sumukshashidhar-archive/eduaction_experiments_book

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College Physics for AP® Courses 2e	Heat and Heat Transfer Methods	Convection	m42229
College Physics for AP® Courses 2e	Heat and Heat Transfer Methods	Radiation	m42230
College Physics for AP® Courses 2e	Thermodynamics	Connection for AP® Courses	m55254
College Physics for AP® Courses 2e	Thermodynamics	The First Law of Thermodynamics	m42232	Heat Q and Work W	Heat transfer ($Q$) and doing work ($W$) are the two everyday means of bringing energy into or taking energy out of a system. The processes are quite different. Heat transfer, a less organized process, is driven by temperature differences. Work, a quite organized process, involves a macroscopic force exerted through a distance. Nevertheless, heat and work can produce identical results.For example, both can cause a temperature increase. Heat transfer into a system, such as when the Sun warms the air in a bicycle tire, can increase its temperature, and so can work done on the system, as when the bicyclist pumps air into the tire. Once the temperature increase has occurred, it is impossible to tell whether it was caused by heat transfer or by doing work. This uncertainty is an important point. Heat transfer and work are both energy in transit—neither is stored as such in a system. However, both can change the internal energy ${E}_{\text{int}}$ of a system. Internal energy is a form of energy completely different from either heat or work.
College Physics for AP® Courses 2e	Thermodynamics	The First Law of Thermodynamics	m42232	Internal Energy Eint	We can think about the internal energy of a system in two different but consistent ways. The first is the atomic and molecular view, which examines the system on the atomic and molecular scale. The internal energy ${E}_{\text{int}}$ of a system is the sum of the kinetic and potential energies of its atoms and molecules. Recall that kinetic plus potential energy is called mechanical energy. Thus internal energy is the sum of atomic and molecular mechanical energy. Because it is impossible to keep track of all individual atoms and molecules, we must deal with averages and distributions. A second way to view the internal energy of a system is in terms of its macroscopic characteristics, which are very similar to atomic and molecular average values.
College Physics for AP® Courses 2e	Thermodynamics	The First Law of Thermodynamics and Some Simple Processes	m42233	PV Diagrams and their Relationship to Work Done on or by a Gas	A process by which a gas does work on a piston at constant pressure is called an isobaric process. Since the pressure is constant, the force exerted is constant and the work done is given as
College Physics for AP® Courses 2e	Thermodynamics	The First Law of Thermodynamics and Some Simple Processes	m42233	Reversible Processes	Both isothermal and adiabatic processes such as shown in [link] are reversible in principle. A reversible process is one in which both the system and its environment can return to exactly the states they were in by following the reverse path. The reverse isothermal and adiabatic paths are BA and CA, respectively. Real macroscopic processes are never exactly reversible. In the previous examples, our system is a gas (like that in [link]), and its environment is the piston, cylinder, and the rest of the universe. If there are any energy-dissipating mechanisms, such as friction or turbulence, then heat transfer to the environment occurs for either direction of the piston. So, for example, if the path BA is followed and there is friction, then the gas will be returned to its original state but the environment will not—it will have been heated in both directions. Reversibility requires the direction of heat transfer to reverse for the reverse path. Since dissipative mechanisms cannot be completely eliminated, real processes cannot be reversible.
College Physics for AP® Courses 2e	Thermodynamics	Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency	m42234	Heat Engines	Now let us consider a device that uses heat transfer to do work. As noted in the previous section, such a device is called a heat engine, and one is shown schematically in [link](b). Gasoline and diesel engines, jet engines, and steam turbines are all heat engines that do work by using part of the heat transfer from some source. Heat transfer from the hot object (or hot reservoir) is denoted as ${Q}_{\text{h}}$, while heat transfer into the cold object (or cold reservoir) is ${Q}_{\text{c}}$, and the work done by the engine is $W$. The temperatures of the hot and cold reservoirs are ${T}_{\text{h}}$ and ${T}_{\text{c}}$, respectively.
College Physics for AP® Courses 2e	Thermodynamics	Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated	m42235
College Physics for AP® Courses 2e	Thermodynamics	Applications of Thermodynamics: Heat Pumps and Refrigerators	m42236	Heat Pumps	The great advantage of using a heat pump to keep your home warm, rather than just burning fuel, is that a heat pump supplies ${Q}_{\text{h}}={Q}_{\text{c}}+W$. Heat transfer is from the outside air, even at a temperature below freezing, to the indoor space. You only pay for $W$, and you get an additional heat transfer of ${Q}_{\text{c}}$ from the outside at no cost; in many cases, at least twice as much energy is transferred to the heated space as is used to run the heat pump. When you burn fuel to keep warm, you pay for all of it. The disadvantage is that the work input (required by the second law of thermodynamics) is sometimes more expensive than simply burning fuel, especially if the work is done by electrical energy.
College Physics for AP® Courses 2e	Thermodynamics	Applications of Thermodynamics: Heat Pumps and Refrigerators	m42236	Air Conditioners and Refrigerators	Air conditioners and refrigerators are designed to cool something down in a warm environment. As with heat pumps, work input is required for heat transfer from cold to hot, and this is expensive. The quality of air conditioners and refrigerators is judged by how much heat transfer ${Q}_{\text{c}}$ occurs from a cold environment compared with how much work input $W$ is required. What is considered the benefit in a heat pump is considered waste heat in a refrigerator. We thus define the coefficient of performance ${\text{(COP}}_{\text{ref}}\text{)}$ of an air conditioner or refrigerator to be
College Physics for AP® Courses 2e	Thermodynamics	Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy	m42237	Entropy and the Unavailability of Energy to Do Work	What does a change in entropy mean, and why should we be interested in it? One reason is that entropy is directly related to the fact that not all heat transfer can be converted into work. The next example gives some indication of how an increase in entropy results in less heat transfer into work.
College Physics for AP® Courses 2e	Thermodynamics	Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy	m42237	Heat Death of the Universe: An Overdose of Entropy	In the early, energetic universe, all matter and energy were easily interchangeable and identical in nature. Gravity played a vital role in the young universe. Although it may have seemed disorderly, and therefore, superficially entropic, in fact, there was enormous potential energy available to do work—all the future energy in the universe.
College Physics for AP® Courses 2e	Thermodynamics	Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy	m42237	Order to Disorder	Entropy is related not only to the unavailability of energy to do work—it is also a measure of disorder. This notion was initially postulated by Ludwig Boltzmann in the 1800s. For example, melting a block of ice means taking a highly structured and orderly system of water molecules and converting it into a disorderly liquid in which molecules have no fixed positions. (See [link].) There is a large increase in entropy in the process, as seen in the following example.
College Physics for AP® Courses 2e	Thermodynamics	Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy	m42237	Life, Evolution, and the Second Law of Thermodynamics	Some people misunderstand the second law of thermodynamics, stated in terms of entropy, to say that the process of the evolution of life violates this law. Over time, complex organisms evolved from much simpler ancestors, representing a large decrease in entropy of the Earth’s biosphere. It is a fact that living organisms have evolved to be highly structured, and much lower in entropy than the substances from which they grow. But it is always possible for the entropy of one part of the universe to decrease, provided the total change in entropy of the universe increases. In equation form, we can write this as
College Physics for AP® Courses 2e	Thermodynamics	Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation	m42238	Coin Tosses	What are the possible outcomes of tossing 5 coins? Each coin can land either heads or tails. On the large scale, we are concerned only with the total heads and tails and not with the order in which heads and tails appear. The following possibilities exist:
College Physics for AP® Courses 2e	Thermodynamics	Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation	m42238	Disorder in a Gas	The fantastic growth in the odds favoring disorder that we see in going from 5 to 100 coins continues as the number of entities in the system increases. Let us now imagine applying this approach to perhaps a small sample of gas. Because counting microstates and macrostates involves statistics, this is called statistical analysis. The macrostates of a gas correspond to its macroscopic properties, such as volume, temperature, and pressure; and its microstates correspond to the detailed description of the positions and velocities of its atoms. Even a small amount of gas has a huge number of atoms: of an ideal gas at 1.0 atm and $0º C$ has $2\text{.}7×{\text{10}}^{\text{19}}$ atoms. So each macrostate has an immense number of microstates. In plain language, this means that there are an immense number of ways in which the atoms in a gas can be arranged, while still having the same pressure, temperature, and so on.
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Connection for AP® Courses	m55270
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Hooke’s Law: Stress and Strain Revisited	m42240	Energy in Hooke’s Law of Deformation	In order to produce a deformation, work must be done. That is, a force must be exerted through a distance, whether you pluck a guitar string or compress a car spring. If the only result is deformation, and no work goes into thermal, sound, or kinetic energy, then all the work is initially stored in the deformed object as some form of potential energy. The potential energy stored in a spring is ${\text{PE}}_{\text{el}}=\frac{1}{2}{\mathrm{kx}}^{2}$. Here, we generalize the idea to elastic potential energy for a deformation of any system that can be described by Hooke’s law. Hence,
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Period and Frequency in Oscillations	m42241
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Simple Harmonic Motion: A Special Periodic Motion	m42242	The Link between Simple Harmonic Motion and Waves	If a time-exposure photograph of the bouncing car were taken as it drove by, the headlight would make a wavelike streak, as shown in [link]. Similarly, [link] shows an object bouncing on a spring as it leaves a wavelike "trace" of its position on a moving strip of paper. Both waves are sine functions. All simple harmonic motion is intimately related to sine and cosine waves.
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	The Simple Pendulum	m42243
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Energy and the Simple Harmonic Oscillator	m42244
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Uniform Circular Motion and Simple Harmonic Motion	m42245
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Damped Harmonic Motion	m42246
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Forced Oscillations and Resonance	m42247
