1.3: How to obtain the data
There are two main principles of sampling: replication and randomization.
Replication suggests that the same effect will be researched several times. This idea derived from the cornerstone math “big numbers” postulate which in simple words is “the more, the better”. When you count replicates, remember that they must be independent. For example, if you research how light influences the plant growth and use five growing chambers, each with ten plants, then number of replicates is five, not fifty. This is because plants withing each chamber are not independent as they all grow in the same environment but we research differences between environments. Five chambers are replicates whereas fifty plants are pseudoreplicates .
Repeated measurements is another complication. For example, in a study of short-term visual memory ten volunteers were planned to look on the same specific object multiple times. The problem here is that people may remember the object and recall it faster towards the end of a sequence. As a result, these multiple times are not replicates, they are repeated measurements which could tell something about learning but not about memory itself. There are only ten true replicates.
Another important question is how many replicates should be collected. There is the immense amount of publications about it, but in essence, there are two answers: (a) as many as possible and (b) 30. Second answer looks a bit funny but this rule of thumb is the result of many years of experience. Typically, samples which size is less than 30, considered to be a small. Nevertheless, even minuscule samples could be useful, and there are methods of data analysis which work with five and even with three replicates. There are also special methods ( power analysis ) which allow to estimate how many objects to collect (we will give one example due course).
Randomization tells among other that every object should have the equal chances to go into the sample. Quite frequently, researchers think that data was randomized while it was not actually collected in the random way.
For example, how to select the sample of 100 trees in the big forest? If we try simply to walk and select trees which somehow attracted the attention, this sample will not be random because these trees are somehow deviated and this is why we spotted them. Since one of the best ways of randomization is to introduce the order which is knowingly absent in nature (or at least not related with the study question), the reliable method is, for example, to use a detailed map of the forest, select two random coordinates, and find the tree which is closest to the selected point. However, trees are not growing homogeneously, some of them (like spruces) tend to grow together whereas others (like oaks) prefer to stay apart. With the method described above, spruces will have a better chance to come into sample so that breaks the rule of randomization. We might employ the second method and make a transect through the forest using rope, then select all trees touched with it, and then select, saying, every fifth tree to make a total of hundred.
Is the last (second) method appropriate? How to improve it?
Now you know enough to answer another question:
Once upon a time, there was an experiment with a goal to research the effect of different chemical poisons to weevils. Weevils were hold in jars, chemicals were put on fragments of filter paper. Researcher opened the jar, then picked up the weevil which first came out of jar, put it on the filter paper and waited until weevil died. Then researcher changed chemical, and start the second run of experiment in the same dish, and so on. But for some unknown reason, the first chemical used was always the strongest (weevils died very fast). Why? How to organize this experiment better?


10.10: X Glossary
Advocacy: The act or process of pleading for, supporting, or recommending a cause of course of action for individuals, groups, organizations, communities, society, or policy issues.
Collective bargaining: Negotiation of wages and other conditions of employment by an organized body of employees.
Evidence-based practice: Integrating scientific evidence with clinical expertise and patient/family preferences and values for delivery of optimal health care. [1]
Grievance process: A process for resolving disagreements between employees and management.
Informatics: Using information and technology to communicate, manage knowledge, mitigate error, and support decision-making. [2]
ISBARR: A mnemonic for the components to include when communicating with another health care team member: Introduction, Situation, Background, Assessment, Request/Recommendations, and Repeat back.
Magnet® Recognition Program: An organizational credential that recognizes quality patient outcomes, nursing excellence, and innovations in professional nursing practice.
Patient-centered care: The patient is the source of control and full partner in providing compassionate and coordinated care based on respect for patient’s preferences, values, and needs. [3]
Quality improvement: Using data to monitor the outcomes of care processes and using improvement methods to design and test changes to continuously improve the quality and safety of health care systems. [4]
Shared governance: A shared leadership model between management and employees working together to achieve common goals.
Social Determinants of Health (SDOH): The conditions in the environments where people live, learn, work, and play that affect a wide range of health, functioning, and quality of life outcomes and risks.
TeamSTEPPS® (Team Strategies and Tools to Enhance Performance and Patient Safety): An evidence-based framework to improve client safety through effective communication in health care environments consisting of four core competencies: communication, leadership, situation monitoring, and mutual support.
Teamwork and collaboration: Functioning effectively within nursing and interprofessional teams, fostering open communication, mutual respect, and shared decision-making to achieve quality patient care. [5]
Whistleblower: A person who exposes any kind of information or activity that is deemed illegal, unethical, or not correct within an organization.
- QSEN. (n.d.). About. https://qsen.org/about-qsen/ ↵
- QSEN. (n.d.). About. https://qsen.org/about-qsen/ ↵
- QSEN. (n.d.). About. https://qsen.org/about-qsen/ ↵
- QSEN. (n.d.). About. https://qsen.org/about-qsen/ ↵
- QSEN. (n.d.). About. https://qsen.org/about-qsen/ ↵


1.15.4: End-of-Chapter Material
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Key takeaways for this Chapter
- Every citizen needs to be climate literate.
- The planet is warming due to the greenhouse effect, also known as global warming.
- The Earths climate is changing causing numerous problems with our weather, oceans, snow/ice, and ecosystems.
- Human health is being negatively impacted by climate change.
- Humans can take actions to increase the health of the planet
Media Attributions
- Earth’s_greenhouse_effect_(US_EPA,_2012) © US EPA is licensed under a Public Domain license
- Muir glacier melt, Alaska 1941 and 2004 © NASA Global Climate Change is licensed under a Public Domain license
- ghg-concentrations_download1_2021 © EPA is licensed under a Public Domain license
- 10 Indicators of a Warming World © US National Oceanic and Atmospheric Administration: National Climatic Data Center is licensed under a Public Domain license
- 1.1 Major U.S. Climate Trends © original figure provided by Allison Crimmins, EPA; Ken Kunkel, CICS-NC, Dave Easterling, NCDC adapted by KFalcone is licensed under a Public Domain license
- Human_population_since_1800 © Bdm25 is licensed under a CC BY-SA (Attribution ShareAlike) license
- Great_Pacific_Garbage_Patch-Map-2017 © L. Lebreton, B. Slat, F. Ferrari, B. Sainte-Rose, J. Aitken, R. Marthouse, S. Hajbane, S. Cunsolo, A. Schwarz, A. Levivier, K. Noble, P. Debeljak, H. Maral, R. Schoeneich-Argent, R. Brambini, and J. Reisser is licensed under a CC BY (Attribution) license
References
- Climate Change Indicators in the United States. (2022, March 31). US EPA. https://www.epa.gov/climate-indicators 14: Environmental Wellness - A Healthy Planet#return-footnote-53-1
- About Ice Cores. (n.d.-b). NSF Ice Core Facility. https://icecores.org/about-ice-cores 14: Environmental Wellness - A Healthy Planet#return-footnote-53-2
- The Impacts of Climate Change on Human Health in the United States: A Scientific Assessment. (2016, April 4). GlobalChange.Gov. https://health2016.globalchange.gov/ 14: Environmental Wellness - A Healthy Planet#return-footnote-53-3
- https://education.nationalgeographic...-garbage-patch 14: Environmental Wellness - A Healthy Planet#return-footnote-53-4
- Trashed: Across the Pacific Ocean, plastics, plastics, everywhere. (2003, November). Natural History Magazine. https://www.naturalhistorymag.com/ht...3_feature.html 14: Environmental Wellness - A Healthy Planet#return-footnote-53-5


7.10: Capacitance (Exercises)
Conceptual Questions
Capacitors and Capacitance
1. Does the capacitance of a device depend on the applied voltage? Does the capacitance of a device depend on the charge residing on it?
