1cc. The figure shows a charged capacitor. What is the net charge on
the capacitor?...a) (+q) + (–q) = 0b) |+q| + |–q| = 0c) |+q| + |–q| =
2qd) (+q) + (–q) = 2qe) q Get solution
1mcq. In the circuit shown in the figure, the capacitance for each capacitor is C. The equivalent capacitance for these three capacitors isa) ...b) ...c) ...d) ...e) C.f) ...... Get solution
2cc. Suppose you charge a parallel plate capacitor using a battery and then remove the battery, isolating the capacitor and leaving it charged. You then move the plates of the capacitor farther apart. The potential difference between the plates willa) increase.b) decrease.c) stay the same.d) not be determinable. Get solution
2mcq. A parallel plate capacitor of capacitance C has plates of area A with distance d between them. When the capacitor is connected to a battery supplying potential difference V, it has a charge of magnitude Q on its plates. While the capacitor is connected to the battery, the distance between the plates is decreased by a factor of 3. The magnitude of the charge on the plates and the capacitance will then bea) 1/3Q and 1/3 C.b) 1/3Q and 3C.c) 3Q and 3C.d) 3Q and 1/3 C. Get solution
3cc. Suppose you have a parallel plate capacitor with area A and plate separation d, but space constraints on a circuit board force you to reduce the area of the capacitor by a factor of 2. What do you have to do to compensate and retain the same value of the capacitance?a) reduce d by a factor of 2b) increase d by a factor of 2c) reduce d by a factor of 4d) increase d by a factor of 4 Get solution
3mcq. The distance between the plates of a parallel plate capacitor is reduced by half and the area of the plates is doubled. What happens to the capacitance?a) It remains unchanged.b) It doubles.c) It quadruples.d) It is reduced by half. Get solution
4cc. If the inner and outer radii of a spherical capacitor are increased by a factor of 2, what happens to the capacitance?a) It is reduced by a factor of 4.b) It is reduced by a factor of 2.c) It stays the same.d) It is increased by a factor of 2.e) It is increased by a factor of 4. Get solution
4mcq. Which of the following capacitors has the largest charge?a) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 2 mm connected to a 10-V batteryb) a parallel plate capacitor with an area of 5 cm2 and a plate separation of 1 mm connected to a 10-V batteryc) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 4 mm connected to a 5-V batteryd) a parallel plate capacitor with an area of 20 cm2 and a plate separation of 2 mm connected to a 20-V batterye) All of the capacitors have the same charge. Get solution
5cc. For a circuit with three capacitors in series, the equivalent capacitance must always bea) equal to the largest of the three individual capacitances.b) equal to the smallest of the three individual capacitances.c) larger than the largest of the three individual capacitances.d) smaller than the smallest of the three individual capacitances. Get solution
5mcq. Two identical parallel plate capacitors are connected in a circuit as shown in the figure. Initially the space between the plates of each capacitor is filled with air. Which of the following changes will double the total amount of charge stored on both capacitors with the same applied potential difference?a) Fill the space between the plates of C1 with glass (dielectric constant of 4) and leave C2 as is.b) Fill the space between the plates of C1 with Teflon (dielectric constant of 2) and leave C2 as is.c) Fill the space between the plates of both C1 and C2 with Teflon (dielectric constant of 2).d) Fill the space between the plates of both C1 and C2 with glass (dielectric constant of 4).... Get solution
6cc. The potential drop for a circuit with three capacitors of different individual capacitances in series connection isa) the same across each capacitor and has the same value as the potential difference supplied by the battery.b) the same across each capacitor and has 1/3 of the value of the potential difference supplied by the battery.c) largest across the capacitor with the smallest capacitance.d) largest across the capacitor with the largest capacitance. Get solution
6mcq. The space between the plates of an isolated parallel plate capacitor is filled with a slab of dielectric material. The magnitude of the charge Q on each plate is kept constant. If the dielectric material is removed the energy stored in the capacitora) increases.b) stays the same.c) decreases.d) may increase or decrease. Get solution
7cc. Three capacitors, each with capacitance C, are connected as shown in the figure. What is the equivalent capacitance for this arrangement of capacitors?...a) C/3b) 3Cc) C/9d) 9Ce) none of the above Get solution
7mcq. Which of the following is (are) proportional to the capacitance of a parallel plate capacitor?a) the charge stored on each conducting plateb) the potential difference between the two platesc) the separation distance between the two platesd) the area of each platee) all of the abovef) none of the above Get solution
8cc. Three capacitors, each with capacitance C, are connected as shown in the figure. What is the equivalent capacitance for this arrangement of capacitors?...a) C/3b) 3Cc) C/9d) 9Ce) none of the above Get solution
8mcq. A dielectric with the dielectric constant κ = 4 is inserted into a parallel plate capacitor, filling 1/3 of the volume, as shown in the figure. If the capacitance of the capacitor without the dielectric is C, what is the capacitance of the capacitor with the dielectric?...a) 0.75Cb) Cc) 2Cd) 4Ce) 6C Get solution
9cc. Three capacitors are connected to a battery as shown in the figure. If C1 = C2 = C3 = 10.0 μF and V = 10.0 V, what is the charge on capacitor C3?...a) 66.7 μCb) 100. μCc) 150. μCd) 300. μCe) 457. μC Get solution
9mcq. A parallel plate capacitor is connected to a battery for charging. After some time, while the battery is still connected to the capacitor, the distance between the capacitor plates is doubled. Which of the following is (are) true?a) The electric field between the plates is halved.b) The potential difference of the battery is halved.c) The capacitance doubles.d) The potential difference across the plates does not change.e) The charge on the plates does not change. Get solution
10cc. How much energy is stored in the 180-μF capacitor of a camera flash unit charged to 300.0 V?a) 1.22 Jb) 8.10 Jc) 45.0 Jd) 115 Je) 300 J Get solution
10mcq. Referring to the figure, decide which of the following equations is (are) true. Assume that all of the capacitors have different capacitances. The potential difference across capacitor C1 is V1. The potential difference across capacitor C2 is V2. The potential difference across capacitor C3 is V3. The potential difference across capacitor C4 is V4. The charge stored in capacitor C1 is q1. The charge stored in capacitor C2 is q2. The charge stored in capacitor C3 is q3. The charge stored in capacitor C4 is q4.a) q1 = q3b) V1 + V2 = Vc) q1 + q2 = q3 + q4d) V1 + V2 = V3 + V4e) V1 + V3 = V... Get solution
11cc. Suppose you charge a parallel plate capacitor with a dielectric between the plates using a battery and then remove the battery, isolating the capacitor and leaving it charged. You then remove the dielectric from between the plates. The potential difference between the plates willa) increase.b) decrease.c) stay the same.d) not be determinable. Get solution
11mcq. You have N identical capacitors, each with capacitance C, connected in series. The equivalent capacitance of this system of capacitors isa) NC.b) C/N.c) N2C.d) C/N2.e) C. Get solution
12cc. What would happen if the dielectric in the capacitor of Example 24.5 were pulled halfway out and then released?a) The dielectric would be pulled back into the capacitor.b) The dielectric would heat up rapidly.c) The dielectric would be pushed out of the capacitor.d) The capacitor plates would heat up rapidly.e) The dielectric would remain in the halfway position, and no heating would be observed.Example 24.5 Parallel Plate Capacitor with a Dielectric...... Get solution
12mcq. You have N identical capacitors, each with capacitance C, connected in parallel. The equivalent capacitance of this system of capacitors isa) NC.b) C/N.c) N2C.d) C/N2.e) C. Get solution
13cc. State whether each of the following statements about an isolated parallel plate capacitor is true or false.a) When the distance between the plates of the capacitor is doubled, the energy stored in the capacitor doubles.b) Increasing the distance between the plates increases the electric field between the plates.c) When the distance between the plates is halved, the charge on the plates stays the same.d) Inserting a dielectric between the plates increases the charge on the plates.e) Inserting a dielectric between the plates decreases the energy stored in the capacitor. Get solution
13mcq. When a dielectric is placed between the plates of a charged, isolated capacitor, the electric field inside the capacitora) increases.b) decreases.c) stays the same.d) increases if the charge on the plates is positive.e) decreases if the charge on the plates is positive. Get solution
