Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for College Physics
If the electric field lines in the figure above were perpendicular to the object, would it necessarily be a conductor? Explain.The discussion of the electric field between two parallel conducting plates, in this module states that edge effects are less important if the plates are close together. What does close mean? That is, is the actual plate separation crucial, or is the ratio of plate separation to plate area crucial?Would the self-created electric field at the end of a pointed conductor, such as a lightning rod, remove positive or negative charge from the conductor? Would the same sign charge be removed from a neutral pointed conductor by the application of a similar externally created electric field? (The answers to both questions have implications for charge transfer utilizing points.)Why is a golfer with a metal dub over her shoulder vulnerable to lightning in an open fairway? Would she be any safer under a tree?Can the belt of aVan de Graaff accelerator he a conductor? Explain.Are you relatively safe from lightning inside an automobile? Give two reasons.Discuss pros and cons of a lightning rod being grounded versus simply being attached to a building.Using the symmetry of the arrangement, show that the net Coulomb force on the charge q at the center of the square below (Figure 18.46) is zero if the charges on the four corners are exactly equal. Figure 18.46 Four point charges qa, qb, q, and qtd lie on the corners of a square and q is located at its center.(a) Using the symmetry of the arrangement, show that the electric field at the center of the square in figure 18.46 is zero if the charges on the four comers are exactly equal. (b) Show that this is also true for any combination of charges in which qa= qd and qa = qc(a) What is the direction of the total Coulomb force on q in Figure 18.46 if q is negative, qa= qcand both are negative, and qb= qcand both are positive? (b) What is the direction of the electric field at the center of the square in this situation?Considering Figure 18.46, suppose that qa= qdand qb= qc. First show that q is in static equilibrium. (You may neglect the gravitational force.) Then discuss whether the equilibrium is stable or unstable, noting that this may depend on the signs of the charges and the direction of displacement of q from the center of the square.If qa = 0 in Figure 18-46, under what conditions will there be no net Coulomb force on q?In regions of low humidity, one develops a special "grip” when opening car doors, or touching metal door knobs. This involves placing as much of the hand on the device as possible, not just the ends of one’s fingers. Discuss the induced charge and explain why this is done.Tollbooth stations on roadways and bridges usually have a piece of wire stuck in the pavement before them that will touch a car as it approaches. Why is this done?Suppose a woman carries an excess charge. To maintain her charged status can she he standing on just any pair of shoes? How would you discharge her? What are the consequences if she simply walks away?Common static electricity involves charges ranging from nanocoulombs to microcoulombs. (a) How many electrons are needed to form a charge of 2.00 nC (b) How many electrons must be removed from a neutral object to leave a net charge of 0.500 C ?If 1.801020electrons move through a pocket calculator during a full day’s operation, how many coulombs of charge moved through it?To start a car engine, the car battery moves 3.751021 electrons through the starter motor. How many coulombs of charge were moved?A certain lightning bolt moves 40.0 C of charge. How many fundamental units of charge | qe\ is this?Suppose a speck of dust in an electrostatic precipitator has l.0000 1012 protons in it and has a net charge of5.00 nC (a very large charge for a small speck). How many electrons does it have?An amoeba has 1.001016protons and a net charge of 0.300 pC. (a) How many fewer electrons are there than protons? (b) If you paired them up, what fraction of the protons would have no electrons?A 50.0 g ball of copper has a net charge of 2.00 C. What fraction of the copper s electrons has been removed? (Each copper atom has 29 protons, and copper has an atomic mass of 63.5.)What net charge would you place on a 100 g piece of sulfur if you put an extra electron on 1 in 1012 of its atoms? (Sulfur has an atomic mass of 32.1.)How many coulombs of positive charge are there in 4.00 kg of plutonium, given its atomic mass is 244 and that each plutonium atom has 94 protons?What is the repulsive force between two pith balls that are 8.00 cm apart and have equal charges of 30.0 nC?