2. Would you place the plates of a parallel-plate capacitor closer together or farther apart to increase their capacitance?
3. The value of the capacitance is zero if the plates are not charged. True or false?
4. If the plates of a capacitor have different areas, will they acquire the same charge when the capacitor is connected across a battery?
5. Does the capacitance of a spherical capacitor depend on which sphere is charged positively or negatively?
Capacitors in Series and in Parallel
6. If you wish to store a large amount of charge in a capacitor bank, would you connect capacitors in series or in parallel? Explain.
7. What is the maximum capacitance you can get by connecting three 1.0-μF capacitors? What is the minimum capacitance?
Energy Stored in a Capacitor
8. If you wish to store a large amount of energy in a capacitor bank, would you connect capacitors in series or parallel? Explain.
Capacitor with a Dielectric
9. Discuss what would happen if a conducting slab rather than a dielectric were inserted into the gap between the capacitor plates.
10. Discuss how the energy stored in an empty but charged capacitor changes when a dielectric is inserted if (a) the capacitor is isolated so that its charge does not change; (b) the capacitor remains connected to a battery so that the potential difference between its plates does not change.
Molecular Model of a Dielectric
11. Distinguish between dielectric strength and dielectric constant.
12. Water is a good solvent because it has a high dielectric constant. Explain.
13. Water has a high dielectric constant. Explain why it is then not used as a dielectric material in capacitors.
14. Elaborate on why molecules in a dielectric material experience net forces on them in a non-uniform electrical field but not in a uniform field.
15. Explain why the dielectric constant of a substance containing permanent molecular electric dipoles decreases with increasing temperature.
16. Give a reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. How does a dielectric material also allow a greater voltage to be applied to a capacitor? (The dielectric thus increases C and permits a greater V .)
17. Elaborate on the way in which the polar character of water molecules helps to explain water’s relatively large dielectric constant.
18. Sparks will occur between the plates of an air-filled capacitor at a lower voltage when the air is humid than when it is dry. Discuss why, considering the polar character of water molecules.
Application - RC Circuits
RC1. When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC constant of the circuit—it is not possible to measure time variations shorter than RC. How would you manipulate R and C in the circuit to allow the necessary measurements?
RC2. A battery, switch, capacitor, and lamp are connected in series. Describe what happens to the lamp when the switch is closed.
Problems
Capacitors and Capacitance
19. What charge is stored in a 180.0-μF capacitor when 120.0 V is applied to it?
20. Find the charge stored when 5.50 V is applied to an 8.00-pF capacitor.
21. Calculate the voltage applied to a 2.00-μF capacitor when it holds 3.10μC of charge.
22. What voltage must be applied to an 8.00-nF capacitor to store 0.160 mC of charge?
23. What capacitance is needed to store 3.00μC of charge at a voltage of 120 V?
24. What is the capacitance of a large Van de Graaff generator’s terminal, given that it stores 8.00 mC of charge at a voltage of 12.0 MV?
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?
26. A 60.0-pF vacuum capacitor has a plate area of \(\displaystyle 0.010m^2\). What is the separation between its plates?
27. A set of parallel plates has a capacitance of 5.0µF . How much charge must be added to the plates to increase the potential difference between them by 100 V?
28. Consider Earth to be a spherical conductor of radius 6400 km and calculate its capacitance.
29. If the capacitance per unit length of a cylindrical capacitor is 20 pF/m, what is the ratio of the radii of the two cylinders?
30. An empty parallel-plate capacitor has a capacitance of 20µF . How much charge must leak off its plates before the voltage across them is reduced by 100 V?
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 \(\displaystyle C_1=2.0μF, C_2=3.0μF,\) and \(\displaystyle C_3=6.0μF\), 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.
34.  What is the smallest number of capacitors you could connect together to achieve your goal, and how would you connect them?
35. What total capacitances can you make by connecting a 5.00-μF and a 8.00-μF capacitor?
36. Find the equivalent capacitance of the combination of series and parallel capacitors shown below.
37. Find the net capacitance of the combination of series and parallel capacitors shown below.
38. A 40-pF capacitor is charged to a potential difference of 500 V. Its terminals are then connected to those of an uncharged 10-pF capacitor. Calculate:
(a) the original charge on the 40-pF capacitor;
(b) the charge on each capacitor after the connection is made; and
(c) the potential difference across the plates of each capacitor after the connection.
39. A 2.0-μF capacitor and a 4.0-μF capacitor are connected in series across a 1.0-kV potential. The charged capacitors are then disconnected from the source and connected to each other with terminals of like sign together. Find the charge on each capacitor and the voltage across each capacitor.
Energy Stored in a Capacitor
40. How much energy is stored in an 8.00-μF capacitor whose plates are at a potential difference of 6.00 V?
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?
42. How much energy is stored in the electrical field of a metal sphere of radius 2.0 m that is kept at a 10.0-V potential?
43. (a) What is the energy stored in the 10.0-μF capacitor of a heart defibrillator charged to \(\displaystyle 9.00×10^3V\)?
(b) Find the amount of the stored charge.
44. In open-heart surgery, a much smaller amount of energy will defibrillate the heart.
(a) What voltage is applied to the 8.00-μF capacitor of a heart defibrillator that stores 40.0 J of energy?
(b) Find the amount of the stored charge.
45. A 165-μF capacitor is used in conjunction with a dc motor. How much energy is stored in it when 119 V is applied?
46. Suppose you have a 9.00-V battery, a 2.00-μF capacitor, and a 7.40-μF capacitor.
(a) Find the charge and energy stored if the capacitors are connected to the battery in series.
(b) Do the same for a parallel connection.
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 \(\displaystyle 1.00×10^2m\) 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. 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?