14mcq. A parallel plate capacitor with a dielectric filling the volume between its plates is charged. The charge isa) stored on the plates.b) stored on the dielectric.c) stored both on the plates and in the dielectric. Get solution
16cq. Does it take more work to separate the plates of a charged parallel plate capacitor while it remains connected to the charging battery or after it has been disconnected from the charging battery? Get solution
18cq. Table 24.1 does not list a value of the dielectric constant for any good conductor. What value would you assign to it?Table 24.1 Dielectric Constants and Dielectric Strengths for Some Representative Materials... Get solution
17cq. When working on a piece of equipment, electricians and electronics technicians sometimes attach a grounding wire to the equipment even after turning the device off and unplugging it. Why would they do this? Get solution
19cq. A parallel plate capacitor is charged with a battery and then disconnected from the battery, leaving a certain amount of energy stored in the capacitor. The separation between the plates is then increased. What happens to the energy stored in the capacitor? Discuss your answer in terms of energy conservation. Get solution
20cq. You have an electric device containing a 10.0-µF capacitor, but an application requires an 18.0-µF capacitor. What modification can you make to your device to increase its capacitance to 18.0-µF? Get solution
22cq. Two capacitors, with capacitances C1 and C2, are connected in series. A potential difference, V0, is applied across the combination of capacitors. Find the potential differences V1 and V2 across the individual capacitors, in terms of V0, C1, and C2. Get solution
23cq. An isolated solid spherical conductor of radius 5.00 cm is surrounded by dry air. It is given a charge and acquires potential V, with the potential at infinity assumed to be zero.a) Calculate the maximum magnitude V can have.b) Explain clearly and concisely why there is a maximum. Get solution
25cq. A parallel plate capacitor with square plates of edge length L separated by a distance d is given a charge Q, then disconnected from its power source. A close-fitting square slab of dielectric, with dielectric constant κ, is then inserted into the previously empty space between the plates. Calculate the force with which the slab is pulled into the capacitor during the insertion process. Get solution
26cq. A cylindrical capacitor has an outer radius R and a separation d between the cylinders. Determine what the capacitance approaches in the limit where d R. (Hint: Express the capacitance in terms of the ratio d/R and then examine what happens as that ratio becomes very small compared to 1.) Explain why the limit on the capacitance makes sense. Get solution
27cq. A parallel plate capacitor is constructed from two plates of different areas. If this capacitor is initially uncharged and then connected to a battery, how will the amount of charge on the big plate compare to the amount of charge on the small plate? Get solution
28cq. A parallel plate capacitor is connected to a battery. As the plates are moved farther apart, what happens to each of the following?a) the potential difference across the platesb) the charge on the platesc) the electric field between the plates Get solution
29. Supercapacitors, with capacitances of 1.00 F or more, are made with plates that have a spongelike structure with a very large surface area. Determine the surface area of a supercapacitor that has a capacitance of 1.00 F and an effective separation between the plates of d = 1.00 mm. Get solution
30. A potential difference of 100. V is applied across the two collinear conducting cylinders shown in the figure. The radius of the outer cylinder is 15.0 cm, the radius of the inner cylinder is 10.0 cm, and the length of the two cylinders is 40.0 cm. How much charge is applied to each of the cylinders? What is the magnitude of the electric field between the two cylinders?... Get solution
31. What is the radius of an isolated spherical conductor that has a capacitance of 1.00 F? Get solution
32. A spherical capacitor is made from two thin concentric conducting shells. The inner shell has radius r1, and the outer shell has radius r2. What is the fractional difference in the capacitances of this spherical capacitor and a parallel plate capacitor made from plates that have the same area as the inner sphere and the same separation d = r2 – r1 between them? Get solution
33. Calculate the capacitance of the Earth. Treat the Earth as an isolated spherical conductor of radius 6371 km. Get solution
34. Two concentric metal spheres are found to have a potential difference of 900. V when a charge of 6.726 · 10–8 C is applied to them. The radius of the outer sphere is 0.210 m. What is the radius of the inner sphere? Get solution
35. A capacitor consists of two parallel plates, but one of them can move relative to the other as shown in the figure. Air fills the space between the plates, and the capacitance is 32.0 pF when the separation between plates is d = 0.500 cm.a) A battery supplying a potential difference V = 9.00 V is connected to the plates. What is the charge distribution, σ, on the left plate? What are the capacitance, C', and the charge distribution, σ ', when d is changed to 0.250 cm?b) With d = 0.500 cm, the battery is disconnected from the plates. The plates are then moved so that d = 0.250 cm. What is the potential difference V', between the plates?... Get solution
36. Determine all the values of equivalent capacitance you can create using any combination of three identical capacitors with capacitance C. Get solution
37. A large parallel plate capacitor with plates that are square with side length 1.00 cm and are separated by a distance of 1.00 mm is dropped and damaged. Half of the areas of the two plates are pushed closer together to a distance of 0.500 mm. What is the capacitance of the damaged capacitor? Get solution
38. Three capacitors with capacitances C1 = 3.10 nF, C2 = 1.30 nF, and C3 = 3.70 nF are wired to a battery with V = 14.9 V, as shown in the figure. What is the potential drop across capacitor C2?... Get solution
39. Four capacitors with capacitances C1 = 3.50 nF, C2 = 2.10 nF, C3 = 1.30 nF, and C4 = 4.90 nF are wired to a battery with V = 10.3 V, as shown in the figure. What is the equivalent capacitance of this set of capacitors?... Get solution
40. The capacitors in the circuit shown in the figure have capacitances C1 = 18.0 µF, C2 = 11.3 µF, C3 = 33.0 µF, and C4 = 44.0 µF. The potential difference is V = 10.0 V. What is the total charge the power source must supply to charge this arrangement of capacitors?... Get solution
41. Six capacitors are connected as shown in the figure.a) If C3 = 2.300 nF, what does C2 have to be to yield an equivalent capacitance of 5.000 nF for the combination of the two capacitors?b) For the same values of C2 and C3 as in part (a), what is the value of C1 that will give an equivalent capacitance of 1.914 nF for the combination of the three capacitors?c) For the same values of C1, C2, and C3 as in part (b), what is the equivalent capacitance of the whole set of capacitors if the values of the other capacitances are C4 = 1.300 nF, C5 = 1.700 nF, and C6 = 4.700 nF?d) If a battery with a potential difference of 11.70 V is connected to the capacitors as shown in the figure, what is the total charge on the six capacitors?e) What is the potential drop across C5 in this case?... Get solution
42. A potential difference of V = 80.0 V is applied across a circuit with capacitances C1 = 15.0 nF, C2 = 7.00 nF, and C3 = 20.0 nF, as shown in the figure. What is the magnitude and sign of q3l, the charge on the left plate of C3 (marked by point A)? What is the electric potential, V3, across C3? What is the magnitude and sign of the charge q2r, on the right plate of C2 (marked by point B)?... Get solution
43. Fifty parallel plate capacitors are connected in series. The distance between the plates is d for the first capacitor, 2d for the second capacitor, 3d for the third capacitor, and so on. The area of the plates is the same for all the capacitors. Express the equivalent capacitance of the whole set in terms of C1 (the capacitance of the first capacitor). Get solution
44. A 5.00-nF capacitor charged to 60.0 V and a 7.00-nF capacitor charged to 40.0 V are connected negative plate to negative plate. What is the final charge on the 7.00-nF capacitor? Get solution
45. When a capacitor has a charge of magnitude 60.0 µC on each plate, the potential difference across the plates is 12.0 V. How much energy is stored in this capacitor when the potential difference across its plates is 120. V? Get solution
46. The capacitor in an automatic external defibrillator is charged to 7.50 kV and stores 2400. J of energy. What is its capacitance? Get solution
47. The Earth has an electric field of 150. V/m near its surface. Find the electrical energy contained in each cubic meter of air near the surface. Get solution