(a) How strong is the attractive force between a glass rod with a 0.700 C charge and a silk cloth with a 0.600 C charge, which are 12.0 cm apart, using the approximation that they act like point charges? (b) Discuss how the answer to this problem might be affected if the charges are distributed over some area and do not act like point charges.Two point charges exert a 5.00 N force on each other. What will the force become if the distance between them is increased by a factor of three?Two point charges are brought closer together, increasing the force between them by a factor of 25. By what factor was their separation decreased?How far apart must two point charges of 75.0 nC (typical of static electricity) be to have a force of 1.00 N between them?If two equal charges each of 1 C each are separated in air by a distance of 1 km, what is the magnitude of the force acting between them? You will see that even at a distance as large as 1 km, the repulsive force is substantial because 1 C is a very significant amount of charge.A test charge of +2C is placed halfway between a charge of +6 C and another of +4 /C separated by 10 cm. (a) What is the magnitude of the force on the test charge? (b) What is the direction of this force (away from or toward the +6 C charge)?Bare free charges do not remain stationary when close together. To illustrate this, calculate the acceleration of two isolated protons separated by 2.00 nm (a typical distance between gas atoms). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.(a) By what factor must you change the distance between two point charges to change the force between them by a factor of 10? (b) Explain how the distance can either increase or decrease by this factor and still cause a factor of 10 change in the forceSuppose you have a total charge qtot that you can split in any manner. Once split, the separation distance is fixed. How do you split the charge to achieve the greatest force?(a) Common transparent tape becomes charged when pulled from a dispenser. If one piece is placed above another, the repulsive force can be great enough to support the top piece’s weight. Assuming equal point charges (only an approximation), calculate the magnitude of the charge if electrostatic force is great enough to support the weight of a mg piece of tape held 1.00 cm above another. (b) Discuss whether the magnitude of this charge is consistent with what is typical of static electricity.Find the ratio of the electrostatic to gravitational force between two electrons. (b) What is this ratio for two protons? (c) Why is the ratio different for electrons and protons?At what distance is the electrostatic force between two protons equal to the weight of one proton?A certain five cent coin contains 5.00 g of nickel. What fraction of the nickel atoms’ electrons, removed and placed 1.00 m above it, would support the weight of this coin? The atomic mass of nickel is 53.7, and each nickel atom contains 28 electrons and 28 protons(a) Two point charges totaling 8.00 C exert a repulsive force of 0.150 N on one another when separated by 0.500 m. What is the charge on each? (b) What is the charge on each if the force is attractive?Point charges of 5.00 C and 3.00/C are placed 0.250 m apart. (a) Where can a third charge be placed so that the net force on it is zero? (b) What if both charges are positive?(a) Two point charges q1 and q23.00 m apart, and their total charge is 20 C. (a) If the force of repulsion between them is 0.075N, what are magnitudes of the two charges? (b) If one charge attracts the other with a force of 0.150 N, what are the magnitudes of the two charges? Note that you may need to solve a quadratic equation to reach your answer.What is the magnitude and direction of an electric field that exerts a 2.0010-5 N upward force on a -1.75 C charge?What is the magnitude and direction of the force exerted on a 3.50 /C charge by a 250 N/C electric field that points due east?Calculate the magnitude of the electric field 2.00 m from a point charge of 5.00 mC (such as found on the terminal of a Van de Graaff).(a) What magnitude point charge creates a 10,000 N/C electric field at a distance of 0.250 m? (b) How large is the field at 10.0 m?Calculate the initial (from rest) acceleration of a proton in a 5.00X106 N/C electric field (such as created by a research Van de Graaff). ). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.(a) Find the direction and magnitude of an electric field that exerts a 4.801017 N westward force on an electron (b) What magnitude and direction force does this field exert on a proton?(a) Sketch the electric field lines near a point charge +q (b) Do the same for a point charge +q. (b) Do the same for a point charge 3.00q.Sketch the electric field lines a long distance from the charge distributions shown in Figure 18.26 (a) and (b)Figure 18.47 shows the electric field lines near two charges q j and g2. What is the ratio of their magnitudes? (b) Sketch the electric field lines a long distance from the charges shown in the figure.Sketch the electric field lines in the vicinity of two opposite charges, where the negative charge is three times greater in magnitude than the positive. (See Figure 1S.47 for a similar situation).Sketch the electric field lires in the vicinity of the conductor in Figure 18.48 given the field was originally uniform and parallel to the object's long axis. Is the resulting field small near the long side of the object?Sketch the electric field lines in the vicinity of the conductor in Figure 18.49 given the field was originally uniform and parallel to the object's long axis. Is the resulting field small near the long side of the object?Sketch the electric field between the two conducting plates shown in Figure 18.50, given the top plate is positive and an equal amount of negative charge is on the bottom plate. Be certain to indicate the distribution of charge on the plates.Sketch the electric field lines in the vicinity of the charged insulator in Figure 18.51 noting its nonuniform charge distribution. Figure 18.51 A charged insulating rod such as might be used in a classroom demonstration.What is the force on the charge located at x = 8.00 cm in Figure 18.52(a) given that q = 1.00 C?