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Waves	m42248	Transverse and Longitudinal Waves	A simple wave consists of a periodic disturbance that propagates from one place to another. The wave in [link] propagates in the horizontal direction while the surface is disturbed in the vertical direction. Such a wave is called a transverse wave or shear wave; in such a wave, the disturbance is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation. [link] shows an example of a longitudinal wave. The size of the disturbance is its amplitude X and is completely independent of the speed of propagation ${v}_{\text{w}}$.
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Superposition and Interference	m42249	Standing Waves	Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk in a refrigerator, for example. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed by the superposition of two or more moving waves, such as illustrated in [link] for two identical waves moving in opposite directions. The waves move through each other with their disturbances adding as they go by. If the two waves have the same amplitude and wavelength, then they alternate between constructive and destructive interference. The resultant looks like a wave standing in place and, thus, is called a standing wave. Waves on the glass of milk are one example of standing waves. There are other standing waves, such as on guitar strings and in organ pipes. With the glass of milk, the two waves that produce standing waves may come from reflections from the side of the glass.
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Superposition and Interference	m42249	Beats	Striking two adjacent keys on a piano produces a warbling combination usually considered to be unpleasant. The superposition of two waves of similar but not identical frequencies is the culprit. Another example is often noticeable in jet aircraft, particularly the two-engine variety, while taxiing. The combined sound of the engines goes up and down in loudness. This varying loudness happens because the sound waves have similar but not identical frequencies. The discordant warbling of the piano and the fluctuating loudness of the jet engine noise are both due to alternately constructive and destructive interference as the two waves go in and out of phase. [link] illustrates this graphically.
College Physics for AP® Courses 2e	Oscillatory Motion and Waves	Energy in Waves: Intensity	m42250
College Physics for AP® Courses 2e	Physics of Hearing	Connection for AP® Courses	m55286
College Physics for AP® Courses 2e	Physics of Hearing	Sound	m42255
College Physics for AP® Courses 2e	Physics of Hearing	Speed of Sound, Frequency, and Wavelength	m42256
College Physics for AP® Courses 2e	Physics of Hearing	Sound Intensity and Sound Level	m42257
College Physics for AP® Courses 2e	Physics of Hearing	Doppler Effect and Sonic Booms	m42712	Sonic Booms to Bow Wakes	What happens to the sound produced by a moving source, such as a jet airplane, that approaches or even exceeds the speed of sound? The answer to this question applies not only to sound but to all other waves as well.
College Physics for AP® Courses 2e	Physics of Hearing	Sound Interference and Resonance: Standing Waves in Air Columns	m42296
College Physics for AP® Courses 2e	Physics of Hearing	Hearing	m42297
College Physics for AP® Courses 2e	Physics of Hearing	Ultrasound	m42298	Ultrasound in Medical Therapy	Ultrasound, like any wave, carries energy that can be absorbed by the medium carrying it, producing effects that vary with intensity. When focused to intensities of ${\text{10}}^{\text{3}}$ to ${\text{10}}^{\text{5}}$ ${\text{W/m}}^{\text{2}}$, ultrasound can be used to shatter gallstones or pulverize cancerous tissue in surgical procedures. (See [link].) Intensities this great can damage individual cells, variously causing their protoplasm to stream inside them, altering their permeability, or rupturing their walls through cavitation. Cavitation is the creation of vapor cavities in a fluid—the longitudinal vibrations in ultrasound alternatively compress and expand the medium, and at sufficient amplitudes the expansion separates molecules. Most cavitation damage is done when the cavities collapse, producing even greater shock pressures.
College Physics for AP® Courses 2e	Physics of Hearing	Ultrasound	m42298	Ultrasound in Medical Diagnostics	When used for imaging, ultrasonic waves are emitted from a transducer, a crystal exhibiting the piezoelectric effect (the expansion and contraction of a substance when a voltage is applied across it, causing a vibration of the crystal). These high-frequency vibrations are transmitted into any tissue in contact with the transducer. Similarly, if a pressure is applied to the crystal (in the form of a wave reflected off tissue layers), a voltage is produced which can be recorded. The crystal therefore acts as both a transmitter and a receiver of sound. Ultrasound is also partially absorbed by tissue on its path, both on its journey away from the transducer and on its return journey. From the time between when the original signal is sent and when the reflections from various boundaries between media are received, (as well as a measure of the intensity loss of the signal), the nature and position of each boundary between tissues and organs may be deduced.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Connection for AP® Courses	m55297
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Static Electricity and Charge: Conservation of Charge	m42300	Charge Carried by Electrons and Protons	Franklin wrote in his letters and books that he could see the effects of electric charge but did not understand what caused the phenomenon. Today we have the advantage of knowing that normal matter is made of atoms, and that atoms contain positive and negative charges, usually in equal amounts.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Static Electricity and Charge: Conservation of Charge	m42300	Separation of Charge in Atoms	Charges in atoms and molecules can be separated—for example, by rubbing materials together. Some atoms and molecules have a greater affinity for electrons than others and will become negatively charged by close contact in rubbing, leaving the other material positively charged. (See [link].) Positive charge can similarly be induced by rubbing. Methods other than rubbing can also separate charges. Batteries, for example, use combinations of substances that interact in such a way as to separate charges. Chemical interactions may transfer negative charge from one substance to the other, making one battery terminal negative and leaving the first one positive.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Conductors and Insulators	m42306	Charging by Contact	[link] shows an electroscope being charged by touching it with a positively charged glass rod. Because the glass rod is an insulator, it must actually touch the electroscope to transfer charge to or from it. (Note that the extra positive charges reside on the surface of the glass rod as a result of rubbing it with silk before starting the experiment.) Since only electrons move in metals, we see that they are attracted to the top of the electroscope. There, some are transferred to the positive rod by touch, leaving the electroscope with a net positive charge.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Conductors and Insulators	m42306	Charging by Induction	It is not necessary to transfer excess charge directly to an object in order to charge it. [link] shows a method of induction wherein a charge is created in a nearby object, without direct contact. Here we see two neutral metal spheres in contact with one another but insulated from the rest of the world. A positively charged rod is brought near one of them, attracting negative charge to that side, leaving the other sphere positively charged.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Conductors and Electric Fields in Static Equilibrium	m42317	Earth’s Electric Field	A near uniform electric field of approximately 150 N/C, directed downward, surrounds Earth, with the magnitude increasing slightly as we get closer to the surface. What causes the electric field? At around 100 km above the surface of Earth we have a layer of charged particles, called the ionosphere. The ionosphere is responsible for a range of phenomena including the electric field surrounding Earth. In fair weather the ionosphere is positive and the Earth largely negative, maintaining the electric field ([link](a)).
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Conductors and Electric Fields in Static Equilibrium	m42317	Electric Fields on Uneven Surfaces	So far we have considered excess charges on a smooth, symmetrical conductor surface. What happens if a conductor has sharp corners or is pointed? Excess charges on a nonuniform conductor become concentrated at the sharpest points. Additionally, excess charge may move on or off the conductor at the sharpest points.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Conductors and Electric Fields in Static Equilibrium	m42317	Applications of Conductors	On a very sharply curved surface, such as shown in [link], the charges are so concentrated at the point that the resulting electric field can be great enough to remove them from the surface. This can be useful.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Coulomb’s Law	m42308
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Electric Field: Concept of a Field Revisited	m42310	Concept of a Field	A field is a way of conceptualizing and mapping the force that surrounds any object and acts on another object at a distance without apparent physical connection. For example, the gravitational field surrounding the earth (and all other masses) represents the gravitational force that would be experienced if another mass were placed at a given point within the field.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Electric Field Lines: Multiple Charges	m42312
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Electric Forces in Biology	m42315	Polarity of Water Molecules	The best example of this charge screening is the water molecule, represented as ${\text{H}}_{2}\text{O}$. Water is a strongly polar molecule. Its 10 electrons (8 from the oxygen atom and 2 from the two hydrogen atoms) tend to remain closer to the oxygen nucleus than the hydrogen nuclei. This creates two centers of equal and opposite charges—what is called a dipole, as illustrated in [link]. The magnitude of the dipole is called the dipole moment.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Applications of Electrostatics	m42329	The Van de Graaff Generator	Van de Graaff generators (or Van de Graaffs) are not only spectacular devices used to demonstrate high voltage due to static electricity—they are also used for serious research. The first was built by Robert Van de Graaff in 1931 (based on original suggestions by Lord Kelvin) for use in nuclear physics research. [link] shows a schematic of a large research version. Van de Graaffs utilize both smooth and pointed surfaces, and conductors and insulators to generate large static charges and, hence, large voltages.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Applications of Electrostatics	m42329	Xerography	Most copy machines use an electrostatic process called xerography—a word coined from the Greek words xeros for dry and graphos for writing. The heart of the process is shown in simplified form in [link].
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Applications of Electrostatics	m42329	Laser Printers	Laser printers use the xerographic process to make high-quality images on paper, employing a laser to produce an image on the photoconducting drum as shown in [link]. In its most common application, the laser printer receives output from a computer, and it can achieve high-quality output because of the precision with which laser light can be controlled. Many laser printers do significant information processing, such as making sophisticated letters or fonts, and may contain a computer more powerful than the one giving them the raw data to be printed.