48. The potential difference across two capacitors in series is 120. V. The capacitances are C1 = 1.00 · 103 µF and C2 = 1.50 · 103 µF.a) What is the total capacitance of this pair of capacitors?b) What is the charge on each capacitor?c) What is the potential difference across each capacitor?d) What is the total energy stored by the capacitors? Get solution
49. Neutron stars are thought to have electric dipole ... layers at their surfaces. If a neutron star with a 10.0-km radius has a dipole layer 1.00 cm thick with charge distributions of +1.00 µC/cm2 and –1.00 µC/cm2 on the surface, as indicated in the figure, what is the capacitance of this star? What is the electric potential energy stored in the neutron star’s dipole layer?... Get solution
50. A 4.00 · 103-nF parallel plate capacitor is connected to a 12.0-V battery and charged.a) What is the charge Q on the positive plate of the capacitor?b) What is the electric potential energy stored in the capacitor?The 4.00 · 103-nF capacitor is then disconnected from the 12.0-V battery and used to charge three uncharged capacitors, a 100.-nF capacitor, a 200.-nF capacitor, and a 300.-nF capacitor, connected in series.c) After charging, what is the potential difference across each of the four capacitors?d) How much of the electrical energy stored in the 4.00 · 103-nF capacitor was transferred to the other three capacitors? Get solution
51. The figure shows a circuit with V =12.0 V, C1 = 500. pF, and C2 = 500. pF. The switch is closed, to A, and the capacitor C1 is fully charged. Find (a) the energy delivered by the battery and (b) the energy stored in C1. Then the switch is thrown to B and the circuit is allowed to reach equilibrium. Find (c) the total energy stored at C1 and C2. (d) Explain the energy loss, if there is any.... Get solution
52. The Earth is held together by its own gravity. But it is also a charge-bearing conductor.a) The Earth can be regarded as a conducting sphere of radius 6371 km, with electric field ... =(–150. V/m)... at its surface, where ... is a unit vector directed radially outward. Calculate the total electric potential energy associated with the Earth’s electric charge and field.b) The Earth has gravitational potential energy, akin to the electric potential energy. Calculate this energy, treating the Earth as a uniform solid sphere. (Hint: dU = –(Gm/r)dm.)c) Use the results of parts (a) and (b) to address this question: To what extent do electrostatic forces affect the structure of the Earth? Get solution
53. Two parallel plate capacitors have identical plate areas and identical plate separations. The maximum energy each can store is determined by the maximum potential difference that can be applied before dielectric breakdown occurs. One capacitor has air between its plates, and the other has Mylar. Find the ratio of the maximum energy the Mylar capacitor can store to the maximum energy the air capacitor can store. Get solution
54. A capacitor has parallel plates, with half of the space between the plates filled with a dielectric material of constant κ and the other half filled with air as shown in the figure. Assume that the plates are square, with sides of length L, and that the separation between the plates is s. Determine the capacitance as a function of L.... Get solution
55. Calculate the maximum surface charge distribution that can be maintained on any surface surrounded by dry air. Get solution
56. Thermocoax is a type of coaxial cable used for high-frequency filtering in cryogenic quantum computing experiments. Its stainless steel shield has an inner diameter of 0.350 mm, and its Nichrome conductor has a diameter of 0.170 mm. Nichrome is used because its resistance doesn’t change much in going from room temperature to near absolute zero. The insulating dielectric is magnesium oxide (MgO), which has a dielectric constant of 9.70. Calculate the capacitance per meter of Thermocoax. Get solution
57. A parallel plate capacitor has square plates of side L = 10.0 cm and a distance d = 1.00 cm between the plates. Of the space between the plates, 1/5 is filled with a dielectric with dielectric constant κ1 = 20.0. The remaining 4/5 of the space is filled with a different dielectric, with κ2= 5.00. Find the capacitance of the capacitor. Get solution
58. A 4.0-nF parallel plate capacitor with a sheet of Mylar (κ = 3.1) filling the space between the plates is charged to a potential difference of 120 V and is then disconnected.a) How much work is required to completely remove the sheet of Mylar from the space between the two plates?b) What is the potential difference between the plates of the capacitor once the Mylar is completely removed? Get solution
59. The volume between the two cylinders of a cylindrical capacitor is half filled with a dielectric whose dielectric constant is κ and is connected to a battery with a potential difference ∆V. What is the charge placed on the capacitor? What is the ratio of this charge to the charge placed on an identical capacitor with no dielectric connected in the same way across the same potential drop? Get solution
60. A dielectric slab with thickness d and dielectric constant κ = 2.31 is inserted in a parallel place capacitor that has been charged by a 110.-V battery and has area A = 100. cm2 and separation distance d = 2.50 cm.a) Find the capacitance, C, the potential difference, V, the electric field, E, the total charge stored on the capacitor Q, and electric potential energy stored in the capacitor, U, before the dielectric material is inserted.b) Find C, V, E, Q, and U when the dielectric slab has been inserted and the battery is still connected.c) Find C, V, E, Q, and U when the dielectric slab is in place and the battery is disconnected. Get solution
61. A parallel plate capacitor has a capacitance of 120. pF and a plate area of 100. cm2. The space between the plates is filled with mica whose dielectric constant is 5.40. The plates of the capacitor are kept at 50.0 V.a) What is the strength of the electric field in the mica?b) What is the amount of free charge on the plates?c) What is the amount of charge induced on the mica? Get solution
62. Design a parallel plate capacitor with a capacitance of 47.0 pF and a capacity of 7.50 nC. You have available conducting plates, which can be cut to any size, and Plexiglas sheets, which can be cut to any size and machined to any thickness. Plexiglas has a dielectric constant of 3.40 and a dielectric strength of 3.00 · 107 V/m. You must make your capacitor as compact as possible. Specify all relevant dimensions. Ignore any fringe field at the edges of the capacitor plates. Get solution
63. A parallel plate capacitor consisting of a pair of rectangular plates, each measuring 1.00 cm by 10.0 cm, with a separation between the plates of 0.100 mm, is charged by a power supply at a potential difference of 1.00 · 103 V. The power supply is then removed, and without being discharged, the capacitor is placed in a vertical position over a container holding de-ionized water, with the short sides of the plates in contact with the water, as shown in the figure. Using energy considerations, show that the water will rise between the plates. Neglecting other effects, determine the system of equations that can be used to calculate the height to which the water rises between the plates. You do not have to solve the system.... Get solution
64. Two circular metal plates of radius 0.610 m and thickness 7.10 mm are used in a parallel plate capacitor. A gap of 2.10 mm is left between the plates, and half of the space (a semicircle) between them is filled with a dielectric for which κ = 11.1 and the other half is filled with air. What is the capacitance of this capacitor? Get solution
65. Considering the dielectric strength of air, what is the maximum amount of charge that can be stored on the plates of a capacitor that are a distance of 15 mm apart and have an area of 25 cm2? Get solution
66. The figure shows three capacitors in a circuit: C1 = 2.00 nF and C2 = C3 = 4.00 nF. Find the charge on each capacitor when the potential difference applied is V = 1.50 V.... Get solution
67. A capacitor with a vacuum between its plates is connected to a battery and then the gap is filled with Mylar. By what percentage is its energy-storing capacity increased? Get solution
68. A parallel plate capacitor with a plate area of 12.0 cm2 and air in the space between the plates, which are separated by 1.50 mm, is connected to a 9.00-V battery. If the plates are pulled back so that the separation increases to 2.75 mm, how much work is done? Get solution
69. Suppose you want to make a 1.00-F capacitor using two square sheets of aluminum foil. If the sheets of foil are separated by a single piece of paper (thickness of about 0.100 mm and κ = 5.00), find the size of the sheets of foil (the length of each edge). Get solution
71. A four-capacitor circuit is charged by a battery, as shown in the figure. The capacitances are C1 = 1.00 mF, C2 = 2.00 mF, C3 = 3.00 mF, and C4 = 4.00 mF, and the battery potential is VB = 1.00 V. When the circuit is at equilibrium, point D has potential VD = 0.00 V. What is the potential, VA, at point A?... Get solution
72. How much energy can be stored in a capacitor with two parallel plates, each with an area of 64.0 cm2 and separated by a gap of 1.30 mm, filled with porcelain whose dielectric constant is 7.00, and holding equal and opposite charges of magnitude 420. µC? Get solution