49. Suppose that the capacitance of a variable capacitor can be manually changed from 100 pF to 800 pF by turning a dial, connected to one set of plates by a shaft, from 0° to 180°. With the dial set at 180°180° (corresponding to C= 800pF ), the capacitor is connected to a 500-V source. After charging, the capacitor is disconnected from the source, and the dial is turned to 0° . If friction is negligible, how much work is required to turn the dial from 180° to 0° ?
Capacitor with a Dielectric
50. Show that for a given dielectric material, the maximum energy a parallel-plate capacitor can store is directly proportional to the volume of dielectric.
51. An air-filled capacitor is made from two flat parallel plates 1.0 mm apart. The inside area of each plate is 8.0cm28.0cm2.
(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?
52. A capacitor is made from two concentric spheres, one with radius 5.00 cm, the other with radius 8.00 cm.
(a) What is the capacitance of this set of conductors?
(b) If the region between the conductors is filled with a material whose dielectric constant is 6.00, what is the capacitance of the system?
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 \(\kappa = 5\) 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?
54. Some cell walls in the human body have a layer of negative charge on the inside surface. Suppose that the surface charge densities are \(\displaystyle ±0.50×10^{−3}C/m^2\), the cell wall is \(\displaystyle 5.0×10^{−9}m\) thick, and the cell wall material has a dielectric constant of κ=5.4.
(a) Find the magnitude of the electric field in the wall between two charge layers.
(b) Find the potential difference between the inside and the outside of the cell. Which is at higher potential?
(c) A typical cell in the human body has volume \(\displaystyle 10^{−16}m^3\). Estimate the total electrical field energy stored in the wall of a cell of this size when assuming that the cell is spherical. ( Hint: Calculate the volume of the cell wall.)
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?
Molecular Model of a Dielectric
56. Two flat plates containing equal and opposite charges are separated by material 4.0 mm thick with a dielectric constant of 5.0. If the electrical field in the dielectric is 1.5 MV/m, what are
(a) the charge density on the capacitor plates, and
(b) the induced charge density on the surfaces of the dielectric?
57. For a Teflon™-filled, parallel-plate capacitor, the area of the plate is \(\displaystyle 50.0cm^2\) and the spacing between the plates is 0.50 mm. If the capacitor is connected to a 200-V battery, find
(a) the free charge on the capacitor plates,
(b) the electrical field in the dielectric, and
(c) the induced charge on the dielectric surfaces.
58. Find the capacitance of a parallel-plate capacitor having plates with a surface area of \(\displaystyle 5.00m^2\) and separated by 0.100 mm of Teflon™.
59. (a) What is the capacitance of a parallel-plate capacitor with plates of area \(\displaystyle 1.50m^2\) that are separated by 0.0200 mm of neoprene rubber?
(b) What charge does it hold when 9.00 V is applied to it?
60. Two parallel plates have equal and opposite charges. When the space between the plates is evacuated, the electrical field is \(\displaystyle E=3.20×10^5V/m\). When the space is filled with dielectric, the electrical field is \(\displaystyle E=2.50×10^5V/m\).
(a) What is the surface charge density on each surface of the dielectric?
(b) What is the dielectric constant?
61. The dielectric to be used in a parallel-plate capacitor has a dielectric constant of 3.60 and a dielectric strength of \(\displaystyle 1.60×10^7V/m\). The capacitor has to have a capacitance of 1.25 nF and must be able to withstand a maximum potential difference 5.5 kV. What is the minimum area the plates of the capacitor may have?
62. When a 360-nF air capacitor is connected to a power supply, the energy stored in the capacitor is 18.5μJ . While the capacitor is connected to the power supply, a slab of dielectric is inserted that completely fills the space between the plates. This increases the stored energy by 23.2μJ .
(a) What is the potential difference between the capacitor plates?
(b) What is the dielectric constant of the slab?
63. A parallel-plate capacitor has square plates that are 8.00 cm on each side and 3.80 mm apart. The space between the plates is completely filled with two square slabs of dielectric, each 8.00 cm on a side and 1.90 mm thick. One slab is Pyrex glass and the other slab is polystyrene. If the potential difference between the plates is 86.0 V, find how much electrical energy can be stored in this capacitor.
Application - RC Circuits
RC1 (49). The timing device in an automobile’s intermittent wiper system is based on an RC time constant and utilizes a 0.500-μF capacitor and a variable resistor. Over what range must R be made to vary to achieve time constants from 2.00 to 15.0 s?
RC2. A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?
RC3. The duration of a photographic flash is related to an RC time constant, which is 0.100μs for a certain camera.
(a) If the resistance of the flash lamp is 0.0400Ω during discharge, what is the size of the capacitor supplying its energy?
(b) What is the time constant for charging the capacitor, if the charging resistance is 800kΩ ?
RC4. A 2.00- and a 7.50-μF capacitor can be connected in series or parallel, as can a 25.0- and a 100-kΩ resistor. Calculate the four RC time constants possible from connecting the resulting capacitance and resistance in series.
RC5. A 500-Ω resistor, an uncharged 1.50-μF capacitor, and a 6.16-V source voltage are connected in series.
(a) What is the initial current?
(b) What is the RC time constant?
(c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?
RC6. A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator.
(a) If the defibrillator has a capacitance of 8.00μF, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.)
(b) If the initial voltage is 12.0 kV, how long does it take to decline to \(6.00×10^2V\)?
RC7. An ECG monitor must have an RC time constant less than \(1.00×10^2μs\) to be able to measure variations in voltage over small time intervals.
(a) If the resistance of the circuit (due mostly to that of the patient’s chest) is 1.00kΩ , what is the maximum capacitance of the circuit?
(b) Would it be difficult in practice to limit the capacitance to less than the value found in (a)?
RC8. Using the exact exponential treatment, determine how much time is required to charge an initially uncharged 100-pF capacitor through a 75.0-MΩ resistor to 90.0% of its final voltage.
RC9. If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an RC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RC constant is acceptable, and given that the flash is driven by a 600-μF capacitor, what is the resistance in the flash tube?
Additional Problems
64. A capacitor is made from two flat parallel plates placed 0.40 mm apart. When a charge of 0.020μC is placed on the plates the potential difference between them is 250 V.
(a) What is the capacitance of the plates?
(b) What is the area of each plate?
(c) What is the charge on the plates when the potential difference between them is 500 V?
(d) What maximum potential difference can be applied between the plates so that the magnitude of electrical fields between the plates does not exceed 3.0 MV/m?
65. An air-filled (empty) parallel-plate capacitor is made from two square plates that are 25 cm on each side and 1.0 mm apart. The capacitor is connected to a 50-V battery and fully charged. It is then disconnected from the battery and its plates are pulled apart to a separation of 2.00 mm.
(a) What is the capacitance of this new capacitor?
(b) What is the charge on each plate?
(c) What is the electrical field between the plates?