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Applications of Electrostatics	m42329	Ink Jet Printers and Electrostatic Painting	The ink jet printer, commonly used to print computer-generated text and graphics, also employs electrostatics. A nozzle makes a fine spray of tiny ink droplets, which are then given an electrostatic charge. (See [link].)
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Applications of Electrostatics	m42329	Smoke Precipitators and Electrostatic Air Cleaning	Another important application of electrostatics is found in air cleaners, both large and small. The electrostatic part of the process places excess (usually positive) charge on smoke, dust, pollen, and other particles in the air and then passes the air through an oppositely charged grid that attracts and retains the charged particles. (See [link].)
College Physics for AP® Courses 2e	Electric Charge and Electric Field	Applications of Electrostatics	m42329	Integrated Concepts	The Integrated Concepts exercises for this module involve concepts such as electric charges, electric fields, and several other topics. Physics is most interesting when applied to general situations involving more than a narrow set of physical principles. The electric field exerts force on charges, for example, and hence the relevance of Dynamics: Force and Newton’s Laws of Motion. The following topics are involved in some or all of the problems labeled “Integrated Concepts”: * Kinematics * Two-Dimensional Kinematics * Dynamics: Force and Newton’s Laws of Motion * Uniform Circular Motion and Gravitation * Statics and Torque * Fluid Statics
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Connection for AP® Courses	m55349
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Electric Potential Energy: Potential Difference	m42324	The Electron Volt	The energy per electron is very small in macroscopic situations like that in the previous example—a tiny fraction of a joule. But on a submicroscopic scale, such energy per particle (electron, proton, or ion) can be of great importance. For example, even a tiny fraction of a joule can be great enough for these particles to destroy organic molecules and harm living tissue. The particle may do its damage by direct collision, or it may create harmful x rays, which can also inflict damage. It is useful to have an energy unit related to submicroscopic effects. [link] shows a situation related to the definition of such an energy unit. An electron is accelerated between two charged metal plates as it might be in an old-model television tube or oscilloscope. The electron is given kinetic energy that is later converted to another form—light in the television tube, for example. (Note that downhill for the electron is uphill for a positive charge.) Since energy is related to voltage by $\text{ΔPE}=q\Delta V,$ we can think of the joule as a coulomb-volt.
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Electric Potential Energy: Potential Difference	m42324	Conservation of Energy	The total energy of a system is conserved if there is no net addition (or subtraction) of work or heat transfer. For conservative forces, such as the electrostatic force, conservation of energy states that mechanical energy is a constant.
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Electric Potential in a Uniform Electric Field	m42326
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Electrical Potential Due to a Point Charge	m42328
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Equipotential Lines	m42331
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Capacitors and Dielectrics	m42333	Parallel Plate Capacitor	The parallel plate capacitor shown in [link] has two identical conducting plates, each having a surface area $A$, separated by a distance $d$ (with no material between the plates). When a voltage $V$ is applied to the capacitor, it stores a charge $Q$, as shown. We can see how its capacitance depends on $A$ and $d$ by considering the characteristics of the Coulomb force. We know that like charges repel, unlike charges attract, and the force between charges decreases with distance. So it seems quite reasonable that the bigger the plates are, the more charge they can store—because the charges can spread out more. Thus $C$ should be greater for larger $A$. Similarly, the closer the plates are together, the greater the attraction of the opposite charges on them. So $C$ should be greater for smaller $d$.
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Capacitors and Dielectrics	m42333	Dielectric	The previous example highlights the difficulty of storing a large amount of charge in capacitors. If $d$ is made smaller to produce a larger capacitance, then the maximum voltage must be reduced proportionally to avoid breakdown (since $E=V/d$). An important solution to this difficulty is to put an insulating material, called a dielectric, between the plates of a capacitor and allow $d$ to be as small as possible. Not only does the smaller $d$ make the capacitance greater, but many insulators can withstand greater electric fields than air before breaking down.
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Capacitors in Series and Parallel	m42336	Capacitance in Series	[link](a) shows a series connection of three capacitors with a voltage applied. As for any capacitor, the capacitance of the combination is related to charge and voltage by $C=\frac{Q}{V}$.
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Capacitors in Series and Parallel	m42336	Capacitors in Parallel	[link](a) shows a parallel connection of three capacitors with a voltage applied. Here the total capacitance is easier to find than in the series case. To find the equivalent total capacitance ${C}_{\text{p}}$, we first note that the voltage across each capacitor is $V$, the same as that of the source, since they are connected directly to it through a conductor. (Conductors are equipotentials, and so the voltage across the capacitors is the same as that across the voltage source.) Thus the capacitors have the same charges on them as they would have if connected individually to the voltage source. The total charge $Q$ is the sum of the individual charges:
College Physics for AP® Courses 2e	Electric Potential and Electric Field	Energy Stored in Capacitors	m42395
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Connection for AP® Courses	m55354
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Current	m42341	Electric Current	Electric current is defined to be the rate at which charge flows. A large current, such as that used to start a truck engine, moves a large amount of charge in a small time, whereas a small current, such as that used to operate a hand-held calculator, moves a small amount of charge over a long period of time. In equation form, electric current $I$ is defined to be
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Current	m42341	Drift Velocity	Electrical signals are known to move very rapidly. Telephone conversations carried by currents in wires cover large distances without noticeable delays. Lights come on as soon as a switch is flicked. Most electrical signals carried by currents travel at speeds on the order of ${\text{10}}^{8}{\rule{0.25em}{0ex}}\text{m/s}$, a significant fraction of the speed of light. Interestingly, the individual charges that make up the current move much more slowly on average, typically drifting at speeds on the order of ${\text{10}}^{-4}{\rule{0.25em}{0ex}}\text{m/s}$. How do we reconcile these two speeds, and what does it tell us about standard conductors?
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Ohm’s Law: Resistance and Simple Circuits	m42344	Ohm’s Law	The current that flows through most substances is directly proportional to the voltage $V$ applied to it. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied:
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Ohm’s Law: Resistance and Simple Circuits	m42344	Resistance and Simple Circuits	If voltage drives current, what impedes it? The electric property that impedes current (crudely similar to friction and air resistance) is called resistance $R$. Collisions of moving charges with atoms and molecules in a substance transfer energy to the substance and limit current. Resistance is defined as inversely proportional to current, or
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Resistance and Resistivity	m42346	Material and Shape Dependence of Resistance	The resistance of an object depends on its shape and the material of which it is composed. The cylindrical resistor in [link] is easy to analyze, and, by so doing, we can gain insight into the resistance of more complicated shapes. As you might expect, the cylinder’s electric resistance $R$ is directly proportional to its length $L$, similar to the resistance of a pipe to fluid flow. The longer the cylinder, the more collisions charges will make with its atoms. The greater the diameter of the cylinder, the more current it can carry (again similar to the flow of fluid through a pipe). In fact, $R$ is inversely proportional to the cylinder’s cross-sectional area $A$.
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Resistance and Resistivity	m42346	Temperature Variation of Resistance	The resistivity of all materials depends on temperature. Some even become superconductors (zero resistivity) at very low temperatures. (See [link].) Conversely, the resistivity of conductors increases with increasing temperature. Since the atoms vibrate more rapidly and over larger distances at higher temperatures, the electrons moving through a metal make more collisions, effectively making the resistivity higher. Over relatively small temperature changes (about $\text{100º}\text{C}$ or less), resistivity $\rho$ varies with temperature change $\Delta T$ as expressed in the following equation
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Electric Power and Energy	m42714	Power in Electric Circuits	Power is associated by many people with electricity. Knowing that power is the rate of energy use or energy conversion, what is the expression for electric power? Power transmission lines might come to mind. We also think of lightbulbs in terms of their power ratings in watts. Let us compare a 25-W bulb with a 60-W bulb. (See [link](a).) Since both operate on the same voltage, the 60-W bulb must draw more current to have a greater power rating. Thus the 60-W bulb’s resistance must be lower than that of a 25-W bulb. If we increase voltage, we also increase power. For example, when a 25-W bulb that is designed to operate on 120 V is connected to 240 V, it briefly glows very brightly and then burns out. Precisely how are voltage, current, and resistance related to electric power?
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Electric Power and Energy	m42714	The Cost of Electricity	The more electric appliances you use and the longer they are left on, the higher your electric bill. This familiar fact is based on the relationship between energy and power. You pay for the energy used. Since $P=E/t$, we see that
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Alternating Current versus Direct Current	m42348	Alternating Current	Most of the examples dealt with so far, and particularly those utilizing batteries, have constant voltage sources. Once the current is established, it is thus also a constant. Direct current (DC) is the flow of electric charge in only one direction. It is the steady state of a constant-voltage circuit. Most well-known applications, however, use a time-varying voltage source. Alternating current (AC) is the flow of electric charge that periodically reverses direction. If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating current circuit. Examples include the commercial and residential power that serves so many of our needs. [link] shows graphs of voltage and current versus time for typical DC and AC power. The AC voltages and frequencies commonly used in homes and businesses vary around the world.