73. A quantum mechanical device known as the Josephson junction consists of two overlapping layers of superconducting metal (for example, aluminum at 1.00 K) separated by 20.0 nm of aluminum oxide, which has a dielectric constant of 9.10. If this device has an area of 100. µm2 and a parallel plate configuration, estimate its capacitance. Get solution
75. For a science project, a fourth-grader cuts the tops and bottoms off two soup cans of equal height, 7.24 cm, and with radii of 3.02 cm and 4.16 cm, puts the smaller one inside the larger, and hot-glues them both on a sheet of plastic, as shown in the figure. Then she fills the gap between the cans with a special “soup” (dielectric constant of 63.0). What is the capacitance of this arrangement?... Get solution
77. A parallel plate capacitor with air in the gap between the plates is connected to a 6.00-V battery. After charging, the energy stored in the capacitor is 72.0 nJ. Without disconnecting the capacitor from the battery, a dielectric is inserted into the gap and an additional 317 nJ of energy flows from the battery to the capacitor.a) What is the dielectric constant of the dielectric?b) If each of the plates has an area of 50.0 cm2, what is the charge on the positive plate of the capacitor after the dielectric has been inserted?c) What is the magnitude of the electric field between the plates before the dielectric is inserted?d) What is the magnitude of the electric field between the plates after the dielectric is inserted? Get solution
76. The Earth can be thought of as a spherical capacitor. If the net charge on the Earth is –7.80 · 105 C , find (a) the capacitance of the Earth and (b) the electric potential energy stored on the Earth’s surface. Get solution
78. An 8.00-µF capacitor is fully charged by a 240.-V battery, which is then disconnected. Next, the capacitor is connected to an initially uncharged capacitor of capacitance C, and the potential difference across it is found to be 80.0 V. What is C? How much energy ends up being stored in the second capacitor? Get solution
79. A parallel plate capacitor consists of square plates of edge length 2.00 cm separated by a distance of 1.00 mm. The capacitor is charged with a 15.0-V battery, and the battery is then removed. A 1.00-mm-thick sheet of nylon (dielectric constant of 3.50) is slid between the plates. What is the average force (magnitude and direction) on the nylon sheet as it is inserted into the capacitor? Get solution
80. A proton traveling along the x-axis at a speed of 1.00 · 106 m/s enters the gap between the plates of a 2.00-cm-wide parallel plate capacitor. The surface charge distributions on the plates are given by σ = ±1.00 · 10–6 C/m2. How far has the proton been deflected sideways (∆y) when it reaches the far edge of the capacitor? Assume that the electric field is uniform inside the capacitor and zero outside. Get solution
81. A parallel plate capacitor has square plates of side L = 10.0 cm separated by a distance d = 2.50 mm, as shown in the figure. The capacitor is charged by a battery with potential difference V0 = 75.0 V; the battery is then disconnected.a) Determine the capacitance, C0, and the electric potential energy, U0, stored in the capacitor at this point.b) A slab made of Plexiglas (κ = 3.40) is then inserted so that it fills 2/3 of the volume between the plates, as shown in the figure. Determine the new capacitance, C', the new potential difference between the plates, V', and the new electric potential energy, U', stored in the capacitor.c) Neglecting gravity, did the inserter of the dielectric slab have to do work or not?... Get solution
82. A typical AAA battery has stored energy of about 3400 J. (Battery capacity is typically listed as 625 mA h, meaning that much charge can be delivered at approximately 1.5 V.) Suppose you want to build a parallel plate capacitor to store this amount of energy, using a plate separation of 1.0 mm and with air filling the space between the plates.a) Assuming that the potential difference across the capacitor is 1.50 V, what must the area of each plate be?b) Assuming that the potential difference across the capacitor is the maximum that can be applied without dielectric breakdown occurring, what must the area of each plate be?c) Is either capacitor a practical replacement for the AAA battery? Get solution
83. Two parallel plate capacitors, C1 and C2, are connected in series to a 96.0-V battery. Both capacitors have plates with an area of 1.00 cm2 and a separation of 0.100 mm; C1 has air between its plates, and C2 has that space filled with porcelain (dielectric constant of 7.00 and dielectric strength of 5.70 kV/mm).a) After charging, what are the charges on each capacitor?b) What is the total energy stored in the two capacitors?c) What is the electric field between the plates of C2? Get solution
84. The plates of parallel plate capacitor A consist of two metal discs of identical radius, R1 = 4.00 cm, separated by a distance d = 2.00 mm, as shown in the figure.a) Calculate the capacitance of this parallel plate capacitor with the space between the plates filled with air.b) A dielectric in the shape of a thick-walled cylinder of outer radius R1 = 4.00 cm, inner radius R2 = 2.00 cm, thickness d = 2.00 mm, and dielectric constant κ = 2.00 is placed between the plates, coaxial with them, as shown in the figure. Calculate the capacitance of capacitor B, with this dielectric.c) The dielectric cylinder is removed, and instead a solid disc of radius R1 made of the same dielectric is placed between the plates to form capacitor C, as shown in the figure. What is the new capacitance?... Get solution
86. The capacitance of a spherical capacitor consisting of two concentric conducting spheres with radii r1 and r2 (r2 > r1) is given by C = 4πε0r1r2/(r2 – r1). Suppose that the space between the spheres, from r1 up to a radius R (r1 R r2) is fi lled with a dielectric for which ε = 10 ε0. Find an expression for the capacitance, and check the limits when R = r1 and R = r2. Get solution
87. In the figure, a parallel plate capacitor is connected to a 300.-V battery. With the capacitor connected, a proton is fired with a speed of 2.00 · 105 m/s from (through) the negative plate of the capacitor at an angle θ with the normal to the plate.a) Show that the proton cannot reach the positive plate of the capacitor, regardless of what the angle θ is.b) Sketch the trajectory of the proton between the plates.c) Assuming that V = 0 at the negative plate, calculate the potential at the point between the plates where the proton reverses its motion in the x-direction.d) Assuming that the plates are long enough for the proton to stay between them throughout its motion, calculate the speed (magnitude only) of the proton as it collides with the negative plate.... Get solution
88. For the parallel plate capacitor with dielectric shown in the figure, prove that for a given thickness of the dielectric slab, the capacitance does not depend on the position of the slab relative to the two conducting plates (that is, it does not depend on the values of d1 and d3).... Get solution
89. The battery of an electric car stores 53.63 MJ of energy. How many supercapacitors, each with capacitance C = 3.361 kF at a potential difference of 2.121 V, are required to supply this amount of energy? Get solution
90. The battery of an electric car stores 60.51 MJ of energy. If 6990 supercapacitors, each with capacitance C = 3.423 kF, are required to supply this amount of energy, what is the potential difference across each supercapacitor? Get solution
91. The battery of an electric car stores 67.39 MJ of energy. If 6845 supercapacitors, each with capacitance C and charged to a potential difference of 2.377 V, can supply this amount of energy, what is the value of C for each supercapacitor? Get solution
92. A parallel plate capacitor with vacuum between the plates has a capacitance of 3.547 μF. A dielectric material with κ = 4.617 is placed between the plates, completely filling the volume between them. The capacitor is then connected to a battery that maintains a potential difference of 10.03 V across the plates. How much work is required to pull the dielectric material out of the capacitor? Get solution
93. A parallel plate capacitor with vacuum between the plates has a capacitance of 3.607 μF. A dielectric material is placed between the plates, completely filling the volume between them. The capacitor is then connected to a battery that maintains a potential difference of 11.33 V across the plates. The dielectric material is pulled out of the capacitor, which requires 4.804 · 10–4 J of work. What is the dielectric constant of the material? Get solution
94. A parallel plate capacitor with vacuum between the plates has a capacitance of 3.669 μF. A dielectric material with κ = 3.533 is placed between the plates, completely filling the volume between them. The capacitor is then connected to a battery that maintains a potential difference V across the plates. Th e dielectric material is pulled out of the capacitor, which requires 7.389 · 10–4 J of work. What is the potential difference, V? Get solution