66. Suppose that the capacitance of a variable capacitor can be manually changed from 100 to 800 pF by turning a dial connected to one set of plates by a shaft, from 0° to 180° . With the dial set at 180° (corresponding to C= 800pF ), the capacitor is connected to a 500-V source. After charging, the capacitor is disconnected from the source, and the dial is turned to 0° . (a) What is the charge on the capacitor? (b) What is the voltage across the capacitor when the dial is set to 0° ?
67. Earth can be considered as a spherical capacitor with two plates, where the negative plate is the surface of Earth and the positive plate is the bottom of the ionosphere, which is located at an altitude of approximately 70 km. The potential difference between Earth’s surface and the ionosphere is about 350,000 V.
(a) Calculate the capacitance of this system.
(b) Find the total charge on this capacitor.
(c) Find the energy stored in this system.
68. A 4.00-μF capacitor and a 6.00-μF capacitor are connected in parallel across a 600-V supply line.
(a) Find the charge on each capacitor and voltage across each.
(b) The charged capacitors are disconnected from the line and from each other. They are then reconnected to each other with terminals of unlike sign together. Find the final charge on each capacitor and the voltage across each.
69. Three capacitors having capacitances of 8.40, 8.40, and 4.20 μF , respectively, are connected in series across a 36.0-V potential difference.
(a) What is the charge on the 4.20-μF capacitor?
(b) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination?
70. A parallel-plate capacitor with capacitance 5.0μF is charged with a 12.0-V battery, after which the battery is disconnected. Determine the minimum work required to increase the separation between the plates by a factor of 3.
71. (a) How much energy is stored in the electrical fields in the capacitors (in total) shown below?
(b) Is this energy equal to the work done by the 400-V source in charging the capacitors?
72. Three capacitors having capacitances 8.4, 8.4, and 4.2 μF are connected in series across a 36.0-V potential difference.
(a) What is the total energy stored in all three capacitors?
(b) The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other with the positively charged plates connected together. What is the total energy now stored in the capacitors?
73. (a) An 8.00-μF capacitor is connected in parallel to another capacitor, producing a total capacitance of 5.00μF . What is the capacitance of the second capacitor?
(b) What is unreasonable about this result?
(c) Which assumptions are unreasonable or inconsistent?
74 . (a) On a particular day, it takes \(\displaystyle 9.60×10^3J\) of electrical energy to start a truck’s engine. Calculate the capacitance of a capacitor that could store that amount of energy at 12.0 V.
(b) What is unreasonable about this result?
(c) Which assumptions are responsible?
75. (a) A certain parallel-plate capacitor has plates of area \(\displaystyle 4.00m^2\), separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage?
(b) What is unreasonable about this result?
(c) Which assumptions are responsible or inconsistent?
76. A prankster applies 450 V to an 80.0-μF capacitor and then tosses it to an unsuspecting victim. The victim’s finger is burned by the discharge of the capacitor through 0.200 g of flesh. Estimate, what is the temperature increase of the flesh? Is it reasonable to assume that no thermodynamic phase change happened?
Advanced Problems
AP1. A circuit contains a D cell battery, a switch, a 20-Ω resistor, and four 20-mF capacitors connected in series.
(a) What is the equivalent capacitance of the circuit?
(b) What is the RC time constant?
(c) How long before the current decreases to 50% of the initial value once the switch is closed?
AP2. A circuit contains a D-cell battery, a switch, a 20-Ω resistor, and three 20-mF capacitors. The capacitors are connected in parallel, and the parallel connection of capacitors are connected in series with the switch, the resistor and the battery.
(a) What is the equivalent capacitance of the circuit?
(b) What is the RC time constant?
(c) How long before the current decreases to 50% of the initial value once the switch is closed?
AP3. Consider the circuit below. The battery has an source voltage of ε=30.00V and an internal resistance of r=1.00Ω .
(a) Find the equivalent resistance of the circuit and the current out of the battery.
(b) Find the current through each resistor.
(c) Find the potential drop across each resistor.
(d) Find the power dissipated by each resistor.
(e) Find the total power supplied by the batteries.
AP4. A homemade capacitor is constructed of 2 sheets of aluminum foil with an area of 2.00 square meters, separated by paper, 0.05 mm thick, of the same area and a dielectric constant of 3.7. The homemade capacitor is connected in series with a 100.00-Ω resistor, a switch, and a 6.00-V voltage source.
(a) What is the RC time constant of the circuit?
(b) What is the initial current through the circuit, when the switch is closed? (c) How long does it take the current to reach one third of its initial value?
AP5. A student makes a homemade resistor from a graphite pencil 5.00 cm long, where the graphite is 0.05 mm in diameter. The resistivity of the graphite is \(ρ=1.38×10^{−5}Ω/m\). The homemade resistor is place in series with a switch, a 10.00-mF capacitor and a 0.50-V power source.
(a) What is the RC time constant of the circuit?
(b) What is the potential drop across the pencil 1.00 s after the switch is closed?
AP6. The rather simple circuit shown below is known as a voltage divider. The symbol consisting of three horizontal lines is represents “ground” and can be defined as the point where the potential is zero. The voltage divider is widely used in circuits and a single voltage source can be used to provide reduced voltage to a load resistor as shown in the second part of the figure. (a) What is the output voltage \(V_{out}\) of circuit
(a) in terms of \(R_1,R_2,\) and \(V_{in}\)?
(b) What is the output voltage \(V_{out}\) of circuit (b) in terms of \(R_1,R_2,R_L,\) and \(V_{in}\)?
AP7. Three 300-Ω resistors are connect in series with an AAA battery with a rating of 3 AmpHours. (a) How long can the battery supply the resistors with power? (b) If the resistors are connected in parallel, how long can the battery last?
AP8. Consider a circuit that consists of a real battery with an source voltage εε and an internal resistance of r connected to a variable resistor R.
(a) In order for the terminal voltage of the battery to be equal to the source voltage of the battery, what should the resistance of the variable resistor be adjusted to?
(b) In order to get the maximum current from the battery, what should the resistance of the variable resistor be adjusted to?
(c) In order for the maximum power output of the battery to be reached, what should the resistance of the variable resistor be set to?
AP9. Consider the circuit shown below. What is the energy stored in each capacitor after the switch has been closed for a very long time?
AP10. Consider a circuit consisting of a battery with an source voltage εε and an internal resistance of r connected in series with a resistorR and a capacitor C. Show that the total energy supplied by the battery while charging the battery is equal to \(ε^2C\).
AP11. Consider the circuit shown below. The terminal voltages of the batteries are shown.
(a) Find the equivalent resistance of the circuit and the current out of the battery.
(b) Find the current through each resistor.
(c) Find the potential drop across each resistor.
(d) Find the power dissipated by each resistor.
(e) Find the total power supplied by the batteries.