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Alternating Current versus Direct Current	m42348	Why Use AC for Power Distribution?	Most large power-distribution systems are AC. Moreover, the power is transmitted at much higher voltages than the 120-V AC (240 V in most parts of the world) we use in homes and on the job. Economies of scale make it cheaper to build a few very large electric power-generation plants than to build numerous small ones. This necessitates sending power long distances, and it is obviously important that energy losses en route be minimized. High voltages can be transmitted with much smaller power losses than low voltages, as we shall see. (See [link].) For safety reasons, the voltage at the user is reduced to familiar values. The crucial factor is that it is much easier to increase and decrease AC voltages than DC, so AC is used in most large power distribution systems.
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Electric Hazards and the Human Body	m42350	Thermal Hazards	Electric power causes undesired heating effects whenever electric energy is converted to thermal energy at a rate faster than it can be safely dissipated. A classic example of this is the short circuit, a low-resistance path between terminals of a voltage source. An example of a short circuit is shown in [link]. Insulation on wires leading to an appliance has worn through, allowing the two wires to come into contact. Such an undesired contact with a high voltage is called a short. Since the resistance of the short, $r$, is very small, the power dissipated in the short, $P={V}^{2}/r$, is very large. For example, if $V$ is 120 V and $r$ is $0\text{.}\text{100}{\rule{0.25em}{0ex}}\Omega$, then the power is 144 kW, much greater than that used by a typical household appliance. Thermal energy delivered at this rate will very quickly raise the temperature of surrounding materials, melting or perhaps igniting them.
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Electric Hazards and the Human Body	m42350	Shock Hazards	Electrical currents through people produce tremendously varied effects. An electrical current can be used to block back pain. The possibility of using electrical current to stimulate muscle action in paralyzed limbs, perhaps allowing paraplegics to walk, is under study. TV dramatizations in which electrical shocks are used to bring a heart attack victim out of ventricular fibrillation (a massively irregular, often fatal, beating of the heart) are more than common. Yet most electrical shock fatalities occur because a current put the heart into fibrillation. A pacemaker uses electrical shocks to stimulate the heart to beat properly. Some fatal shocks do not produce burns, but warts can be safely burned off with electric current (though freezing using liquid nitrogen is now more common). Of course, there are consistent explanations for these disparate effects. The major factors upon which the effects of electrical shock depend are
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Nerve Conduction–Electrocardiograms	m42352	Nerve Conduction	Electric currents in the vastly complex system of billions of nerves in our body allow us to sense the world, control parts of our body, and think. These are representative of the three major functions of nerves. First, nerves carry messages from our sensory organs and others to the central nervous system, consisting of the brain and spinal cord. Second, nerves carry messages from the central nervous system to muscles and other organs. Third, nerves transmit and process signals within the central nervous system. The sheer number of nerve cells and the incredibly greater number of connections between them makes this system the subtle wonder that it is. Nerve conduction is a general term for electrical signals carried by nerve cells. It is one aspect of bioelectricity, or electrical effects in and created by biological systems.
College Physics for AP® Courses 2e	Electric Current, Resistance, and Ohm's Law	Nerve Conduction–Electrocardiograms	m42352	Electrocardiograms	Just as nerve impulses are transmitted by depolarization and repolarization of adjacent membrane, the depolarization that causes muscle contraction can also stimulate adjacent muscle cells to depolarize (fire) and contract. Thus, a depolarization wave can be sent across the heart, coordinating its rhythmic contractions and enabling it to perform its vital function of propelling blood through the circulatory system. [link] is a simplified graphic of a depolarization wave spreading across the heart from the sinoarterial (SA) node, the heart’s natural pacemaker.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Connection for AP® Courses	m55364
College Physics for AP® Courses 2e	Circuits and DC Instruments	Resistors in Series and Parallel	m42356	Resistors in Series	When are resistors in series? Resistors are in series whenever the flow of charge, called the current, must flow through devices sequentially. For example, if current flows through a person holding a screwdriver and into the Earth, then ${R}_{1}$ in [link](a) could be the resistance of the screwdriver’s shaft, ${R}_{2}$ the resistance of its handle, ${R}_{3}$ the person’s body resistance, and ${R}_{4}$ the resistance of her shoes.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Resistors in Series and Parallel	m42356	Resistors in Parallel	[link] shows resistors in parallel, wired to a voltage source. Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires having negligible resistance. Each resistor thus has the full voltage of the source applied to it.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Resistors in Series and Parallel	m42356	Combinations of Series and Parallel	More complex connections of resistors are sometimes just combinations of series and parallel. These are commonly encountered, especially when wire resistance is considered. In that case, wire resistance is in series with other resistances that are in parallel.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Resistors in Series and Parallel	m42356	Practical Implications	One implication of this last example is that resistance in wires reduces the current and power delivered to a resistor. If wire resistance is relatively large, as in a worn (or a very long) extension cord, then this loss can be significant. If a large current is drawn, the $\text{IR}$ drop in the wires can also be significant.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Electromotive Force: Terminal Voltage	m42357	Electromotive Force	You can think of many different types of voltage sources. Batteries themselves come in many varieties. There are many types of mechanical/electrical generators, driven by many different energy sources, ranging from nuclear to wind. Solar cells create voltages directly from light, while thermoelectric devices create voltage from temperature differences.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Electromotive Force: Terminal Voltage	m42357	Internal Resistance	As noted before, a 12-V truck battery is physically larger, contains more charge and energy, and can deliver a larger current than a 12-V motorcycle battery. Both are lead-acid batteries with identical emf, but, because of its size, the truck battery has a smaller internal resistance $r$. Internal resistance is the inherent resistance to the flow of current within the source itself.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Electromotive Force: Terminal Voltage	m42357	Terminal Voltage	The voltage output of a device is measured across its terminals and, thus, is called its terminal voltage${\rule{0.25em}{0ex}}V$. Terminal voltage is given by
College Physics for AP® Courses 2e	Circuits and DC Instruments	Electromotive Force: Terminal Voltage	m42357	Multiple Voltage Sources	There are two voltage sources when a battery charger is used. Voltage sources connected in series are relatively simple. When voltage sources are in series, their internal resistances add and their emfs add algebraically. (See [link].) Series connections of voltage sources are common—for example, in flashlights, toys, and other appliances. Usually, the cells are in series in order to produce a larger total emf.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Electromotive Force: Terminal Voltage	m42357	Animals as Electrical Detectors	A number of animals both produce and detect electrical signals. Fish, sharks, platypuses, and echidnas (spiny anteaters) all detect electric fields generated by nerve activity in prey. Electric eels produce their own emf through biological cells (electric organs) called electroplaques, which are arranged in both series and parallel as a set of batteries.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Electromotive Force: Terminal Voltage	m42357	Solar Cell Arrays	Another example dealing with multiple voltage sources is that of combinations of solar cells—wired in both series and parallel combinations to yield a desired voltage and current. Photovoltaic generation (PV), the conversion of sunlight directly into electricity, is based upon the photoelectric effect, in which photons hitting the surface of a solar cell create an electric current in the cell.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Kirchhoff’s Rules	m42359	Kirchhoff’s First Rule	Kirchhoff’s first rule (the junction rule) is an application of the conservation of charge to a junction; it is illustrated in [link]. Current is the flow of charge, and charge is conserved; thus, whatever charge flows into the junction must flow out. Kirchhoff’s first rule requires that ${I}_{1}={I}_{2}+{I}_{3}$ (see figure). Equations like this can and will be used to analyze circuits and to solve circuit problems.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Kirchhoff’s Rules	m42359	Kirchhoff’s Second Rule	Kirchhoff’s second rule (the loop rule) is an application of conservation of energy. The loop rule is stated in terms of potential, $V$, rather than potential energy, but the two are related since ${\text{PE}}_{\text{elec}}=\text{qV}$. Recall that emf is the potential difference of a source when no current is flowing. In a closed loop, whatever energy is supplied by emf must be transferred into other forms by devices in the loop, since there are no other ways in which energy can be transferred into or out of the circuit. [link] illustrates the changes in potential in a simple series circuit loop.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Kirchhoff’s Rules	m42359	Applying Kirchhoff’s Rules	By applying Kirchhoff’s rules, we generate equations that allow us to find the unknowns in circuits. The unknowns may be currents, emfs, or resistances. Each time a rule is applied, an equation is produced. If there are as many independent equations as unknowns, then the problem can be solved. There are two decisions you must make when applying Kirchhoff’s rules. These decisions determine the signs of various quantities in the equations you obtain from applying the rules.
College Physics for AP® Courses 2e	Circuits and DC Instruments	DC Voltmeters and Ammeters	m42360	Analog Meters: Galvanometers	Analog meters have a needle that swivels to point at numbers on a scale, as opposed to digital meters, which have numerical readouts similar to a hand-held calculator. The heart of most analog meters is a device called a galvanometer, denoted by G. Current flow through a galvanometer, ${I}_{\text{G}}$, produces a proportional needle deflection. (This deflection is due to the force of a magnetic field upon a current-carrying wire.)
College Physics for AP® Courses 2e	Circuits and DC Instruments	DC Voltmeters and Ammeters	m42360	Taking Measurements Alters the Circuit	When you use a voltmeter or ammeter, you are connecting another resistor to an existing circuit and, thus, altering the circuit. Ideally, voltmeters and ammeters do not appreciably affect the circuit, but it is instructive to examine the circumstances under which they do or do not interfere.
College Physics for AP® Courses 2e	Circuits and DC Instruments	Null Measurements	m42362	The Potentiometer	Suppose you wish to measure the emf of a battery. Consider what happens if you connect the battery directly to a standard voltmeter as shown in [link]. (Once we note the problems with this measurement, we will examine a null measurement that improves accuracy.) As discussed before, the actual quantity measured is the terminal voltage $V$, which is related to the emf of the battery by $V=\text{emf}-\text{Ir}$, where $I$ is the current that flows and $r$ is the internal resistance of the battery.