1mcq. In the circuit shown in the figure, the capacitance for each capacitor is C. The equivalent capacitance for these three capacitors isa) ...b) ...c) ...d) ...e) C.f) ...... Get solution
2cc. Suppose you charge a parallel plate capacitor using a battery and then remove the battery, isolating the capacitor and leaving it charged. You then move the plates of the capacitor farther apart. The potential difference between the plates willa) increase.b) decrease.c) stay the same.d) not be determinable. Get solution
2mcq. A parallel plate capacitor of capacitance C has plates of area A with distance d between them. When the capacitor is connected to a battery supplying potential difference V, it has a charge of magnitude Q on its plates. While the capacitor is connected to the battery, the distance between the plates is decreased by a factor of 3. The magnitude of the charge on the plates and the capacitance will then bea) 1/3Q and 1/3 C.b) 1/3Q and 3C.c) 3Q and 3C.d) 3Q and 1/3 C. Get solution
3cc. Suppose you have a parallel plate capacitor with area A and plate separation d, but space constraints on a circuit board force you to reduce the area of the capacitor by a factor of 2. What do you have to do to compensate and retain the same value of the capacitance?a) reduce d by a factor of 2b) increase d by a factor of 2c) reduce d by a factor of 4d) increase d by a factor of 4 Get solution
3mcq. The distance between the plates of a parallel plate capacitor is reduced by half and the area of the plates is doubled. What happens to the capacitance?a) It remains unchanged.b) It doubles.c) It quadruples.d) It is reduced by half. Get solution
4cc. If the inner and outer radii of a spherical capacitor are increased by a factor of 2, what happens to the capacitance?a) It is reduced by a factor of 4.b) It is reduced by a factor of 2.c) It stays the same.d) It is increased by a factor of 2.e) It is increased by a factor of 4. Get solution
4mcq. Which of the following capacitors has the largest charge?a) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 2 mm connected to a 10-V batteryb) a parallel plate capacitor with an area of 5 cm2 and a plate separation of 1 mm connected to a 10-V batteryc) a parallel plate capacitor with an area of 10 cm2 and a plate separation of 4 mm connected to a 5-V batteryd) a parallel plate capacitor with an area of 20 cm2 and a plate separation of 2 mm connected to a 20-V batterye) All of the capacitors have the same charge. Get solution
5cc. For a circuit with three capacitors in series, the equivalent capacitance must always bea) equal to the largest of the three individual capacitances.b) equal to the smallest of the three individual capacitances.c) larger than the largest of the three individual capacitances.d) smaller than the smallest of the three individual capacitances. Get solution
5mcq. Two identical parallel plate capacitors are connected in a circuit as shown in the figure. Initially the space between the plates of each capacitor is filled with air. Which of the following changes will double the total amount of charge stored on both capacitors with the same applied potential difference?a) Fill the space between the plates of C1 with glass (dielectric constant of 4) and leave C2 as is.b) Fill the space between the plates of C1 with Teflon (dielectric constant of 2) and leave C2 as is.c) Fill the space between the plates of both C1 and C2 with Teflon (dielectric constant of 2).d) Fill the space between the plates of both C1 and C2 with glass (dielectric constant of 4).... Get solution
6cc. The potential drop for a circuit with three capacitors of different individual capacitances in series connection isa) the same across each capacitor and has the same value as the potential difference supplied by the battery.b) the same across each capacitor and has 1/3 of the value of the potential difference supplied by the battery.c) largest across the capacitor with the smallest capacitance.d) largest across the capacitor with the largest capacitance. Get solution
6mcq. The space between the plates of an isolated parallel plate capacitor is filled with a slab of dielectric material. The magnitude of the charge Q on each plate is kept constant. If the dielectric material is removed the energy stored in the capacitora) increases.b) stays the same.c) decreases.d) may increase or decrease. Get solution
7cc. Three capacitors, each with capacitance C, are connected as shown in the figure. What is the equivalent capacitance for this arrangement of capacitors?...a) C/3b) 3Cc) C/9d) 9Ce) none of the above Get solution
7mcq. Which of the following is (are) proportional to the capacitance of a parallel plate capacitor?a) the charge stored on each conducting plateb) the potential difference between the two platesc) the separation distance between the two platesd) the area of each platee) all of the abovef) none of the above Get solution
8cc. Three capacitors, each with capacitance C, are connected as shown in the figure. What is the equivalent capacitance for this arrangement of capacitors?...a) C/3b) 3Cc) C/9d) 9Ce) none of the above Get solution
8mcq. A dielectric with the dielectric constant κ = 4 is inserted into a parallel plate capacitor, filling 1/3 of the volume, as shown in the figure. If the capacitance of the capacitor without the dielectric is C, what is the capacitance of the capacitor with the dielectric?...a) 0.75Cb) Cc) 2Cd) 4Ce) 6C Get solution
9cc. Three capacitors are connected to a battery as shown in the figure. If C1 = C2 = C3 = 10.0 μF and V = 10.0 V, what is the charge on capacitor C3?...a) 66.7 μCb) 100. μCc) 150. μCd) 300. μCe) 457. μC Get solution
9mcq. A parallel plate capacitor is connected to a battery for charging. After some time, while the battery is still connected to the capacitor, the distance between the capacitor plates is doubled. Which of the following is (are) true?a) The electric field between the plates is halved.b) The potential difference of the battery is halved.c) The capacitance doubles.d) The potential difference across the plates does not change.e) The charge on the plates does not change. Get solution
10cc. How much energy is stored in the 180-μF capacitor of a camera flash unit charged to 300.0 V?a) 1.22 Jb) 8.10 Jc) 45.0 Jd) 115 Je) 300 J Get solution
10mcq. Referring to the figure, decide which of the following equations is (are) true. Assume that all of the capacitors have different capacitances. The potential difference across capacitor C1 is V1. The potential difference across capacitor C2 is V2. The potential difference across capacitor C3 is V3. The potential difference across capacitor C4 is V4. The charge stored in capacitor C1 is q1. The charge stored in capacitor C2 is q2. The charge stored in capacitor C3 is q3. The charge stored in capacitor C4 is q4.a) q1 = q3b) V1 + V2 = Vc) q1 + q2 = q3 + q4d) V1 + V2 = V3 + V4e) V1 + V3 = V... Get solution
11cc. Suppose you charge a parallel plate capacitor with a dielectric between the plates using a battery and then remove the battery, isolating the capacitor and leaving it charged. You then remove the dielectric from between the plates. The potential difference between the plates willa) increase.b) decrease.c) stay the same.d) not be determinable. Get solution
11mcq. You have N identical capacitors, each with capacitance C, connected in series. The equivalent capacitance of this system of capacitors isa) NC.b) C/N.c) N2C.d) C/N2.e) C. Get solution
12cc. What would happen if the dielectric in the capacitor of Example 24.5 were pulled halfway out and then released?a) The dielectric would be pulled back into the capacitor.b) The dielectric would heat up rapidly.c) The dielectric would be pushed out of the capacitor.d) The capacitor plates would heat up rapidly.e) The dielectric would remain in the halfway position, and no heating would be observed.Example 24.5 Parallel Plate Capacitor with a Dielectric...... Get solution
12mcq. You have N identical capacitors, each with capacitance C, connected in parallel. The equivalent capacitance of this system of capacitors isa) NC.b) C/N.c) N2C.d) C/N2.e) C. Get solution
13cc. State whether each of the following statements about an isolated parallel plate capacitor is true or false.a) When the distance between the plates of the capacitor is doubled, the energy stored in the capacitor doubles.b) Increasing the distance between the plates increases the electric field between the plates.c) When the distance between the plates is halved, the charge on the plates stays the same.d) Inserting a dielectric between the plates increases the charge on the plates.e) Inserting a dielectric between the plates decreases the energy stored in the capacitor. Get solution
13mcq. When a dielectric is placed between the plates of a charged, isolated capacitor, the electric field inside the capacitora) increases.b) decreases.c) stays the same.d) increases if the charge on the plates is positive.e) decreases if the charge on the plates is positive. Get solution
