) (a) A battery charges up a parallel-plate capacitor. (b) The battery is removed and a slab of dielectric material is inserted between the plates. Fig 26-20, p.814

Figure 26.20 (Example 26.7) (a) A battery charges up a parallel-plate capacitor. Fig 26-20a, p.814

Figure 26.20 (Example 26.7) (b) The battery is removed and a slab of dielectric material is inserted between the plates. Fig 26-20b, p.814

Figure 26.21. The electric dipole moment of this configuration is defined as the vector p directed from q toward q along the line joining the charges and having magnitude 2aq : (26.16) Figure 26.21 An electric dipole consists of two charges of equal magnitude and opposite sign separated by a distance of 2a. The electric dipole moment p is directed from q toward q. Fig 26-21, p.815

O on the negative charge is also of magnitude Fa sin ; here again, the force tends to Figure 26.22 An electric dipole in a uniform external electric field. The dipole moment p is at an angle to the field, causing the dipole to experience a torque. Fig 26-22, p.815

water molecule and other polar molecules as dipoles because the average positions of the positive and negative charges act as point charges. As a result, we can apply our discussion of dipoles to the behavior of polar molecules. Microwave ovens take advantage of the polar nature of the water molecule. When Figure 26.23 The water molecule, H2O, has a permanent polarization resulting from its nonlinear geometry. The center of the positive charge distribution is at the point . Fig 26-23, p.816

left, as shown in Figure 26.24b, would cause the center of the positive charge distribu-tion to shift to the left from its initial position and the center of the negative charge Figure 26.24 (a) A linear symmetric molecule has no permanent polarization. (b) An external electric field induces a polarization in the molecule. Fig 26-24, p.816

Figure 26.27 The nonuniform electric field near the edges of a parallel-plate capacitor causes a dielectric to be pulled into the capacitor. Note that the field acts on the induced surface charges on the dielectric, which are nonuniformly distributed. Fig 26-27, p.818

Figure 26.28 (Example 26.9) (a) A parallel-plate capacitor of plate separation d partially filled with a metallic slab of thickness a. (b) The equivalent circuit of the device in part (a) consists of two capacitors in series, each having a plate separation (d= a)/2. Fig 26-28, p.819

Figure 26.28 (Example 26.9) (b) The equivalent circuit of the device in part (a) consists of two capacitors in series, each having a plate separation (d= a)/2. Fig 26-28b, p.819

Figure 26.29 (Example 26.10) (a) A parallel-plate capacitor of plate separation d partially filled with a dielectric of thickness d/3. (b) The equivalent circuit of the capacitor consists of two capacitors connected in series. Fig 26-29, p.820

Figure 26.29 (Example 26.10) (a) A parallel-plate capacitor of plate separation d partially filled with a dielectric of thickness d/3. Fig 26-29a, p.820

Figure 26.29 (Example 26.10) (b) The equivalent circuit of the capacitor consists of two capacitors connected in series. Fig 26-29b, p.820

Figure 26.15 A charged capacitor (a) before and (b) after insertion of a dielectric between the plates. The charge on the plates remains unchanged, but the potential difference decreases from V0 to V= V0/k . Thus, the capacitance increases from C0 to C0. Fig 26-15a, p.811

Figure 26.15 A charged capacitor (a) before and (b) after insertion of a dielectric between the plates. The charge on the plates remains unchanged, but the potential difference decreases from V0 to V= V0/k . Thus, the capacitance increases from C0 to C0. Fig 26-15b, p.811

Figure 26. 19 (Quick Quiz 26. 8) A stud-finder Figure 26.19 (Quick Quiz 26.8) A stud-finder. (a) The materials between the plates of the capacitor are the wallboard and air. Fig 26-19a, p.813

Figure 26. 19 (Quick Quiz 26. 8) A stud-finder Figure 26.19 (Quick Quiz 26.8) A stud-finder. (b) When the capacitor moves across a stud in the wall, the materials between the plates are the wallboard and the wood. The change in the dielectric constant causes a signal light to illuminate. Fig 26-19b, p.813

Fig P26-10, p.823

Fig P26-18, p.823

Fig P26-21, p.824

Fig P26-22, p.824

Fig P26-23, p.824

Fig P26-27, p.824

Fig P26-29, p.824

Fig P26-30, p.825

Fig P26-38, p.825

Fig P26-49, p.826

Fig P26-54, p.827

Fig P26-55, p.827

Fig P26-57, p.827

Fig P26-61, p.828

Fig P26-61, p.828

Fig P26-64, p.828

Fig P26-70, p.829

Fig P26-72, p.829

Fig P26-75, p.829