College Physics for AP® Courses 2e

Heat and Heat Transfer Methods

Convection

m42229

College Physics for AP® Courses 2e

Heat and Heat Transfer Methods

Radiation

m42230

College Physics for AP® Courses 2e

Thermodynamics

Connection for AP® Courses

m55254

College Physics for AP® Courses 2e

Thermodynamics

The First Law of Thermodynamics

m42232

Heat *Q* and Work *W*

Heat transfer ($Q$) and doing work ($W$) are the two everyday means of bringing energy into or taking energy out of a system. The processes are quite different. Heat transfer, a less organized process, is driven by temperature differences. Work, a quite organized process, involves a macroscopic force exerted through a distance. Nevertheless, heat and work can produce identical results.For example, both can cause a temperature increase. Heat transfer into a system, such as when the Sun warms the air in a bicycle tire, can increase its temperature, and so can work done on the system, as when the bicyclist pumps air into the tire. Once the temperature increase has occurred, it is impossible to tell whether it was caused by heat transfer or by doing work. This uncertainty is an important point. Heat transfer and work are both energy in transit—neither is stored as such in a system. However, both can change the internal energy ${E}_{\text{int}}$ of a system. Internal energy is a form of energy completely different from either heat or work.

College Physics for AP® Courses 2e

Thermodynamics

The First Law of Thermodynamics

m42232

Internal Energy *E*int

We can think about the internal energy of a system in two different but consistent ways. The first is the atomic and molecular view, which examines the system on the atomic and molecular scale. The internal energy ${E}_{\text{int}}$ of a system is the sum of the kinetic and potential energies of its atoms and molecules. Recall that kinetic plus potential energy is called mechanical energy. Thus internal energy is the sum of atomic and molecular mechanical energy. Because it is impossible to keep track of all individual atoms and molecules, we must deal with averages and distributions. A second way to view the internal energy of a system is in terms of its macroscopic characteristics, which are very similar to atomic and molecular average values.

College Physics for AP® Courses 2e

Thermodynamics

The First Law of Thermodynamics and Some Simple Processes

m42233

*PV* Diagrams and their Relationship to Work Done on or by a Gas

A process by which a gas does work on a piston at constant pressure is called an isobaric process. Since the pressure is constant, the force exerted is constant and the work done is given as

College Physics for AP® Courses 2e

Thermodynamics

The First Law of Thermodynamics and Some Simple Processes

m42233

Reversible Processes

Both isothermal and adiabatic processes such as shown in [link] are reversible in principle. A reversible process is one in which both the system and its environment can return to exactly the states they were in by following the reverse path. The reverse isothermal and adiabatic paths are BA and CA, respectively. Real macroscopic processes are never exactly reversible. In the previous examples, our system is a gas (like that in [link]), and its environment is the piston, cylinder, and the rest of the universe. If there are any energy-dissipating mechanisms, such as friction or turbulence, then heat transfer to the environment occurs for either direction of the piston. So, for example, if the path BA is followed and there is friction, then the gas will be returned to its original state but the environment will not—it will have been heated in both directions. Reversibility requires the direction of heat transfer to reverse for the reverse path. Since dissipative mechanisms cannot be completely eliminated, real processes cannot be reversible.

College Physics for AP® Courses 2e

Thermodynamics

Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency

m42234

Heat Engines

Now let us consider a device that uses heat transfer to do work. As noted in the previous section, such a device is called a heat engine, and one is shown schematically in [link](b). Gasoline and diesel engines, jet engines, and steam turbines are all heat engines that do work by using part of the heat transfer from some source. Heat transfer from the hot object (or hot reservoir) is denoted as ${Q}_{\text{h}}$, while heat transfer into the cold object (or cold reservoir) is ${Q}_{\text{c}}$, and the work done by the engine is $W$. The temperatures of the hot and cold reservoirs are ${T}_{\text{h}}$ and ${T}_{\text{c}}$, respectively.

College Physics for AP® Courses 2e

Thermodynamics

Carnot’s Perfect Heat Engine: The Second Law of Thermodynamics Restated

m42235

College Physics for AP® Courses 2e

Thermodynamics

Applications of Thermodynamics: Heat Pumps and Refrigerators

m42236

Heat Pumps

The great advantage of using a heat pump to keep your home warm, rather than just burning fuel, is that a heat pump supplies ${Q}_{\text{h}}={Q}_{\text{c}}+W$. Heat transfer is from the outside air, even at a temperature below freezing, to the indoor space. You only pay for $W$, and you get an additional heat transfer of ${Q}_{\text{c}}$ from the outside at no cost; in many cases, at least twice as much energy is transferred to the heated space as is used to run the heat pump. When you burn fuel to keep warm, you pay for all of it. The disadvantage is that the work input (required by the second law of thermodynamics) is sometimes more expensive than simply burning fuel, especially if the work is done by electrical energy.

College Physics for AP® Courses 2e

Thermodynamics

Applications of Thermodynamics: Heat Pumps and Refrigerators

m42236

Air Conditioners and Refrigerators

Air conditioners and refrigerators are designed to cool something down in a warm environment. As with heat pumps, work input is required for heat transfer from cold to hot, and this is expensive. The quality of air conditioners and refrigerators is judged by how much heat transfer ${Q}_{\text{c}}$ occurs from a cold environment compared with how much work input $W$ is required. What is considered the benefit in a heat pump is considered waste heat in a refrigerator. We thus define the coefficient of performance ${\text{(COP}}_{\text{ref}}\text{)}$ of an air conditioner or refrigerator to be

College Physics for AP® Courses 2e

Thermodynamics

Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy

m42237

Entropy and the Unavailability of Energy to Do Work

What does a change in entropy mean, and why should we be interested in it? One reason is that entropy is directly related to the fact that not all heat transfer can be converted into work. The next example gives some indication of how an increase in entropy results in less heat transfer into work.

College Physics for AP® Courses 2e

Thermodynamics

Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy

m42237

Heat Death of the Universe: An Overdose of Entropy

In the early, energetic universe, all matter and energy were easily interchangeable and identical in nature. Gravity played a vital role in the young universe. Although it may have *seemed* disorderly, and therefore, superficially entropic, in fact, there was enormous potential energy available to do work—all the future energy in the universe.

College Physics for AP® Courses 2e

Thermodynamics

Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy

m42237

Order to Disorder

Entropy is related not only to the unavailability of energy to do work—it is also a measure of disorder. This notion was initially postulated by Ludwig Boltzmann in the 1800s. For example, melting a block of ice means taking a highly structured and orderly system of water molecules and converting it into a disorderly liquid in which molecules have no fixed positions. (See [link].) There is a large increase in entropy in the process, as seen in the following example.

College Physics for AP® Courses 2e

Thermodynamics

Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy

m42237

Life, Evolution, and the Second Law of Thermodynamics

Some people misunderstand the second law of thermodynamics, stated in terms of entropy, to say that the process of the evolution of life violates this law. Over time, complex organisms evolved from much simpler ancestors, representing a large decrease in entropy of the Earth’s biosphere. It is a fact that living organisms have evolved to be highly structured, and much lower in entropy than the substances from which they grow. But it is *always* possible for the entropy of one part of the universe to decrease, provided the total change in entropy of the universe increases. In equation form, we can write this as

College Physics for AP® Courses 2e

Thermodynamics

Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

m42238

Coin Tosses

What are the possible outcomes of tossing 5 coins? Each coin can land either heads or tails. On the large scale, we are concerned only with the total heads and tails and not with the order in which heads and tails appear. The following possibilities exist:

College Physics for AP® Courses 2e

Thermodynamics

Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

m42238

Disorder in a Gas

The fantastic growth in the odds favoring disorder that we see in going from 5 to 100 coins continues as the number of entities in the system increases. Let us now imagine applying this approach to perhaps a small sample of gas. Because counting microstates and macrostates involves statistics, this is called statistical analysis. The macrostates of a gas correspond to its macroscopic properties, such as volume, temperature, and pressure; and its microstates correspond to the detailed description of the positions and velocities of its atoms. Even a small amount of gas has a huge number of atoms: of an ideal gas at 1.0 atm and $0º C$ has $2\text{.}7×{\text{10}}^{\text{19}}$ atoms. So each macrostate has an immense number of microstates. In plain language, this means that there are an immense number of ways in which the atoms in a gas can be arranged, while still having the same pressure, temperature, and so on.

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Connection for AP® Courses

m55270

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Hooke’s Law: Stress and Strain Revisited

m42240

Energy in Hooke’s Law of Deformation

In order to produce a deformation, work must be done. That is, a force must be exerted through a distance, whether you pluck a guitar string or compress a car spring. If the only result is deformation, and no work goes into thermal, sound, or kinetic energy, then all the work is initially stored in the deformed object as some form of potential energy. The potential energy stored in a spring is ${\text{PE}}_{\text{el}}=\frac{1}{2}{\mathrm{kx}}^{2}$. Here, we generalize the idea to elastic potential energy for a deformation of any system that can be described by Hooke’s law. Hence,

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Period and Frequency in Oscillations

m42241

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Simple Harmonic Motion: A Special Periodic Motion

m42242

The Link between Simple Harmonic Motion and Waves

If a time-exposure photograph of the bouncing car were taken as it drove by, the headlight would make a wavelike streak, as shown in [link]. Similarly, [link] shows an object bouncing on a spring as it leaves a wavelike "trace" of its position on a moving strip of paper. Both waves are sine functions. All simple harmonic motion is intimately related to sine and cosine waves.