(a) Find the total electric field at x = 1.00 cm in Figure 18.52(b) given that q =5.00 nC. (b) Find the total electric field at x = 11.00 cm in Figure 18.52(b). (c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, double charge; etc., and what will its value(s) he?)(a) Find the electric field at x = 5.00 cm in Figure 18.52 (a), given that q = 1.00 C. (b) at what position between 3.00 and 8.00 cm is the total electric field the same as that for ? 2q alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the light of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)(a) Find the total Coulomb force on a charge of 2.00 nC located at x = 4.00 cm in Figure 18.52 (b): given that q = 1,00C . (b) Find the x-position at which the electric field is zero in Figure 18.52 (b).Using the symmetry of the arrangement, determine the direction of the force on q in the figure below, given that qa=qb=+7.50C and qc = qd = 7.50C. (b) Calculate the magnitude of the force on the charge q, given that the square is 10.0 cm on a side and q = 2.00 C.(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in Figure 18.53, given that qa= 1.00C and qc=qd= +1.00 C. (b) Calculate the magnitude of the electric field at the location of q, given that the square is 5.00 cm on a side.Find the electric field at the location of qain Figure 18.53 given that qb=qc= qd=+2.00 nC, q= -1.00 nC, and the square is 20.0 cm on a side.48. Find the total Coulomb force on a charge q in Figure 18.53, given that q = 1.00 C, qa=2.00 C, qb=-3.00 C, qc,=-4.00C, and qd= + 1.00 C. The square is 50.0 cm on a side.Find the electric field at the location of qain Figure 18.54, given that qb=+10.00 C and qc= -5.00 C.(b) What is the force on qa, given that qa,=+1.50nC?(a) Find the electric field at the center of the triangular configuration of charges in Figure 18-54., given that qa=+ 2.50 nC, qb=-8.00 nC, and qc=+ 1.50 nC. (b) Is there any combination of charges, other than qa= qb=qc,that will produce a zero strength electric field at the center of the triangular configuration?(a) What is the electric field 5.00 m from the center of the terminal of a Van de Graaff with a 3.00 mC charge, noting that the field is equivalent to that of a point charge at the center of the terminal? (b) At this distance, what force does the field exert on a 2.00 C charge on the Van de Graaff’s belt?(a) What is the direction and magnitude of an electric field that supports the weight of a free electron near the surface of Earth? (b) Discuss what the small value for this field implies regarding the relative strength of the gravitational and electrostatic forces.A simple and common technique for accelerating electrons is shown in Figure 18.55, where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. (a) Calculate the acceleration of the electorn if the field strength is 2.50104 N/C. (b) Explain why the electron will not be pulled back to the positive plate once it moves through the hole.Earth has a net charge that produces an electric field of approximately 150 N/C downward at its surface. (a) What is the magnitude and sign of the excess charge, noting the electric field of a conducting sphere is equivalent to a point charge at its center? (b) What acceleration will the field produce on a free electron near Earth’s surface? (c) What mass object with a single extra electron will have its weight supported by this field?Point charges of 25.0 C and 45.0 (2 are placed 0.500 m apart. (a) At what point along the line between them is the electric field zero? (b) What is the electric field halfway between them?What can you say about two charges q1and q2, if the electric field one-fourth of the way from q1to q2is zero?Integrated Concepts Calculate the angular velocity ? of an electron orbiting a proton in the hydrogen atom, given the radius of the orbit is 0.53 10-10 m. You may assume that the proton is stationary and the centripetal force is supplied by Coulomb attraction.Integrated Concepts An electron has an initial velocity of 5.00106m/s in a uniform 2.00105N/C strength electric field. the field accelerates the electron in the direction opposite to its initial velocity. (a) What is the direction of the electric field? (b) How far does the electron travel before coming to rest? (c) How long does it take the electron to come to rest? (d) What is the electron’s velocity when it returns