AP12. Consider the circuit shown below.
(a) What is the terminal voltage of the battery?
(b) What is the potential drop across resistor \(R_2\)?
AP13. Consider the circuit shown below.
(a)Determine the equivalent resistance and the current from the battery with switch \(S_1\)open.
(b) Determine the equivalent resistance and the current from the battery with switch \(S_1\) closed.
AP14. Two resistors, one having a resistance of 145Ω , are connected in parallel to produce a total resistance of 150Ω .
(a) What is the value of the second resistance?
(b) What is unreasonable about this result?
(c) Which assumptions are unreasonable or inconsistent?
AP15. Two resistors, one having a resistance of 900kΩ , are connected in series to produce a total resistance of 0.500MΩ .
(a) What is the value of the second resistance?
(b) What is unreasonable about this result?
(c) Which assumptions are unreasonable or inconsistent?
AP16. Apply the junction rule at point a shown below.
AP17. Apply the loop rule to Loop akledcba in the preceding problem.
AP18. Find the currents flowing in the circuit in the preceding problem. Explicitly show how you follow the steps in the Problem-Solving Strategy: Series and Parallel Resistors.
AP19. Consider the circuit shown below.
(a) Find the current through each resistor.
(b) Check the calculations by analyzing the power in the circuit.
AP20. A flashing lamp in a Christmas earring is based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V.
(a) What energy does it dissipate?
(b) How much charge moves through the lamp?
(c) Find the capacitance.
(d) What is the resistance of the lamp? (Since average values are given for some quantities, the shape of the pulse profile is not needed.)
AP21. A 160-μF capacitor charged to 450 V is discharged through a 31.2-kΩ resistor.
(a) Find the time constant.
(b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is 1.67kJ/kg⋅°C , noting that most of the thermal energy is retained in the short time of the discharge.
(c) Calculate the new resistance, assuming it is pure carbon.
(d) Does this change in resistance seem significant?
Challenge Problems
77. A spherical capacitor is formed from two concentric spherical conducting spheres separated by vacuum. The inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor.
(a) What is the capacitance of the capacitor?
(b) What is the magnitude of the electrical field at r=12.6cm , just outside the inner sphere?
(c) What is the magnitude of the electrical field at r=14.7cm , just inside the outer sphere?
(d) For a parallel-plate capacitor the electrical field is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor?
78. The network of capacitors shown below are all uncharged when a 300-V potential is applied between points A and B with the switch S open.
(a) What is the potential difference \(\displaystyle V_E−V_D\)?
(b) What is the potential at point E after the switch is closed?
(c) How much charge flows through the switch after it is closed?
79. Electronic flash units for cameras contain a capacitor for storing the energy used to produce the flash. In one such unit the flash lasts for 1/675 fraction of a second with an average light power output of 270 kW.
(a) If the conversion of electrical energy to light is 95% efficient (because the rest of the energy goes to thermal energy), how much energy must be stored in the capacitor for one flash?
(b) The capacitor has a potential difference between its plates of 125 V when the stored energy equals the value stored in part (a). What is the capacitance?
80. A spherical capacitor is formed from two concentric spherical conducting shells separated by a vacuum. The inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor.
(a) What is the energy density at r=12.6cm , just outside the inner sphere?
(b) What is the energy density at r=14.7cm , just inside the outer sphere?
(c) For the parallel-plate capacitor the energy density is uniform in the region between the plates, except near the edges of the plates. Is this also true for the spherical capacitor?
81. A metal plate of thickness t is held in place between two capacitor plates by plastic pegs, as shown below. The effect of the pegs on the capacitance is negligible. The area of each capacitor plate and the area of the top and bottom surfaces of the inserted plate are all A. What is the capacitance of this system?
82. A parallel-plate capacitor is filled with two dielectrics, as shown below. When the plate area is A and separation between plates is d, show that the capacitance is given by \(\displaystyle C=ε_0\frac{A}{d}\frac{κ_1+κ_2}{2}\).
83. A parallel-plate capacitor is filled with two dielectrics, as shown below. Show that the capacitance is given by \(\displaystyle C=2ε_0\frac{A}{d}\frac{κ_1κ_2}{κ_1+κ_2}\).
84. A capacitor has parallel plates of area \(\displaystyle 12cm^2\) separated by 2.0 mm. The space between the plates is filled with polystyrene.
(a) Find the maximum permissible voltage across the capacitor to avoid dielectric breakdown.
(b) When the voltage equals the value found in part (a), find the surface charge density on the surface of the dielectric.
Contributors and Attributions
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a
Creative Commons Attribution License (by 4.0)
.


2.5: References
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American Atheists. (n.d.). What is atheism? Retrieved from http :// atheists . org / activism / resources / what – is-atheism
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Carteret, M. (2010, October 21). Cultural values of Asian patients and families. Retrieved from http://www.dimensionsofculture.com/2010/10/cultural-values-of-asian-patients-and-families/
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Carteret, M. (2010, October 21). Healthcare for Middle Eastern patients and families. Retrieved from http://www.dimensionsofculture.com/2010/10/health-care-for-middle-eastern-patients-families/
Carteret, M. (2010, October 21). Traditional Asian health beliefs and healing practices. Retrieved from http://www.dimensionsofculture.com/2010/10/traditional-asian-health-beliefs-healing-practices/
Carteret, M. (2010, November 3). Cultural aspects of death and dying. http://www.dimensionsofculture.com/2010/11/cultural-aspects-of-death-and-dying/
Carteret, M. (2010, November 3). The importance of familismo . Retrieved from http://www.dimensionsofculture.com/2010/11/the-importance-of-familismo/
Carteret, M. (2011, March 15). Cultural values of Latino patients and families. Retrieved from http://www.dimensionsofculture.com/2011/03/cultural-values-of-latino-patients-and-families/
Carteret, M. (2011, May 16). Healthcare for African American patients/families. Retrieved from http :// www . dimensionsofculture . com /2011/05/ health – care – for – african – american – patients families /
Do-not-resuscitate order. (2014, May 7). In A . D . A . M . Medical Encyclopedia . Retrieved fro http :// www . nlm . nih . gov / medlineplus / ency / patientinstructions /000473. htm
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Kauai’s Hindu Monastery. (n.d.). Basics of Hinduism. Retrieved from https://www.himalayanacademy.com/readlearn/basics/nine-beliefs
Leahy, W., Fuzy, J., & Grafe, J. (2013). Providing home care : A textbook for home health aides (4th ed.). Albuquerque, NM: Hartman.
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9.4.4: Tropical Steppe Climate
The tropical steppe climate is a transitional climate between the tropical wet and tropical dry climates. The controlling factors of the climate are similar to that of the tropical dry climate, though temperatures are cooler and annual precipitation is higher. This is why we consider a steppe climate semi-arid rather than arid.