14mcq. A parallel plate capacitor with a dielectric filling the volume between its plates is charged. The charge isa) stored on the plates.b) stored on the dielectric.c) stored both on the plates and in the dielectric. Get solution
16cq. Does it take more work to separate the plates of a charged parallel plate capacitor while it remains connected to the charging battery or after it has been disconnected from the charging battery? Get solution
18cq. Table 24.1 does not list a value of the dielectric constant for any good conductor. What value would you assign to it?Table 24.1 Dielectric Constants and Dielectric Strengths for Some Representative Materials... Get solution
17cq. When working on a piece of equipment, electricians and electronics technicians sometimes attach a grounding wire to the equipment even after turning the device off and unplugging it. Why would they do this? Get solution
19cq. A parallel plate capacitor is charged with a battery and then disconnected from the battery, leaving a certain amount of energy stored in the capacitor. The separation between the plates is then increased. What happens to the energy stored in the capacitor? Discuss your answer in terms of energy conservation. Get solution
20cq. You have an electric device containing a 10.0-µF capacitor, but an application requires an 18.0-µF capacitor. What modification can you make to your device to increase its capacitance to 18.0-µF? Get solution
22cq. Two capacitors, with capacitances C1 and C2, are connected in series. A potential difference, V0, is applied across the combination of capacitors. Find the potential differences V1 and V2 across the individual capacitors, in terms of V0, C1, and C2. Get solution
23cq. An isolated solid spherical conductor of radius 5.00 cm is surrounded by dry air. It is given a charge and acquires potential V, with the potential at infinity assumed to be zero.a) Calculate the maximum magnitude V can have.b) Explain clearly and concisely why there is a maximum. Get solution
25cq. A parallel plate capacitor with square plates of edge length L separated by a distance d is given a charge Q, then disconnected from its power source. A close-fitting square slab of dielectric, with dielectric constant κ, is then inserted into the previously empty space between the plates. Calculate the force with which the slab is pulled into the capacitor during the insertion process. Get solution
26cq. A cylindrical capacitor has an outer radius R and a separation d between the cylinders. Determine what the capacitance approaches in the limit where d R. (Hint: Express the capacitance in terms of the ratio d/R and then examine what happens as that ratio becomes very small compared to 1.) Explain why the limit on the capacitance makes sense. Get solution
27cq. A parallel plate capacitor is constructed from two plates of different areas. If this capacitor is initially uncharged and then connected to a battery, how will the amount of charge on the big plate compare to the amount of charge on the small plate? Get solution
28cq. A parallel plate capacitor is connected to a battery. As the plates are moved farther apart, what happens to each of the following?a) the potential difference across the platesb) the charge on the platesc) the electric field between the plates Get solution
29. Supercapacitors, with capacitances of 1.00 F or more, are made with plates that have a spongelike structure with a very large surface area. Determine the surface area of a supercapacitor that has a capacitance of 1.00 F and an effective separation between the plates of d = 1.00 mm. Get solution
30. A potential difference of 100. V is applied across the two collinear conducting cylinders shown in the figure. The radius of the outer cylinder is 15.0 cm, the radius of the inner cylinder is 10.0 cm, and the length of the two cylinders is 40.0 cm. How much charge is applied to each of the cylinders? What is the magnitude of the electric field between the two cylinders?... Get solution
31. What is the radius of an isolated spherical conductor that has a capacitance of 1.00 F? Get solution
32. A spherical capacitor is made from two thin concentric conducting shells. The inner shell has radius r1, and the outer shell has radius r2. What is the fractional difference in the capacitances of this spherical capacitor and a parallel plate capacitor made from plates that have the same area as the inner sphere and the same separation d = r2 – r1 between them? Get solution
33. Calculate the capacitance of the Earth. Treat the Earth as an isolated spherical conductor of radius 6371 km. Get solution
34. Two concentric metal spheres are found to have a potential difference of 900. V when a charge of 6.726 · 10–8 C is applied to them. The radius of the outer sphere is 0.210 m. What is the radius of the inner sphere? Get solution
35. A capacitor consists of two parallel plates, but one of them can move relative to the other as shown in the figure. Air fills the space between the plates, and the capacitance is 32.0 pF when the separation between plates is d = 0.500 cm.a) A battery supplying a potential difference V = 9.00 V is connected to the plates. What is the charge distribution, σ, on the left plate? What are the capacitance, C', and the charge distribution, σ ', when d is changed to 0.250 cm?b) With d = 0.500 cm, the battery is disconnected from the plates. The plates are then moved so that d = 0.250 cm. What is the potential difference V', between the plates?... Get solution
36. Determine all the values of equivalent capacitance you can create using any combination of three identical capacitors with capacitance C. Get solution
37. A large parallel plate capacitor with plates that are square with side length 1.00 cm and are separated by a distance of 1.00 mm is dropped and damaged. Half of the areas of the two plates are pushed closer together to a distance of 0.500 mm. What is the capacitance of the damaged capacitor? Get solution
38. Three capacitors with capacitances C1 = 3.10 nF, C2 = 1.30 nF, and C3 = 3.70 nF are wired to a battery with V = 14.9 V, as shown in the figure. What is the potential drop across capacitor C2?... Get solution
39. Four capacitors with capacitances C1 = 3.50 nF, C2 = 2.10 nF, C3 = 1.30 nF, and C4 = 4.90 nF are wired to a battery with V = 10.3 V, as shown in the figure. What is the equivalent capacitance of this set of capacitors?... Get solution
40. The capacitors in the circuit shown in the figure have capacitances C1 = 18.0 µF, C2 = 11.3 µF, C3 = 33.0 µF, and C4 = 44.0 µF. The potential difference is V = 10.0 V. What is the total charge the power source must supply to charge this arrangement of capacitors?... Get solution
41. Six capacitors are connected as shown in the figure.a) If C3 = 2.300 nF, what does C2 have to be to yield an equivalent capacitance of 5.000 nF for the combination of the two capacitors?b) For the same values of C2 and C3 as in part (a), what is the value of C1 that will give an equivalent capacitance of 1.914 nF for the combination of the three capacitors?c) For the same values of C1, C2, and C3 as in part (b), what is the equivalent capacitance of the whole set of capacitors if the values of the other capacitances are C4 = 1.300 nF, C5 = 1.700 nF, and C6 = 4.700 nF?d) If a battery with a potential difference of 11.70 V is connected to the capacitors as shown in the figure, what is the total charge on the six capacitors?e) What is the potential drop across C5 in this case?... Get solution
42. A potential difference of V = 80.0 V is applied across a circuit with capacitances C1 = 15.0 nF, C2 = 7.00 nF, and C3 = 20.0 nF, as shown in the figure. What is the magnitude and sign of q3l, the charge on the left plate of C3 (marked by point A)? What is the electric potential, V3, across C3? What is the magnitude and sign of the charge q2r, on the right plate of C2 (marked by point B)?... Get solution
43. Fifty parallel plate capacitors are connected in series. The distance between the plates is d for the first capacitor, 2d for the second capacitor, 3d for the third capacitor, and so on. The area of the plates is the same for all the capacitors. Express the equivalent capacitance of the whole set in terms of C1 (the capacitance of the first capacitor). Get solution
44. A 5.00-nF capacitor charged to 60.0 V and a 7.00-nF capacitor charged to 40.0 V are connected negative plate to negative plate. What is the final charge on the 7.00-nF capacitor? Get solution
45. When a capacitor has a charge of magnitude 60.0 µC on each plate, the potential difference across the plates is 12.0 V. How much energy is stored in this capacitor when the potential difference across its plates is 120. V? Get solution
46. The capacitor in an automatic external defibrillator is charged to 7.50 kV and stores 2400. J of energy. What is its capacitance? Get solution
47. The Earth has an electric field of 150. V/m near its surface. Find the electrical energy contained in each cubic meter of air near the surface. Get solution
48. The potential difference across two capacitors in series is 120. V. The capacitances are C1 = 1.00 · 103 µF and C2 = 1.50 · 103 µF.a) What is the total capacitance of this pair of capacitors?b) What is the charge on each capacitor?c) What is the potential difference across each capacitor?d) What is the total energy stored by the capacitors? Get solution