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

The Simple Pendulum

m42243

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Energy and the Simple Harmonic Oscillator

m42244

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Uniform Circular Motion and Simple Harmonic Motion

m42245

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Damped Harmonic Motion

m42246

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Forced Oscillations and Resonance

m42247

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Waves

m42248

Transverse and Longitudinal Waves

A simple wave consists of a periodic disturbance that propagates from one place to another. The wave in [link] propagates in the horizontal direction while the surface is disturbed in the vertical direction. Such a wave is called a transverse wave or shear wave; in such a wave, the disturbance is perpendicular to the direction of propagation. In contrast, in a longitudinal wave or compressional wave, the disturbance is parallel to the direction of propagation. [link] shows an example of a longitudinal wave. The size of the disturbance is its amplitude *X* and is completely independent of the speed of propagation ${v}_{\text{w}}$.

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Superposition and Interference

m42249

Standing Waves

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk in a refrigerator, for example. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed by the superposition of two or more moving waves, such as illustrated in [link] for two identical waves moving in opposite directions. The waves move through each other with their disturbances adding as they go by. If the two waves have the same amplitude and wavelength, then they alternate between constructive and destructive interference. The resultant looks like a wave standing in place and, thus, is called a standing wave. Waves on the glass of milk are one example of standing waves. There are other standing waves, such as on guitar strings and in organ pipes. With the glass of milk, the two waves that produce standing waves may come from reflections from the side of the glass.

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Superposition and Interference

m42249

Beats

Striking two adjacent keys on a piano produces a warbling combination usually considered to be unpleasant. The superposition of two waves of similar but not identical frequencies is the culprit. Another example is often noticeable in jet aircraft, particularly the two-engine variety, while taxiing. The combined sound of the engines goes up and down in loudness. This varying loudness happens because the sound waves have similar but not identical frequencies. The discordant warbling of the piano and the fluctuating loudness of the jet engine noise are both due to alternately constructive and destructive interference as the two waves go in and out of phase. [link] illustrates this graphically.

College Physics for AP® Courses 2e

Oscillatory Motion and Waves

Energy in Waves: Intensity

m42250

College Physics for AP® Courses 2e

Physics of Hearing

Connection for AP® Courses

m55286

College Physics for AP® Courses 2e

Physics of Hearing

Sound

m42255

College Physics for AP® Courses 2e

Physics of Hearing

Speed of Sound, Frequency, and Wavelength

m42256

College Physics for AP® Courses 2e

Physics of Hearing

Sound Intensity and Sound Level

m42257

College Physics for AP® Courses 2e

Physics of Hearing

Doppler Effect and Sonic Booms

m42712

Sonic Booms to Bow Wakes

What happens to the sound produced by a moving source, such as a jet airplane, that approaches or even exceeds the speed of sound? The answer to this question applies not only to sound but to all other waves as well.

College Physics for AP® Courses 2e

Physics of Hearing

Sound Interference and Resonance: Standing Waves in Air Columns

m42296

College Physics for AP® Courses 2e

Physics of Hearing

Hearing

m42297

College Physics for AP® Courses 2e

Physics of Hearing

Ultrasound

m42298

Ultrasound in Medical Therapy

Ultrasound, like any wave, carries energy that can be absorbed by the medium carrying it, producing effects that vary with intensity. When focused to intensities of ${\text{10}}^{\text{3}}$ to ${\text{10}}^{\text{5}}$ ${\text{W/m}}^{\text{2}}$, ultrasound can be used to shatter gallstones or pulverize cancerous tissue in surgical procedures. (See [link].) Intensities this great can damage individual cells, variously causing their protoplasm to stream inside them, altering their permeability, or rupturing their walls through *cavitation*. Cavitation is the creation of vapor cavities in a fluid—the longitudinal vibrations in ultrasound alternatively compress and expand the medium, and at sufficient amplitudes the expansion separates molecules. Most cavitation damage is done when the cavities collapse, producing even greater shock pressures.

College Physics for AP® Courses 2e

Physics of Hearing

Ultrasound

m42298

Ultrasound in Medical Diagnostics

When used for imaging, ultrasonic waves are emitted from a transducer, a crystal exhibiting the piezoelectric effect (the expansion and contraction of a substance when a voltage is applied across it, causing a vibration of the crystal). These high-frequency vibrations are transmitted into any tissue in contact with the transducer. Similarly, if a pressure is applied to the crystal (in the form of a wave reflected off tissue layers), a voltage is produced which can be recorded. The crystal therefore acts as both a transmitter and a receiver of sound. Ultrasound is also partially absorbed by tissue on its path, both on its journey away from the transducer and on its return journey. From the time between when the original signal is sent and when the reflections from various boundaries between media are received, (as well as a measure of the intensity loss of the signal), the nature and position of each boundary between tissues and organs may be deduced.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Connection for AP® Courses

m55297

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Static Electricity and Charge: Conservation of Charge

m42300

Charge Carried by Electrons and Protons

Franklin wrote in his letters and books that he could see the effects of electric charge but did not understand what caused the phenomenon. Today we have the advantage of knowing that normal matter is made of atoms, and that atoms contain positive and negative charges, usually in equal amounts.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Static Electricity and Charge: Conservation of Charge

m42300

Separation of Charge in Atoms

Charges in atoms and molecules can be separated—for example, by rubbing materials together. Some atoms and molecules have a greater affinity for electrons than others and will become negatively charged by close contact in rubbing, leaving the other material positively charged. (See [link].) Positive charge can similarly be induced by rubbing. Methods other than rubbing can also separate charges. Batteries, for example, use combinations of substances that interact in such a way as to separate charges. Chemical interactions may transfer negative charge from one substance to the other, making one battery terminal negative and leaving the first one positive.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Conductors and Insulators

m42306

Charging by Contact

[link] shows an electroscope being charged by touching it with a positively charged glass rod. Because the glass rod is an insulator, it must actually touch the electroscope to transfer charge to or from it. (Note that the extra positive charges reside on the surface of the glass rod as a result of rubbing it with silk before starting the experiment.) Since only electrons move in metals, we see that they are attracted to the top of the electroscope. There, some are transferred to the positive rod by touch, leaving the electroscope with a net positive charge.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Conductors and Insulators

m42306

Charging by Induction

It is not necessary to transfer excess charge directly to an object in order to charge it. [link] shows a method of induction wherein a charge is created in a nearby object, without direct contact. Here we see two neutral metal spheres in contact with one another but insulated from the rest of the world. A positively charged rod is brought near one of them, attracting negative charge to that side, leaving the other sphere positively charged.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Conductors and Electric Fields in Static Equilibrium

m42317

Earth’s Electric Field

A near uniform electric field of approximately 150 N/C, directed downward, surrounds Earth, with the magnitude increasing slightly as we get closer to the surface. What causes the electric field? At around 100 km above the surface of Earth we have a layer of charged particles, called the ionosphere. The ionosphere is responsible for a range of phenomena including the electric field surrounding Earth. In fair weather the ionosphere is positive and the Earth largely negative, maintaining the electric field ([link](a)).

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Conductors and Electric Fields in Static Equilibrium

m42317

Electric Fields on Uneven Surfaces

So far we have considered excess charges on a smooth, symmetrical conductor surface. What happens if a conductor has sharp corners or is pointed? Excess charges on a nonuniform conductor become concentrated at the sharpest points. Additionally, excess charge may move on or off the conductor at the sharpest points.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Conductors and Electric Fields in Static Equilibrium

m42317

Applications of Conductors

On a very sharply curved surface, such as shown in [link], the charges are so concentrated at the point that the resulting electric field can be great enough to remove them from the surface. This can be useful.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Coulomb’s Law

m42308

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Electric Field: Concept of a Field Revisited

m42310

Concept of a Field

A field is a way of conceptualizing and mapping the force that surrounds any object and acts on another object at a distance without apparent physical connection. For example, the gravitational field surrounding the earth (and all other masses) represents the gravitational force that would be experienced if another mass were placed at a given point within the field.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Electric Field Lines: Multiple Charges

m42312

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Electric Forces in Biology

m42315

Polarity of Water Molecules

The best example of this charge screening is the water molecule, represented as ${\text{H}}_{2}\text{O}$. Water is a strongly polar molecule. Its 10 electrons (8 from the oxygen atom and 2 from the two hydrogen atoms) tend to remain closer to the oxygen nucleus than the hydrogen nuclei. This creates two centers of equal and opposite charges—what is called a dipole, as illustrated in [link]. The magnitude of the dipole is called the dipole moment.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Applications of Electrostatics

m42329

The Van de Graaff Generator

Van de Graaff generators (or Van de Graaffs) are not only spectacular devices used to demonstrate high voltage due to static electricity—they are also used for serious research. The first was built by Robert Van de Graaff in 1931 (based on original suggestions by Lord Kelvin) for use in nuclear physics research. [link] shows a schematic of a large research version. Van de Graaffs utilize both smooth and pointed surfaces, and conductors and insulators to generate large static charges and, hence, large voltages.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Applications of Electrostatics

m42329

Xerography

Most copy machines use an electrostatic process called xerography—a word coined from the Greek words *xeros* for dry and *graphos* for writing. The heart of the process is shown in simplified form in [link].

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Applications of Electrostatics

m42329

Laser Printers

Laser printers use the xerographic process to make high-quality images on paper, employing a laser to produce an image on the photoconducting drum as shown in [link]. In its most common application, the laser printer receives output from a computer, and it can achieve high-quality output because of the precision with which laser light can be controlled. Many laser printers do significant information processing, such as making sophisticated letters or fonts, and may contain a computer more powerful than the one giving them the raw data to be printed.

