Summary AP Physics C: E&M - OpenStax University Physics Volume 2, Chapter 8 Problems 21, 25, 31, 32, 33, 37, 41, 43, 47, 48, 51, 53, 55

AP Physics C: Electricity and Magnetism. OpenStax University Physics Volume 2, Chapter 8 Problems 21, 25, 31, 32, 33, 37, 41, 43, 47, 48, 51, 53, 55 with Answers and Work. 8.1 Capacitors and Capacitance 21. Calculate the voltage applied to a 2.00-μF capacitor when it holds 3.10μC of charge. 25. The plates of an empty parallel-plate capacitor of capacitance 5.0 pF are 2.0 mm apart. What is the area of each plate? 8.2 Capacitors in Series and in Parallel 31. A 4.00-pF is connected in series with an 8.00-pF capacitor and a 400-V potential difference is applied across the pair. (a) What is the charge on each capacitor? (b) What is the voltage across each capacitor? 32. Three capacitors, with capacitances of C1=2.0μF, C2=3.0μF, and C3=6.0μF, respectively, are connected in parallel. A 500-V potential difference is applied across the combination. Determine the voltage across each capacitor and the charge on each capacitor. 33. Find the total capacitance of this combination of series and parallel capacitors shown below. 37. Find the net capacitance of the combination of series and parallel capacitors shown below. 8.3 Energy Stored in a Capacitor 41. A capacitor has a charge of 2.5μC when connected to a 6.0-V battery. How much energy is stored in this capacitor? 43. (a) What is the energy stored in the 10.0-μF capacitor of a heart defibrillator charged to 9.00×103V ? (b) Find the amount of the stored charge. 47. An anxious physicist worries that the two metal shelves of a wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. (a) What is the capacitance of the empty shelves if they have area 1.00×102m2 and are 0.200 m apart? (b) What is the voltage between them if opposite charges of magnitude 2.00 nC are placed on them? (c) To show that this voltage poses a small hazard, calculate the energy stored. (d) The actual shelves have an area 100 times smaller than these hypothetical shelves with a connection to the same voltage. Are his fears justified? 48. A parallel-plate capacitor is made of two square plates 25 cm on a side and 1.0 mm apart. The capacitor is connected to a 50.0-V battery. With the battery still connected, the plates are pulled apart to a separation of 2.00 mm. What are the energies stored in the capacitor before and after the plates are pulled farther apart? Why does the energy decrease even though work is done in separating the plates? 8.4 Capacitor with a Dielectric 51. An air-filled capacitor is made from two flat parallel plates 1.0 mm apart. The inside area of each plate is 8.0cm2. (a) What is the capacitance of this set of plates? (b) If the region between the plates is filled with a material whose dielectric constant is 6.0, what is the new capacitance? 53. A parallel-plate capacitor has charge of magnitude 9.00μC on each plate and capacitance 3.00μF when there is air between the plates. The plates are separated by 2.00 mm. With the charge on the plates kept constant, a dielectric with κ=5 is inserted between the plates, completely filling the volume between the plates. (a) What is the potential difference between the plates of the capacitor, before and after the dielectric has been inserted? (b) What is the electrical field at the point midway between the plates before and after the dielectric is inserted? 55. A parallel-plate capacitor with only air between its plates is charged by connecting the capacitor to a battery. The capacitor is then disconnected from the battery, without any of the charge leaving the plates. (a) A voltmeter reads 45.0 V when placed across the capacitor. When a dielectric is inserted between the plates, completely filling the space, the voltmeter reads 11.5 V. What is the dielectric constant of the material? (b) What will the voltmeter read if the dielectric is now pulled away out so it fills only one-third of the space between the plates?