49. Neutron stars are thought to have electric dipole ... layers at their surfaces. If a neutron star with a 10.0-km radius has a dipole layer 1.00 cm thick with charge distributions of +1.00 µC/cm2 and –1.00 µC/cm2 on the surface, as indicated in the figure, what is the capacitance of this star? What is the electric potential energy stored in the neutron star’s dipole layer?... Get solution
50. A 4.00 · 103-nF parallel plate capacitor is connected to a 12.0-V battery and charged.a) What is the charge Q on the positive plate of the capacitor?b) What is the electric potential energy stored in the capacitor?The 4.00 · 103-nF capacitor is then disconnected from the 12.0-V battery and used to charge three uncharged capacitors, a 100.-nF capacitor, a 200.-nF capacitor, and a 300.-nF capacitor, connected in series.c) After charging, what is the potential difference across each of the four capacitors?d) How much of the electrical energy stored in the 4.00 · 103-nF capacitor was transferred to the other three capacitors? Get solution
51. The figure shows a circuit with V =12.0 V, C1 = 500. pF, and C2 = 500. pF. The switch is closed, to A, and the capacitor C1 is fully charged. Find (a) the energy delivered by the battery and (b) the energy stored in C1. Then the switch is thrown to B and the circuit is allowed to reach equilibrium. Find (c) the total energy stored at C1 and C2. (d) Explain the energy loss, if there is any.... Get solution
52. The Earth is held together by its own gravity. But it is also a charge-bearing conductor.a) The Earth can be regarded as a conducting sphere of radius 6371 km, with electric field ... =(–150. V/m)... at its surface, where ... is a unit vector directed radially outward. Calculate the total electric potential energy associated with the Earth’s electric charge and field.b) The Earth has gravitational potential energy, akin to the electric potential energy. Calculate this energy, treating the Earth as a uniform solid sphere. (Hint: dU = –(Gm/r)dm.)c) Use the results of parts (a) and (b) to address this question: To what extent do electrostatic forces affect the structure of the Earth? Get solution
53. Two parallel plate capacitors have identical plate areas and identical plate separations. The maximum energy each can store is determined by the maximum potential difference that can be applied before dielectric breakdown occurs. One capacitor has air between its plates, and the other has Mylar. Find the ratio of the maximum energy the Mylar capacitor can store to the maximum energy the air capacitor can store. Get solution
54. A capacitor has parallel plates, with half of the space between the plates filled with a dielectric material of constant κ and the other half filled with air as shown in the figure. Assume that the plates are square, with sides of length L, and that the separation between the plates is s. Determine the capacitance as a function of L.... Get solution
55. Calculate the maximum surface charge distribution that can be maintained on any surface surrounded by dry air. Get solution
56. Thermocoax is a type of coaxial cable used for high-frequency filtering in cryogenic quantum computing experiments. Its stainless steel shield has an inner diameter of 0.350 mm, and its Nichrome conductor has a diameter of 0.170 mm. Nichrome is used because its resistance doesn’t change much in going from room temperature to near absolute zero. The insulating dielectric is magnesium oxide (MgO), which has a dielectric constant of 9.70. Calculate the capacitance per meter of Thermocoax. Get solution
57. A parallel plate capacitor has square plates of side L = 10.0 cm and a distance d = 1.00 cm between the plates. Of the space between the plates, 1/5 is filled with a dielectric with dielectric constant κ1 = 20.0. The remaining 4/5 of the space is filled with a different dielectric, with κ2= 5.00. Find the capacitance of the capacitor. Get solution
58. A 4.0-nF parallel plate capacitor with a sheet of Mylar (κ = 3.1) filling the space between the plates is charged to a potential difference of 120 V and is then disconnected.a) How much work is required to completely remove the sheet of Mylar from the space between the two plates?b) What is the potential difference between the plates of the capacitor once the Mylar is completely removed? Get solution
59. The volume between the two cylinders of a cylindrical capacitor is half filled with a dielectric whose dielectric constant is κ and is connected to a battery with a potential difference ∆V. What is the charge placed on the capacitor? What is the ratio of this charge to the charge placed on an identical capacitor with no dielectric connected in the same way across the same potential drop? Get solution
60. A dielectric slab with thickness d and dielectric constant κ = 2.31 is inserted in a parallel place capacitor that has been charged by a 110.-V battery and has area A = 100. cm2 and separation distance d = 2.50 cm.a) Find the capacitance, C, the potential difference, V, the electric field, E, the total charge stored on the capacitor Q, and electric potential energy stored in the capacitor, U, before the dielectric material is inserted.b) Find C, V, E, Q, and U when the dielectric slab has been inserted and the battery is still connected.c) Find C, V, E, Q, and U when the dielectric slab is in place and the battery is disconnected. Get solution
61. A parallel plate capacitor has a capacitance of 120. pF and a plate area of 100. cm2. The space between the plates is filled with mica whose dielectric constant is 5.40. The plates of the capacitor are kept at 50.0 V.a) What is the strength of the electric field in the mica?b) What is the amount of free charge on the plates?c) What is the amount of charge induced on the mica? Get solution
62. Design a parallel plate capacitor with a capacitance of 47.0 pF and a capacity of 7.50 nC. You have available conducting plates, which can be cut to any size, and Plexiglas sheets, which can be cut to any size and machined to any thickness. Plexiglas has a dielectric constant of 3.40 and a dielectric strength of 3.00 · 107 V/m. You must make your capacitor as compact as possible. Specify all relevant dimensions. Ignore any fringe field at the edges of the capacitor plates. Get solution
63. A parallel plate capacitor consisting of a pair of rectangular plates, each measuring 1.00 cm by 10.0 cm, with a separation between the plates of 0.100 mm, is charged by a power supply at a potential difference of 1.00 · 103 V. The power supply is then removed, and without being discharged, the capacitor is placed in a vertical position over a container holding de-ionized water, with the short sides of the plates in contact with the water, as shown in the figure. Using energy considerations, show that the water will rise between the plates. Neglecting other effects, determine the system of equations that can be used to calculate the height to which the water rises between the plates. You do not have to solve the system.... Get solution
64. Two circular metal plates of radius 0.610 m and thickness 7.10 mm are used in a parallel plate capacitor. A gap of 2.10 mm is left between the plates, and half of the space (a semicircle) between them is filled with a dielectric for which κ = 11.1 and the other half is filled with air. What is the capacitance of this capacitor? Get solution
65. Considering the dielectric strength of air, what is the maximum amount of charge that can be stored on the plates of a capacitor that are a distance of 15 mm apart and have an area of 25 cm2? Get solution
66. The figure shows three capacitors in a circuit: C1 = 2.00 nF and C2 = C3 = 4.00 nF. Find the charge on each capacitor when the potential difference applied is V = 1.50 V.... Get solution
67. A capacitor with a vacuum between its plates is connected to a battery and then the gap is filled with Mylar. By what percentage is its energy-storing capacity increased? Get solution
68. A parallel plate capacitor with a plate area of 12.0 cm2 and air in the space between the plates, which are separated by 1.50 mm, is connected to a 9.00-V battery. If the plates are pulled back so that the separation increases to 2.75 mm, how much work is done? Get solution
69. Suppose you want to make a 1.00-F capacitor using two square sheets of aluminum foil. If the sheets of foil are separated by a single piece of paper (thickness of about 0.100 mm and κ = 5.00), find the size of the sheets of foil (the length of each edge). Get solution
71. A four-capacitor circuit is charged by a battery, as shown in the figure. The capacitances are C1 = 1.00 mF, C2 = 2.00 mF, C3 = 3.00 mF, and C4 = 4.00 mF, and the battery potential is VB = 1.00 V. When the circuit is at equilibrium, point D has potential VD = 0.00 V. What is the potential, VA, at point A?... Get solution
72. How much energy can be stored in a capacitor with two parallel plates, each with an area of 64.0 cm2 and separated by a gap of 1.30 mm, filled with porcelain whose dielectric constant is 7.00, and holding equal and opposite charges of magnitude 420. µC? Get solution