Geographical Location
The tropical steppe climate is located on the periphery of deserts. Tropical steppe climate is found bordering the Great Australian desert, the Sahara of northern Africa, and in southwest Asia.
Controlling Factors
The climate of the tropical steppe is a direct result of its interior continental location and proximity to the subtropical high. The tropical steppe is not as dry as the tropical desert climate as it lies closer to a source of moisture. If on the equatorward side of the desert it is the ITCZ, or the subpolar low and midlatitude cyclones if it is located poleward side.
Distinguishing Characteristics
Temperature
Unlike the midlatitude climates where we mark our seasons by the change from warm temperatures to cold, in the tropical dry climates seasons are distinguished on the basis of it being warm and excessively warm. The generally cloudless conditions that exist in the tropical steppe allows much insolation in to warm the surface. The very high temperatures are also due to the proximity of the climate to cT and mT air mass source regions. Mean annual temperature in the tropical steppe climate is approximately 20 o C (68 o F). Being located poleward of the tropical wet climates, the annual temperature range increases as the variation in sun angle increases at these locations. Annual temperature ranges vary from 10 o C (5.6 o F) to above 20 o C (11 o F). Daily temperature ranges are nearly similar to, or larger than, the annual range of temperature.
Precipitation
The tropical steppe climate is a semi-arid environment. To climatologists, a semi-arid environment can be defined as one where the annual potential evapotranspiration is more than half but less than the total annual precipitation. Potential evapotranspiration is a measure of the demand for water on account of plant transpiration and surface evaporation. In the tropical steppe, much evaporation and plant transpiration would take place if water were available. Meager amounts of precipitation during the relatively long summer droughts stress plants that require water during periods of high temperature. However, during the wet portions of the year, ample precipitation to meet the needs of the natural vegetation usually occurs.
 The seasonality of precipitation is similar to that of the closest humid climate. For example, the steppe climate found between the tropical desert and wet/dry tropical climate of Africa has a high sun wet - low sun dry seasonality to its precipitation. During the low sun period the subtropical high migrates into this region and suppresses convection. The subsiding air lowers the relative humidity making it difficult to bring air to its saturation point. Life sustaining rains come with the movement of the ITCZ into the tropical steppe. However, the tropical steppe located between the tropical desert and the dry summer subtropical (Mediterranean) climate is just the opposite, high sun dry - low sun wet. During the high sun season the tropical steppe is dominated by the subtropical high. During the low sun season cyclones associated with the subpolar low and polar front dominate.
Some regions having a tropical steppe climate are found on the lee side of mountains. As air ascends the windward slopes, water vapor condenses and precipitation occurs. Places located on the leeward side are thus in the "rain shadow" and are dry.


15.2: The Structure and Composition of the Sun
By the end of this section, you will be able to:
- Explain how the composition of the Sun differs from that of Earth
- Describe the various layers of the Sun and their functions
- Explain what happens in the different parts of the Sun’s atmosphere
The Sun , like all stars, is an enormous ball of extremely hot, largely ionized gas, shining under its own power. And we do mean enormous. The Sun could fit 109 Earths side-by-side across its diameter, and it has enough volume (takes up enough space) to hold about 1.3 million Earths.
The Sun does not have a solid surface or continents like Earth, nor does it have a solid core (Figure 15.2). However, it does have a lot of structure and can be discussed as a series of layers, not unlike an onion. In this section, we describe the huge changes that occur in the Sun’s extensive interior and atmosphere, and the dynamic and violent eruptions that occur daily in its outer layers.
Some of the basic characteristics of the Sun are listed in Table 15.1. Although some of the terms in that table may be unfamiliar to you right now, you will get to know them as you read further.
| Characteristic | How Found | Value |
|---|---|---|
| Mean distance | Radar reflection from planets | 1 AU (149,597,892 km) |
| Maximum distance from Earth | 1.521 × 10 8 km | |
| Minimum distance from Earth | 1.471 × 10 8 km | |
| Mass | Orbit of Earth | 333,400 Earth masses (1.99 × 10 30 kg) |
| Mean angular diameter | Direct measure | 31´59´´.3 |
| Diameter of photosphere | Angular size and distance | 109.3 × Earth diameter (1.39 × 10 6 km) |
| Mean density | Mass/volume |
1.41 g/cm
3
(1400 kg/m 3 ) |
| Gravitational acceleration at photosphere (surface gravity) | GM/R 2 | 27.9 × Earth surface gravity = 273 m/s 2 |
| Solar constant | Instrument sensitive to radiation at all wavelengths | 1370 W/m 2 |
| Luminosity | Solar constant × area of spherical surface 1 AU in radius | 3.8 × 10 26 W |
| Spectral class | Spectrum | G2V |
| Effective temperature | Derived from luminosity and radius of the Sun | 5800 K |
| Rotation period at equator | Sunspots and Doppler shift in spectra taken at the edge of the Sun | 24 days 16 hours |
| Inclination of equator to ecliptic | Motions of sunspots | 7°10´.5 |
Composition of the Sun’s Atmosphere
Let’s begin by asking what the solar atmosphere is made of. As explained in Radiation and Spectra, we can use a star’s absorption line spectrum to determine what elements are present. It turns out that the Sun contains the same elements as Earth but not in the same proportions. About 73% of the Sun’s mass is hydrogen, and another 25% is helium. All the other chemical elements (including those we know and love in our own bodies, such as carbon, oxygen, and nitrogen) make up only 2% of our star. The 10 most abundant gases in the Sun’s visible surface layer are listed in Table 15.2. Examine that table and notice that the composition of the Sun’s outer layer is very different from Earth’s crust, where we live. (In our planet’s crust, the three most abundant elements are oxygen, silicon, and aluminum.) Although not like our planet’s, the makeup of the Sun is quite typical of stars in general.
| Element | Percentage by Number of Atoms | Percentage By Mass |
|---|---|---|
| Hydrogen | 92.0 | 73.4 |
| Helium | 7.8 | 25.0 |
| Carbon | 0.02 | 0.20 |
| Nitrogen | 0.008 | 0.09 |
| Oxygen | 0.06 | 0.80 |
| Neon | 0.01 | 0.16 |
| Magnesium | 0.003 | 0.06 |
| Silicon | 0.004 | 0.09 |
| Sulfur | 0.002 | 0.05 |
| Iron | 0.003 | 0.14 |
The fact that our Sun and the stars all have similar compositions and are made up of mostly hydrogen and helium was first shown in a brilliant thesis in 1925 by Cecilia Payne-Gaposchkin , the first woman to get a PhD in astronomy in the United States (Figure 15.3). However, the idea that the simplest light gases—hydrogen and helium—were the most abundant elements in stars was so unexpected and so shocking that she was persuaded her analysis of the data must be wrong. At the time, she wrote, “The enormous abundance derived for these elements in the stellar atmosphere is almost certainly not real.” Even scientists sometimes find it hard to accept new ideas that do not agree with what everyone “knows” to be right.