to its starting point?Integrated Concepts The practical limit to an electric field in air is about 3.001061 N/C. Above this strength, sparking takes place because air begins to ionize and charges flow, reducing the field, (a) Calculate the distance a free proton must travel in this field to reach 3,00% of the speed of light, starting from rest, (b) Is this practical in air, or must it occur in a vacuum?Integrated Concepts A 5.00 g charged insulating ball hangs or a 30.0 cm long string in a uniform horizontal electric field as shown in Figure 18.56. Given the charge on the ball is 1,00 C, find the strength of the field.Integrated Concepts Figure 18.57 shows an electron passing between two charged metal plates that create an 100 N/C vertical electric field perpendicular to the electron's original horizontal velocity. (These can be used to change the electron’s direction, such as in an oscilloscope.) The initial speed of the electron is 3.00106 m/s, and the horizontal distance it travels in the uniform field is 4.00 cm. (a) What is its vertical deflection? (b) What is the vertical component of its final velocity? (c) At what angle does it exit? Neglect any edge effects.Integrated Concepts The classic Millikan oil drop experiment was the first to obtain an accurate measurement of the charge on an electron. In it, oil drops were suspended against the gravitational force by a vertical electric field. (See Figure 18.58.) Given the oil drop to be 1.00 m in radius and have a density of 920 kg/m3: Find the weight of the drop. (b) If the drop has a single excess electron, find the electric field strength needed to balance its weight.Integrated Concepts (a) In Figure 18.59, four equal charges q lie on the corners of a square. A fifth charge Q is on a mass m directly above the center of the square, at a height equal to the length d of one side of the square. Determine the magnitude of q in terms of Q. m, and d, if the Coulomb force is to equal the weight of m. (b) Is this equilibrium stable or unstable? Discuss.Unreasonable Results 64. (a) Calculate the electric field strength near a 10.0 cm diameter conducting sphere that has 1.00 C of excess charge on it. (b) What is unreasonable about this result? (c) Which assumptions are responsible?Unreasonable results (a) Two 0.500 g raindrops in a thunderhead are 1.00 cm apart when they each acquire 1.00 mC charges. Find their acceleration. (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?Unreasonable results A wrecking yard inventor wants to pick up cars by charging a 0.400 m diameter ball and inducing an equal and opposite charge on the car. If a car has a 1000 kg mass and the ball is to be able to lift it from a distance of 1.00 m: (a) What minimum charge must be used? (b) What is the electric field near the surface of the ball? (c) Why are these results unreasonable? (d) Which premise or assumption is responsible?Construct Your Own Problem Consider two insulating balls with evenly distributed equal and opposite charges on their surfaces, held with a certain distance between the centers of the balls. Construct a problem in which you calculate the electric field (magnitude and direction) due to the balls at various points along a line running through the centers of the balls and extending to infinity on either side. Choose interesting points and comment on the meaning of the field at those points. For example, at what points might the field be just that due to one ball and where does the field become negligibly small? Among the things to be considered are the magnitudes of the charges and the distance between the centers of the balls. Your instructor may wish for you to consider the electric field off axis or for a more complex array of charges, such as those in a water molecule.Construct Your Own Problem Consider identical spherical conducting space ships in deep space where gravitational fields from other bodies are negligible compared to the gravitational attraction between the ships. Construct a problem in which you place identical excess charges on the space ships to exactly counter their gravitational attraction. Calculate the amount of excess charge needed. Examine whether that charge depends on the distance between the centers of the ships, the masses of the ships, or any other factors. Discuss whether this would be an easy, difficult, or even impossible thing to do in practice.Voltage is the common word for potential difference. Which term is more descriptive, voltage or potential difference?It the voltage between two points is zero, can a test charge be moved between them with zero net work being done? Can this necessarily be done without exerting a force? Explain.What is the relationship between voltage and energy? Mote precisely, what is the relationship between potential difference and electric potential energy?Voltages are always measured between two points. Why?How are units of volts and electron volts related? How do they differ?Discuss how potential difference and electric field strength are related. Give an example.What is the strength of the electric field in a