73. A quantum mechanical device known as the Josephson junction consists of two overlapping layers of superconducting metal (for example, aluminum at 1.00 K) separated by 20.0 nm of aluminum oxide, which has a dielectric constant of 9.10. If this device has an area of 100. µm2 and a parallel plate configuration, estimate its capacitance. Get solution
75. For a science project, a fourth-grader cuts the tops and bottoms off two soup cans of equal height, 7.24 cm, and with radii of 3.02 cm and 4.16 cm, puts the smaller one inside the larger, and hot-glues them both on a sheet of plastic, as shown in the figure. Then she fills the gap between the cans with a special “soup” (dielectric constant of 63.0). What is the capacitance of this arrangement?... Get solution
77. A parallel plate capacitor with air in the gap between the plates is connected to a 6.00-V battery. After charging, the energy stored in the capacitor is 72.0 nJ. Without disconnecting the capacitor from the battery, a dielectric is inserted into the gap and an additional 317 nJ of energy flows from the battery to the capacitor.a) What is the dielectric constant of the dielectric?b) If each of the plates has an area of 50.0 cm2, what is the charge on the positive plate of the capacitor after the dielectric has been inserted?c) What is the magnitude of the electric field between the plates before the dielectric is inserted?d) What is the magnitude of the electric field between the plates after the dielectric is inserted? Get solution
76. The Earth can be thought of as a spherical capacitor. If the net charge on the Earth is –7.80 · 105 C , find (a) the capacitance of the Earth and (b) the electric potential energy stored on the Earth’s surface. Get solution
78. An 8.00-µF capacitor is fully charged by a 240.-V battery, which is then disconnected. Next, the capacitor is connected to an initially uncharged capacitor of capacitance C, and the potential difference across it is found to be 80.0 V. What is C? How much energy ends up being stored in the second capacitor? Get solution
79. A parallel plate capacitor consists of square plates of edge length 2.00 cm separated by a distance of 1.00 mm. The capacitor is charged with a 15.0-V battery, and the battery is then removed. A 1.00-mm-thick sheet of nylon (dielectric constant of 3.50) is slid between the plates. What is the average force (magnitude and direction) on the nylon sheet as it is inserted into the capacitor? Get solution
80. A proton traveling along the x-axis at a speed of 1.00 · 106 m/s enters the gap between the plates of a 2.00-cm-wide parallel plate capacitor. The surface charge distributions on the plates are given by σ = ±1.00 · 10–6 C/m2. How far has the proton been deflected sideways (∆y) when it reaches the far edge of the capacitor? Assume that the electric field is uniform inside the capacitor and zero outside. Get solution
81. A parallel plate capacitor has square plates of side L = 10.0 cm separated by a distance d = 2.50 mm, as shown in the figure. The capacitor is charged by a battery with potential difference V0 = 75.0 V; the battery is then disconnected.a) Determine the capacitance, C0, and the electric potential energy, U0, stored in the capacitor at this point.b) A slab made of Plexiglas (κ = 3.40) is then inserted so that it fills 2/3 of the volume between the plates, as shown in the figure. Determine the new capacitance, C', the new potential difference between the plates, V', and the new electric potential energy, U', stored in the capacitor.c) Neglecting gravity, did the inserter of the dielectric slab have to do work or not?... Get solution
82. A typical AAA battery has stored energy of about 3400 J. (Battery capacity is typically listed as 625 mA h, meaning that much charge can be delivered at approximately 1.5 V.) Suppose you want to build a parallel plate capacitor to store this amount of energy, using a plate separation of 1.0 mm and with air filling the space between the plates.a) Assuming that the potential difference across the capacitor is 1.50 V, what must the area of each plate be?b) Assuming that the potential difference across the capacitor is the maximum that can be applied without dielectric breakdown occurring, what must the area of each plate be?c) Is either capacitor a practical replacement for the AAA battery? Get solution
83. Two parallel plate capacitors, C1 and C2, are connected in series to a 96.0-V battery. Both capacitors have plates with an area of 1.00 cm2 and a separation of 0.100 mm; C1 has air between its plates, and C2 has that space filled with porcelain (dielectric constant of 7.00 and dielectric strength of 5.70 kV/mm).a) After charging, what are the charges on each capacitor?b) What is the total energy stored in the two capacitors?c) What is the electric field between the plates of C2? Get solution
84. The plates of parallel plate capacitor A consist of two metal discs of identical radius, R1 = 4.00 cm, separated by a distance d = 2.00 mm, as shown in the figure.a) Calculate the capacitance of this parallel plate capacitor with the space between the plates filled with air.b) A dielectric in the shape of a thick-walled cylinder of outer radius R1 = 4.00 cm, inner radius R2 = 2.00 cm, thickness d = 2.00 mm, and dielectric constant κ = 2.00 is placed between the plates, coaxial with them, as shown in the figure. Calculate the capacitance of capacitor B, with this dielectric.c) The dielectric cylinder is removed, and instead a solid disc of radius R1 made of the same dielectric is placed between the plates to form capacitor C, as shown in the figure. What is the new capacitance?... Get solution
86. The capacitance of a spherical capacitor consisting of two concentric conducting spheres with radii r1 and r2 (r2 > r1) is given by C = 4πε0r1r2/(r2 – r1). Suppose that the space between the spheres, from r1 up to a radius R (r1 R r2) is fi lled with a dielectric for which ε = 10 ε0. Find an expression for the capacitance, and check the limits when R = r1 and R = r2. Get solution
87. In the figure, a parallel plate capacitor is connected to a 300.-V battery. With the capacitor connected, a proton is fired with a speed of 2.00 · 105 m/s from (through) the negative plate of the capacitor at an angle θ with the normal to the plate.a) Show that the proton cannot reach the positive plate of the capacitor, regardless of what the angle θ is.b) Sketch the trajectory of the proton between the plates.c) Assuming that V = 0 at the negative plate, calculate the potential at the point between the plates where the proton reverses its motion in the x-direction.d) Assuming that the plates are long enough for the proton to stay between them throughout its motion, calculate the speed (magnitude only) of the proton as it collides with the negative plate.... Get solution
88. For the parallel plate capacitor with dielectric shown in the figure, prove that for a given thickness of the dielectric slab, the capacitance does not depend on the position of the slab relative to the two conducting plates (that is, it does not depend on the values of d1 and d3).... Get solution
89. The battery of an electric car stores 53.63 MJ of energy. How many supercapacitors, each with capacitance C = 3.361 kF at a potential difference of 2.121 V, are required to supply this amount of energy? Get solution
90. The battery of an electric car stores 60.51 MJ of energy. If 6990 supercapacitors, each with capacitance C = 3.423 kF, are required to supply this amount of energy, what is the potential difference across each supercapacitor? Get solution
91. The battery of an electric car stores 67.39 MJ of energy. If 6845 supercapacitors, each with capacitance C and charged to a potential difference of 2.377 V, can supply this amount of energy, what is the value of C for each supercapacitor? Get solution
92. A parallel plate capacitor with vacuum between the plates has a capacitance of 3.547 μF. A dielectric material with κ = 4.617 is placed between the plates, completely filling the volume between them. The capacitor is then connected to a battery that maintains a potential difference of 10.03 V across the plates. How much work is required to pull the dielectric material out of the capacitor? Get solution
93. A parallel plate capacitor with vacuum between the plates has a capacitance of 3.607 μF. A dielectric material is placed between the plates, completely filling the volume between them. The capacitor is then connected to a battery that maintains a potential difference of 11.33 V across the plates. The dielectric material is pulled out of the capacitor, which requires 4.804 · 10–4 J of work. What is the dielectric constant of the material? Get solution
94. A parallel plate capacitor with vacuum between the plates has a capacitance of 3.669 μF. A dielectric material with κ = 3.533 is placed between the plates, completely filling the volume between them. The capacitor is then connected to a battery that maintains a potential difference V across the plates. Th e dielectric material is pulled out of the capacitor, which requires 7.389 · 10–4 J of work. What is the potential difference, V? Get solution