Before Payne-Gaposchkin’s work, everyone assumed that the composition of the Sun and stars would be much like that of Earth. It was 3 years after her thesis that other studies proved beyond a doubt that the enormous abundance of hydrogen and helium in the Sun is indeed real. (And, as we will see, the composition of the Sun and the stars is much more typical of the makeup of the universe than the odd concentration of heavier elements that characterizes our planet.)
Most of the elements found in the Sun are in the form of atoms, with a small number of molecules, all in the form of gases: the Sun is so hot that no matter can survive as a liquid or a solid. In fact, the Sun is so hot that many of the atoms in it are ionized , that is, stripped of one or more of their electrons. This removal of electrons from their atoms means that there is a large quantity of free electrons and positively charged ions in the Sun, making it an electrically charged environment—quite different from the neutral one in which you are reading this text.
In the nineteenth century, scientists observed a spectral line at 530.3 nanometers in the Sun’s outer atmosphere, called the corona (a layer we will discuss in a minute.) This line had never been seen before, and so it was assumed that this line was the result of a new element found in the corona, quickly named coronium. It was not until 60 years later that astronomers discovered that this emission was in fact due to highly ionized iron—iron with 13 of its electrons stripped off. This is how we first discovered that the Sun’s atmosphere had a temperature of more than a million degrees.
The Layers of the Sun beneath the Visible Surface
Figure 15.4 shows what the Sun would look like if we could see all parts of it from the center to its outer atmosphere; the terms in the figure will become familiar to you as you read on.
The Sun’s layers are different from each other, and each plays a part in producing the energy that the Sun ultimately emits. We will begin with the core and work our way out through the layers. The Sun’s core is extremely dense and is the source of all of its energy. Inside the core, nuclear energy is being released (in ways we will discuss in The Sun: A Nuclear Powerhouse). The core is approximately 20% of the size of the solar interior and is thought to have a temperature of approximately 15 million K, making it the hottest part of the Sun.
Above the core is a region known as the radiative zone —named for the primary mode of transporting energy across it. This region starts at about 25% of the distance to the solar surface and extends up to about 70% of the way to the surface. The light generated in the core is transported through the radiative zone very slowly, since the high density of matter in this region means a photon cannot travel too far without encountering a particle, causing it to change direction and lose some energy.
The convective zone is the outermost layer of the solar interior. It is a thick layer approximately 200,000 kilometers deep that transports energy from the edge of the radiative zone to the surface through giant convection cells, similar to a pot of boiling oatmeal. The plasma at the bottom of the convective zone is extremely hot, and it bubbles to the surface where it loses its heat to space. Once the plasma cools, it sinks back to the bottom of the convective zone.
Now that we have given a quick overview of the structure of the whole Sun, in this section, we will embark on a journey through the visible layers of the Sun, beginning with the photosphere—the visible surface.
The Solar Photosphere
Earth’s air is generally transparent. But on a smoggy day in many cities, it can become opaque, which prevents us from seeing through it past a certain point. Something similar happens in the Sun. Its outer atmosphere is transparent, allowing us to look a short distance through it. But when we try to look through the atmosphere deeper into the Sun, our view is blocked. The photosphere is the layer where the Sun becomes opaque and marks the boundary past which we cannot see (Figure 15.5).
As we saw, the energy that emerges from the photosphere was originally generated deep inside the Sun (more on this in The Sun: A Nuclear Powerhouse). This energy is in the form of photons, which make their way slowly toward the solar surface. Outside the Sun, we can observe only those photons that are emitted into the solar photosphere, where the density of atoms is sufficiently low and the photons can finally escape from the Sun without colliding with another atom or ion.
As an analogy, imagine that you are attending a big campus rally and have found a prime spot near the center of the action. Your friend arrives late and calls you on your cell phone to ask you to join her at the edge of the crowd. You decide that friendship is worth more than a prime spot, and so you work your way out through the dense crowd to meet her. You can move only a short distance before bumping into someone, changing direction, and trying again, making your way slowly to the outside edge of the crowd. All this while, your efforts are not visible to your waiting friend at the edge. Your friend can’t see you until you get very close to the edge because of all the bodies in the way. So too photons making their way through the Sun are constantly bumping into atoms, changing direction, working their way slowly outward, and becoming visible only when they reach the atmosphere of the Sun where the density of atoms is too low to block their outward progress.
Astronomers have found that the solar atmosphere changes from almost perfectly transparent to almost completely opaque in a distance of just over 400 kilometers; it is this thin region that we call the photosphere , a word that comes from the Greek for “light sphere.” When astronomers speak of the “diameter” of the Sun, they mean the size of the region surrounded by the photosphere.
The photosphere looks sharp only from a distance. If you were falling into the Sun, you would not feel any surface but would just sense a gradual increase in the density of the gas surrounding you. It is much the same as falling through a cloud while skydiving. From far away, the cloud looks as if it has a sharp surface, but you do not feel a surface as you fall into it. (One big difference between these two scenarios, however, is temperature. The Sun is so hot that you would be vaporized long before you reached the photosphere. Skydiving in Earth’s atmosphere is much safer.)
We might note that the atmosphere of the Sun is not a very dense layer compared to the air in the room where you are reading this text. At a typical point in the photosphere, the pressure is less than 10% of Earth’s pressure at sea level, and the density is about one ten-thousandth of Earth’s atmospheric density at sea level.
Observations with telescopes show that the photosphere has a mottled appearance, resembling grains of rice spilled on a dark tablecloth or a pot of boiling oatmeal. This structure of the photosphere is called granulation (see Figure 15.6). Granules, which are typically 700 to 1000 kilometers in diameter (about the width of Texas), appear as bright areas surrounded by narrow, darker (cooler) regions. The lifetime of an individual granule is only 5 to 10 minutes. Even larger are supergranules, which are about 35,000 kilometers across (about the size of two Earths) and last about 24 hours.
The motions of the granules can be studied by examining the Doppler shifts in the spectra of gases just above them (see The Doppler Effect). The bright granules are columns of hotter gases rising at speeds of 2 to 3 kilometers per second from below the photosphere. As this rising gas reaches the photosphere, it spreads out, cools, and sinks down again into the darker regions between the granules. Measurements show that the centers of the granules are hotter than the intergranular regions by 50 to 100 K.
See the “boiling” action of granulation in this 30-second time-lapse video from the Swedish Institute for Solar Physics.