region where the electric potential is constant?Will a negative charge, initially at rest, move toward higher or lower potential? Explain why.In what region of space is the potential due to a uniformly charged Sphere the same as that of a point charge? In what region does it differ from that of a point charge?Can the potential of a non-uniformly charged sphere be the same as that of a point charge? Explain.What is an equipotential line? What is an equipotential surface?Explain in your own words why equipotential lines and surfaces must be perpendicular to electric field lines.Can different equipotential lines cross? Explain.Does the capacitance of a device depend on the applied voltage? What about the charge stored in it?Use the characteristics of the of the Coulomb force to explain why capacitance should be proportional to the plate area of a capacitor. Similarly, explain why capacitance should be inversely proportional to the separation between plates.Give the reason why a dielectric material increases capacitance compared with what it would be with air between the plates of a capacitor. What is the independent reason that a dielectric material also allows a greater voltage to be applied to a capacitor? (The dielectric thus increases C and permits a greater V.)How does the polar character of water molecules help to explain waters relatively large dielectric constant? (Figure 19.19) Figure 19,19 Artist's conception of a water molecule. There is an inherent separation of charge, and so water is a polar molecule. Electrons in the molecule are attracted to the oxygen nucleus and leave an excess of positive charge near the two hydrogen nuclai. (Note that the schematic on the right is a rough illustration of the distribution of electrons in the water molecule. It does not show the actual numbers of protons and elections involved in the structure.)Sparks will occur between the plates of an air filled capacitor- at lower voltage when the air is humid than when dry. Explain why, considering the polar character of water molecules.Water has a large dielectric constant, but it is rarely used in capacitors. Explain why.Membranes ii living cells, including those in humans, are characterized by a separation of charge across the membrane. Effectively, the membranes are thus charged capacitors with important functions related to the potential difference across the membrane. Is energy required to separate these charges m living membranes and. if so. is its source the metabolization of food energy or some other source? Figure 19.26 The semi permeable membrane of a cell has different concentrations of ions inside and out. Diffusion moves the K+ (potassium) and CI- (chloride) ions n the directions shown. until the Coulomb force halts further transfer. This results in a layer of positive charge on the outside, a layer of negative charge on the inside, and thus a voltage across the cell membrane. The membrane is normally impeftneabte to Na+ (sodium ions).If you wish to store a large amount of energy m a capacitor bank, would you connect capacitors in series or parallel? Explain.How does the energy contained in a charged capacitor change when a dielectric is inserted, assuming the capacitor is isolated and It’s charge is constant? Does this imply that work was done?What happens to the energy stored in a capacitor connected to a battery when a dielectric is inserted? Was work done in the process?Find the ratio of speeds of an electron and a negative hydrogen ion (one having an extra electron) accelerated through the same voltage, assuming non-relativistic final speeds. Take the mass of the hydrogen ion to be 1.6710-27 kg.An evacuated tube uses an accelerating voltage of 40 kV to accelerate electrons to hit a copper plate and produce x rays. Non-relativistically, what would be the maximum speed of these electrons?A bare helium nucleus has two positive charges and a mass of 6.6410-27 kg. (a) Calculate its kinetic energy in joules at 2.00% of the speed of light. (b) What is this in electron volts? (C) What voltage would be needed to obtain this energy?Integrated Concepts Singly charged gas ions are accelerated from rest through a voltage of 13.0 V. At what temperature will the average kinetic energy of gas molecules be the same as that given these ions?Integrated Concepts The temperature near the center of the Sun is thought to be 15 million degrees Celsius (1.5 107). Through what voltage must a singly charged ion be accelerated to have the same energy as the average kinetic energy of ions at this temperature?Integrated Concepts (a) What is the average power output of a heart defibrillator that dissipates 400 J of energy in 10.0 ms? (b) Considering the high-power output, why doesn’t the defibrillator produce serious burns?Integrated Concepts A lightning bolt strikes a tree, moving 20.0 C of charge through a potential difference of 1.00102 MV. (a) What energy was dissipated? (b) What mass of water could be raised from 15°C to the boiling point and then boiled by this energy? (c) Discuss the damage that could be caused to the tree by the expansion