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Applications of Electrostatics

m42329

Ink Jet Printers and Electrostatic Painting

The ink jet printer, commonly used to print computer-generated text and graphics, also employs electrostatics. A nozzle makes a fine spray of tiny ink droplets, which are then given an electrostatic charge. (See [link].)

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Applications of Electrostatics

m42329

Smoke Precipitators and Electrostatic Air Cleaning

Another important application of electrostatics is found in air cleaners, both large and small. The electrostatic part of the process places excess (usually positive) charge on smoke, dust, pollen, and other particles in the air and then passes the air through an oppositely charged grid that attracts and retains the charged particles. (See [link].)

College Physics for AP® Courses 2e

Electric Charge and Electric Field

Applications of Electrostatics

m42329

Integrated Concepts

The Integrated Concepts exercises for this module involve concepts such as electric charges, electric fields, and several other topics. Physics is most interesting when applied to general situations involving more than a narrow set of physical principles. The electric field exerts force on charges, for example, and hence the relevance of Dynamics: Force and Newton’s Laws of Motion. The following topics are involved in some or all of the problems labeled “Integrated Concepts”: * Kinematics * Two-Dimensional Kinematics * Dynamics: Force and Newton’s Laws of Motion * Uniform Circular Motion and Gravitation * Statics and Torque * Fluid Statics

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Connection for AP® Courses

m55349

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Electric Potential Energy: Potential Difference

m42324

The Electron Volt

The energy per electron is very small in macroscopic situations like that in the previous example—a tiny fraction of a joule. But on a submicroscopic scale, such energy per particle (electron, proton, or ion) can be of great importance. For example, even a tiny fraction of a joule can be great enough for these particles to destroy organic molecules and harm living tissue. The particle may do its damage by direct collision, or it may create harmful x rays, which can also inflict damage. It is useful to have an energy unit related to submicroscopic effects. [link] shows a situation related to the definition of such an energy unit. An electron is accelerated between two charged metal plates as it might be in an old-model television tube or oscilloscope. The electron is given kinetic energy that is later converted to another form—light in the television tube, for example. (Note that downhill for the electron is uphill for a positive charge.) Since energy is related to voltage by $\text{ΔPE}=q\Delta V,$ we can think of the joule as a coulomb-volt.

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Electric Potential Energy: Potential Difference

m42324

Conservation of Energy

The total energy of a system is conserved if there is no net addition (or subtraction) of work or heat transfer. For conservative forces, such as the electrostatic force, conservation of energy states that mechanical energy is a constant.

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Electric Potential in a Uniform Electric Field

m42326

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Electrical Potential Due to a Point Charge

m42328

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Equipotential Lines

m42331

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Capacitors and Dielectrics

m42333

Parallel Plate Capacitor

The parallel plate capacitor shown in [link] has two identical conducting plates, each having a surface area $A$, separated by a distance $d$ (with no material between the plates). When a voltage $V$ is applied to the capacitor, it stores a charge $Q$, as shown. We can see how its capacitance depends on $A$ and $d$ by considering the characteristics of the Coulomb force. We know that like charges repel, unlike charges attract, and the force between charges decreases with distance. So it seems quite reasonable that the bigger the plates are, the more charge they can store—because the charges can spread out more. Thus $C$ should be greater for larger $A$. Similarly, the closer the plates are together, the greater the attraction of the opposite charges on them. So $C$ should be greater for smaller $d$.

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Capacitors and Dielectrics

m42333

Dielectric

The previous example highlights the difficulty of storing a large amount of charge in capacitors. If $d$ is made smaller to produce a larger capacitance, then the maximum voltage must be reduced proportionally to avoid breakdown (since $E=V/d$). An important solution to this difficulty is to put an insulating material, called a dielectric, between the plates of a capacitor and allow $d$ to be as small as possible. Not only does the smaller $d$ make the capacitance greater, but many insulators can withstand greater electric fields than air before breaking down.

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Capacitors in Series and Parallel

m42336

Capacitance in Series

[link](a) shows a series connection of three capacitors with a voltage applied. As for any capacitor, the capacitance of the combination is related to charge and voltage by $C=\frac{Q}{V}$.

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Capacitors in Series and Parallel

m42336

Capacitors in Parallel

[link](a) shows a parallel connection of three capacitors with a voltage applied. Here the total capacitance is easier to find than in the series case. To find the equivalent total capacitance ${C}_{\text{p}}$, we first note that the voltage across each capacitor is $V$, the same as that of the source, since they are connected directly to it through a conductor. (Conductors are equipotentials, and so the voltage across the capacitors is the same as that across the voltage source.) Thus the capacitors have the same charges on them as they would have if connected individually to the voltage source. The total charge $Q$ is the sum of the individual charges:

College Physics for AP® Courses 2e

Electric Potential and Electric Field

Energy Stored in Capacitors

m42395

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Connection for AP® Courses

m55354

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Current

m42341

Electric Current

Electric current is defined to be the rate at which charge flows. A large current, such as that used to start a truck engine, moves a large amount of charge in a small time, whereas a small current, such as that used to operate a hand-held calculator, moves a small amount of charge over a long period of time. In equation form, electric current $I$ is defined to be

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Current

m42341

Drift Velocity

Electrical signals are known to move very rapidly. Telephone conversations carried by currents in wires cover large distances without noticeable delays. Lights come on as soon as a switch is flicked. Most electrical signals carried by currents travel at speeds on the order of ${\text{10}}^{8}{\rule{0.25em}{0ex}}\text{m/s}$, a significant fraction of the speed of light. Interestingly, the individual charges that make up the current move *much* more slowly on average, typically drifting at speeds on the order of ${\text{10}}^{-4}{\rule{0.25em}{0ex}}\text{m/s}$. How do we reconcile these two speeds, and what does it tell us about standard conductors?

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Ohm’s Law: Resistance and Simple Circuits

m42344

Ohm’s Law

The current that flows through most substances is directly proportional to the voltage $V$ applied to it. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is *directly proportional to the voltage applied*:

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Ohm’s Law: Resistance and Simple Circuits

m42344

Resistance and Simple Circuits

If voltage drives current, what impedes it? The electric property that impedes current (crudely similar to friction and air resistance) is called resistance $R$. Collisions of moving charges with atoms and molecules in a substance transfer energy to the substance and limit current. Resistance is defined as inversely proportional to current, or

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Resistance and Resistivity

m42346

Material and Shape Dependence of Resistance

The resistance of an object depends on its shape and the material of which it is composed. The cylindrical resistor in [link] is easy to analyze, and, by so doing, we can gain insight into the resistance of more complicated shapes. As you might expect, the cylinder’s electric resistance $R$ is directly proportional to its length $L$, similar to the resistance of a pipe to fluid flow. The longer the cylinder, the more collisions charges will make with its atoms. The greater the diameter of the cylinder, the more current it can carry (again similar to the flow of fluid through a pipe). In fact, $R$ is inversely proportional to the cylinder’s cross-sectional area $A$.

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Resistance and Resistivity

m42346

Temperature Variation of Resistance

The resistivity of all materials depends on temperature. Some even become superconductors (zero resistivity) at very low temperatures. (See [link].) Conversely, the resistivity of conductors increases with increasing temperature. Since the atoms vibrate more rapidly and over larger distances at higher temperatures, the electrons moving through a metal make more collisions, effectively making the resistivity higher. Over relatively small temperature changes (about $\text{100º}\text{C}$ or less), resistivity $\rho$ varies with temperature change $\Delta T$ as expressed in the following equation

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Electric Power and Energy

m42714

Power in Electric Circuits

Power is associated by many people with electricity. Knowing that power is the rate of energy use or energy conversion, what is the expression for electric power? Power transmission lines might come to mind. We also think of lightbulbs in terms of their power ratings in watts. Let us compare a 25-W bulb with a 60-W bulb. (See [link](a).) Since both operate on the same voltage, the 60-W bulb must draw more current to have a greater power rating. Thus the 60-W bulb’s resistance must be lower than that of a 25-W bulb. If we increase voltage, we also increase power. For example, when a 25-W bulb that is designed to operate on 120 V is connected to 240 V, it briefly glows very brightly and then burns out. Precisely how are voltage, current, and resistance related to electric power?

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Electric Power and Energy

m42714

The Cost of Electricity

The more electric appliances you use and the longer they are left on, the higher your electric bill. This familiar fact is based on the relationship between energy and power. You pay for the energy used. Since $P=E/t$, we see that

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Alternating Current versus Direct Current

m42348

Alternating Current

Most of the examples dealt with so far, and particularly those utilizing batteries, have constant voltage sources. Once the current is established, it is thus also a constant. Direct current (DC) is the flow of electric charge in only one direction. It is the steady state of a constant-voltage circuit. Most well-known applications, however, use a time-varying voltage source. Alternating current (AC) is the flow of electric charge that periodically reverses direction. If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating current circuit. Examples include the commercial and residential power that serves so many of our needs. [link] shows graphs of voltage and current versus time for typical DC and AC power. The AC voltages and frequencies commonly used in homes and businesses vary around the world.

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Alternating Current versus Direct Current

m42348

Why Use AC for Power Distribution?

Most large power-distribution systems are AC. Moreover, the power is transmitted at much higher voltages than the 120-V AC (240 V in most parts of the world) we use in homes and on the job. Economies of scale make it cheaper to build a few very large electric power-generation plants than to build numerous small ones. This necessitates sending power long distances, and it is obviously important that energy losses en route be minimized. High voltages can be transmitted with much smaller power losses than low voltages, as we shall see. (See [link].) For safety reasons, the voltage at the user is reduced to familiar values. The crucial factor is that it is much easier to increase and decrease AC voltages than DC, so AC is used in most large power distribution systems.