The Chromosphere
The Sun’s outer gases extend far beyond the photosphere (Figure 15.7). Because they are transparent to most visible radiation and emit only a small amount of light, these outer layers are difficult to observe. The region of the Sun’s atmosphere that lies immediately above the photosphere is called the chromosphere . Until this century, the chromosphere was visible only when the photosphere was concealed by the Moon during a total solar eclipse (see the chapter on Earth, Moon, and Sky). In the seventeenth century, several observers described what appeared to them as a narrow red “streak” or “fringe” around the edge of the Moon during a brief instant after the Sun’s photosphere had been covered. The name chromosphere , from the Greek for “colored sphere,” was given to this red streak.
Observations made during eclipses show that the chromosphere is about 2000 to 3000 kilometers thick, and its spectrum consists of bright emission lines, indicating that this layer is composed of hot gases emitting light at discrete wavelengths. The reddish color of the chromosphere arises from one of the strongest emission lines in the visible part of its spectrum—the bright red line caused by hydrogen, the element that, as we have already seen, dominates the composition of the Sun.
In 1868, observations of the chromospheric spectrum revealed a yellow emission line that did not correspond to any previously known element on Earth. Scientists quickly realized they had found a new element and named it helium (after helios , the Greek word for “Sun”). It took until 1895 for helium to be discovered on our planet. Today, students are probably most familiar with it as the light gas used to inflate balloons, although it turns out to be the second-most abundant element in the universe.
The temperature of the chromosphere is about 10,000 K. This means that the chromosphere is hotter than the photosphere, which should seem surprising. In all the situations we are familiar with, temperatures fall as one moves away from the source of heat, and the chromosphere is farther from the center of the Sun than the photosphere is.
The Transition Region
The increase in temperature does not stop with the chromosphere. Above it is a region in the solar atmosphere where the temperature changes from 10,000 K (typical of the chromosphere) to nearly a million degrees. The hottest part of the solar atmosphere, which has a temperature of a million degrees or more, is called the corona . Appropriately, the part of the Sun where the rapid temperature rise occurs is called the transition region . It is probably only a few tens of kilometers thick. Figure 15.8 summarizes how the temperature of the solar atmosphere changes from the photosphere outward.
In 2013, NASA launched the Interface Region Imaging Spectrograph (IRIS) to study the transition region to understand better how and why this sharp temperature increase occurs. IRIS is the first space mission that is able to obtain high spatial resolution images of the different features produced over this wide temperature range and to see how they change with time and location (Figure 15.9).
Figure 15.4 and the red graph in Figure 15.8 make the Sun seem rather like an onion, with smooth spherical shells, each one with a different temperature. For a long time, astronomers did indeed think of the Sun this way. However, we now know that while this idea of layers—photosphere, chromosphere, transition region, corona—describes the big picture fairly well, the Sun’s atmosphere is really more complicated, with hot and cool regions intermixed. For example, clouds of carbon monoxide gas with temperatures colder than 4000 K have now been found at the same height above the photosphere as the much hotter gas of the chromosphere.
The Corona
The outermost part of the Sun’s atmosphere is called the corona . Like the chromosphere, the corona was first observed during total eclipses (Figure 15.10). Unlike the chromosphere, the corona has been known for many centuries: it was referred to by the Roman historian Plutarch and was discussed in some detail by Kepler.
The corona extends millions of kilometers above the photosphere and emits about half as much light as the full moon. The reason we don’t see this light until an eclipse occurs is the overpowering brilliance of the photosphere. Just as bright city lights make it difficult to see faint starlight, so too does the intense light from the photosphere hide the faint light from the corona. While the best time to see the corona from Earth is during a total solar eclipse, it can be observed easily from orbiting spacecraft. Its brighter parts can now be photographed with a special instrument—a coronagraph—that removes the Sun’s glare from the image with an occulting disk (a circular piece of material held so it is just in front of the Sun).
Studies of its spectrum show the corona to be very low in density. At the bottom of the corona, there are only about 10 9 atoms per cubic centimeter, compared with about 10 16 atoms per cubic centimeter in the upper photosphere and 10 19 molecules per cubic centimeter at sea level in Earth’s atmosphere. The corona thins out very rapidly at greater heights, where it corresponds to a high vacuum by Earth laboratory standards. The corona extends so far into space—far past Earth—that here on our planet, we are technically living in the Sun’s atmosphere.
The Solar Wind
One of the most remarkable discoveries about the Sun’s atmosphere is that it produces a stream of charged particles (mainly protons and electrons) that we call the solar wind . These particles flow outward from the Sun into the solar system at a speed of about 400 kilometers per second (almost 1 million miles per hour)! The solar wind exists because the gases in the corona are so hot and moving so rapidly that they cannot be held back by solar gravity. (This wind was actually discovered by its effects on the charged tails of comets; in a sense, we can see the comet tails blow in the solar breeze the way wind socks at an airport or curtains in an open window flutter on Earth.)
Although the solar wind material is very, very rarified (i.e., extremely low density), the Sun has an enormous surface area. Astronomers estimate that the Sun is losing about 1–2 million tons of material each second through this wind. Although this sounds like a lot, it’s so trivial compared to the enormous mass of the Sun that it can be neglected as we study the Sun.
From where in the Sun does the solar wind emerge? In visible photographs, the solar corona appears fairly uniform and smooth. X-ray and extreme ultraviolet pictures, however, show that the corona has loops, plumes, and both bright and dark regions. Large dark regions of the corona that are relatively cool and quiet are called coronal holes (Figure 15.11). In these regions, magnetic field lines stretch far out into space away from the Sun, rather than looping back to the surface. The solar wind comes predominantly from coronal holes, where gas can stream away from the Sun into space unhindered by magnetic fields. Hot coronal gas, on the other hand, is present mainly where magnetic fields have trapped and concentrated it.
At the surface of Earth, we are protected to some degree from the solar wind by our atmosphere and Earth’s magnetic field (see Earth as a Planet). However, the magnetic field lines come into Earth at the north and south magnetic poles. Here, charged particles accelerated by the solar wind can follow the field down into our atmosphere. As the particles strike molecules of air, they cause them to glow, producing beautiful curtains of light called the auroras , or the northern and southern lights (Figure 15.12).
This NASA video explains and demonstrates the nature of the auroras and their relationship to Earth’s magnetic field.


3.4: Introduction to External Communication
What you’ll learn to do: Discuss appropriate ways to communicate to an audience outside of the company
What are the various types of emails sent outside of company networks? How should employees respond to customer email messages? How should companies handle messages that are critical of the organization? What is the best way to respond to a specific customer request? How would an email sent to a business partner differ from one sent to a customer?
Contributors and Attributions
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- Authored by : Robert Danielson. Provided by : Lumen Learning. License : CC BY: Attribution
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- social media digitization digital. Authored by : Geralt. Provided by : Pixabay. Located at : pixabay.com/en/social-media-digitization-digital-2786261/. License : CC0: No Rights Reserved