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Electric Hazards and the Human Body

m42350

Thermal Hazards

Electric power causes undesired heating effects whenever electric energy is converted to thermal energy at a rate faster than it can be safely dissipated. A classic example of this is the short circuit, a low-resistance path between terminals of a voltage source. An example of a short circuit is shown in [link]. Insulation on wires leading to an appliance has worn through, allowing the two wires to come into contact. Such an undesired contact with a high voltage is called a *short*. Since the resistance of the short, $r$, is very small, the power dissipated in the short, $P={V}^{2}/r$, is very large. For example, if $V$ is 120 V and $r$ is $0\text{.}\text{100}{\rule{0.25em}{0ex}}\Omega$, then the power is 144 kW, *much* greater than that used by a typical household appliance. Thermal energy delivered at this rate will very quickly raise the temperature of surrounding materials, melting or perhaps igniting them.

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Electric Hazards and the Human Body

m42350

Shock Hazards

Electrical currents through people produce tremendously varied effects. An electrical current can be used to block back pain. The possibility of using electrical current to stimulate muscle action in paralyzed limbs, perhaps allowing paraplegics to walk, is under study. TV dramatizations in which electrical shocks are used to bring a heart attack victim out of ventricular fibrillation (a massively irregular, often fatal, beating of the heart) are more than common. Yet most electrical shock fatalities occur because a current put the heart into fibrillation. A pacemaker uses electrical shocks to stimulate the heart to beat properly. Some fatal shocks do not produce burns, but warts can be safely burned off with electric current (though freezing using liquid nitrogen is now more common). Of course, there are consistent explanations for these disparate effects. The major factors upon which the effects of electrical shock depend are

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Nerve Conduction–Electrocardiograms

m42352

Nerve Conduction

Electric currents in the vastly complex system of billions of nerves in our body allow us to sense the world, control parts of our body, and think. These are representative of the three major functions of nerves. First, nerves carry messages from our sensory organs and others to the central nervous system, consisting of the brain and spinal cord. Second, nerves carry messages from the central nervous system to muscles and other organs. Third, nerves transmit and process signals within the central nervous system. The sheer number of nerve cells and the incredibly greater number of connections between them makes this system the subtle wonder that it is. Nerve conduction is a general term for electrical signals carried by nerve cells. It is one aspect of bioelectricity, or electrical effects in and created by biological systems.

College Physics for AP® Courses 2e

Electric Current, Resistance, and Ohm's Law

Nerve Conduction–Electrocardiograms

m42352

Electrocardiograms

Just as nerve impulses are transmitted by depolarization and repolarization of adjacent membrane, the depolarization that causes muscle contraction can also stimulate adjacent muscle cells to depolarize (fire) and contract. Thus, a depolarization wave can be sent across the heart, coordinating its rhythmic contractions and enabling it to perform its vital function of propelling blood through the circulatory system. [link] is a simplified graphic of a depolarization wave spreading across the heart from the *sinoarterial (SA) node***,** the heart’s natural pacemaker.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Connection for AP® Courses

m55364

College Physics for AP® Courses 2e

Circuits and DC Instruments

Resistors in Series and Parallel

m42356

Resistors in Series

When are resistors in series? Resistors are in series whenever the flow of charge, called the current, must flow through devices sequentially. For example, if current flows through a person holding a screwdriver and into the Earth, then ${R}_{1}$ in [link](a) could be the resistance of the screwdriver’s shaft, ${R}_{2}$ the resistance of its handle, ${R}_{3}$ the person’s body resistance, and ${R}_{4}$ the resistance of her shoes.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Resistors in Series and Parallel

m42356

Resistors in Parallel

[link] shows resistors in parallel, wired to a voltage source. Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires having negligible resistance. Each resistor thus has the full voltage of the source applied to it.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Resistors in Series and Parallel

m42356

Combinations of Series and Parallel

More complex connections of resistors are sometimes just combinations of series and parallel. These are commonly encountered, especially when wire resistance is considered. In that case, wire resistance is in series with other resistances that are in parallel.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Resistors in Series and Parallel

m42356

Practical Implications

One implication of this last example is that resistance in wires reduces the current and power delivered to a resistor. If wire resistance is relatively large, as in a worn (or a very long) extension cord, then this loss can be significant. If a large current is drawn, the $\text{IR}$ drop in the wires can also be significant.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Electromotive Force: Terminal Voltage

m42357

Electromotive Force

You can think of many different types of voltage sources. Batteries themselves come in many varieties. There are many types of mechanical/electrical generators, driven by many different energy sources, ranging from nuclear to wind. Solar cells create voltages directly from light, while thermoelectric devices create voltage from temperature differences.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Electromotive Force: Terminal Voltage

m42357

Internal Resistance

As noted before, a 12-V truck battery is physically larger, contains more charge and energy, and can deliver a larger current than a 12-V motorcycle battery. Both are lead-acid batteries with identical emf, but, because of its size, the truck battery has a smaller internal resistance *$r$*. Internal resistance is the inherent resistance to the flow of current within the source itself.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Electromotive Force: Terminal Voltage

m42357

Terminal Voltage

The voltage output of a device is measured across its terminals and, thus, is called its terminal voltage${\rule{0.25em}{0ex}}V$. Terminal voltage is given by

College Physics for AP® Courses 2e

Circuits and DC Instruments

Electromotive Force: Terminal Voltage

m42357

Multiple Voltage Sources

There are two voltage sources when a battery charger is used. Voltage sources connected in series are relatively simple. When voltage sources are in series, their internal resistances add and their emfs add algebraically. (See [link].) Series connections of voltage sources are common—for example, in flashlights, toys, and other appliances. Usually, the cells are in series in order to produce a larger total emf.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Electromotive Force: Terminal Voltage

m42357

Animals as Electrical Detectors

A number of animals both produce and detect electrical signals. Fish, sharks, platypuses, and echidnas (spiny anteaters) all detect electric fields generated by nerve activity in prey. Electric eels produce their own emf through biological cells (electric organs) called electroplaques, which are arranged in both series and parallel as a set of batteries.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Electromotive Force: Terminal Voltage

m42357

Solar Cell Arrays

Another example dealing with multiple voltage sources is that of combinations of solar cells—wired in both series and parallel combinations to yield a desired voltage and current. Photovoltaic generation (PV), the conversion of sunlight directly into electricity, is based upon the photoelectric effect, in which photons hitting the surface of a solar cell create an electric current in the cell.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Kirchhoff’s Rules

m42359

Kirchhoff’s First Rule

Kirchhoff’s first rule (the junction rule) is an application of the conservation of charge to a junction; it is illustrated in [link]. Current is the flow of charge, and charge is conserved; thus, whatever charge flows into the junction must flow out. Kirchhoff’s first rule requires that ${I}_{1}={I}_{2}+{I}_{3}$ (see figure). Equations like this can and will be used to analyze circuits and to solve circuit problems.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Kirchhoff’s Rules

m42359

Kirchhoff’s Second Rule

Kirchhoff’s second rule (the loop rule) is an application of conservation of energy. The loop rule is stated in terms of potential, $V$, rather than potential energy, but the two are related since ${\text{PE}}_{\text{elec}}=\text{qV}$. Recall that emf is the potential difference of a source when no current is flowing. In a closed loop, whatever energy is supplied by emf must be transferred into other forms by devices in the loop, since there are no other ways in which energy can be transferred into or out of the circuit. [link] illustrates the changes in potential in a simple series circuit loop.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Kirchhoff’s Rules

m42359

Applying Kirchhoff’s Rules

By applying Kirchhoff’s rules, we generate equations that allow us to find the unknowns in circuits. The unknowns may be currents, emfs, or resistances. Each time a rule is applied, an equation is produced. If there are as many independent equations as unknowns, then the problem can be solved. There are two decisions you must make when applying Kirchhoff’s rules. These decisions determine the signs of various quantities in the equations you obtain from applying the rules.

College Physics for AP® Courses 2e

Circuits and DC Instruments

DC Voltmeters and Ammeters

m42360

Analog Meters: Galvanometers

Analog meters have a needle that swivels to point at numbers on a scale, as opposed to digital meters, which have numerical readouts similar to a hand-held calculator. The heart of most analog meters is a device called a galvanometer, denoted by G. Current flow through a galvanometer, ${I}_{\text{G}}$, produces a proportional needle deflection. (This deflection is due to the force of a magnetic field upon a current-carrying wire.)

College Physics for AP® Courses 2e

Circuits and DC Instruments

DC Voltmeters and Ammeters

m42360

Taking Measurements Alters the Circuit

When you use a voltmeter or ammeter, you are connecting another resistor to an existing circuit and, thus, altering the circuit. Ideally, voltmeters and ammeters do not appreciably affect the circuit, but it is instructive to examine the circumstances under which they do or do not interfere.

College Physics for AP® Courses 2e

Circuits and DC Instruments

Null Measurements

m42362

The Potentiometer

Suppose you wish to measure the emf of a battery. Consider what happens if you connect the battery directly to a standard voltmeter as shown in [link]. (Once we note the problems with this measurement, we will examine a null measurement that improves accuracy.) As discussed before, the actual quantity measured is the terminal voltage $V$, which is related to the emf of the battery by $V=\text{emf}-\text{Ir}$, where $I$ is the current that flows and $r$ is the internal resistance of the battery.