of the boiling steam.Integrated Concepts: A 12.0 V battery-operated bottle warmer heats 50.0 g of glass, 2.50 102 g of baby formula, and 2.00 102 g of aluminum from 20.0°C to 90.0°C. (a) How much charge is moved by the battery? (b) How many electrons per second flow if it takes 5.00 mm to warm the formula? (Hint: Assume that the specific heat of baby formula is about the same as the specific heat of water.)Integrated Concepts A battery-operated car utilizes a 12.0 V system. Find the charge the batteries must be able to move in order to accelerate the 750 kg car from rest to 25.0 m/s. make it climb a 2.00 102 m high hill, and then cause it to travel at a constant 25.0 m/s by exerting a 5.00 102 N force for an hour.Integrated Concepts Fusion probability is greatly enhanced when appropriate nuclei are brought close together, but mutual Coulomb repulsion must be overcome. This can be done using the kinetic energy of high-temperature gas ions or by accelerating the nuclei toward one another. (a) Calculate the potential energy of two singly charged nuclei separated by 1 .00 10-12 m by finding the voltage of one at that distance and multiplying by the charge of the other. (b) At what temperature will atoms of a gas have an average kinetic energy equal to this needed electrical potential energy?Unreasonable Results (a) Find the voltage near a 10.0 cm diameter metal sphere that has 8.00 C of excess positive charge on it. (b) What is unreasonable about this result? (C) Which assumptions are responsible?Construct Your Own Problem Consider a battery used to supply energy to a cellular phone. Construct a problem in which you determine the energy that must be supplied by the battery, and then calculate the amount of charge it must be able to move in order to supply this energy. Among the things to be considered are the energy needs and battery voltage. You may need to look ahead to interpret manufacturer’s battery ratings in ampere hours as energy in joules.Show that units of Vim and N/C for electric field strength are indeed equivalent.What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of 1 .50 104 V ?The electric field strength between two parallel conducting plates separated by 4.00 cm is 7.50 104 V/m. (a) What is the potential difference between the plates? (b) The plate with the lowest potential is taken to be at zero volts. What is the potential 1.00 cm from that plate (and 3.00 cm from the other)?How far apart are two conducting plates that have an electric field strength of 4.50 103 V/m between them, if their potential difference is 15.0 kV?(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength for air ( 3.0 106 V/m) if the plates are separated by 2.00 mm and a potential difference of 5.0 103 V is applied? (b) How close together can the plates be with this applied voltage?The voltage across a membrane forming a cell wall is 80.0 mV and the membrane is 9.00 nm thick. What is the electric field strength? (The value is surprisingly large. but correct. Membranes are discussed in Capacitors and Dielectrics and Nerve Conduction—Electrocardiograms.) You may assume a uniform electric field.Membrane walls of living cells have surprisingly large electric fields across them due to separation of ions. (Membranes are discussed in some detail in Nerve Conduction—Electrocardiograms.) What is the voltage across an 8.00 nm—thick membrane if the electric field strength across it is 5.50 MV/m? You may assume a uniform electric field.Two parallel conducting plates are separated by 10.0 cm, and one of them is taken to be at zero volts. (a) What is the electric field strength between them, if the potential 8.00 cm from the zero volt plate (and 2.00 cm from the other) is 450 V? (b) What is the voltage between the plates?Find the maximum potential difference between two parallel conducting plates separated by 0.500 cm of air, given the maximum sustainable electric field strength in air to be 3.0106 V/m.A doubly charged ion is accelerated to an energy of 32.0 keV by the electric field between two parallel conducting plates separated by 2.00 cm. What is the electric field strength between the plates?An electron is to be accelerated in a uniform electric field having a strength of 2.00106 V/m. (a) What energy in keV is given to the electron if it is accelerated through 0.400 m? (b) Over what distance would it have to be accelerated to increase its energy by 50.0 GeV?A 0.500 cm diameter plastic sphere, used in a static electricity demonstration, has a uniformly distributed 40.0 pC charge on its surface. What is the potential near its surface?What is the potential 0.530 x 10-10 m from a proton (the average distance between the proton and electron in a hydrogen atom)?(a) A sphere has a surface uniformly charged with 1.00 C. At what distance from its center is the potential 5.00 MV? (b) What does your answer imply about the practical aspect of isolating such a large charge?How far from a 1.00 C point charge will the potential be 100 V? At what distance will it be 2.00 102 v?What are the sign and magnitude of a point charge that produces a potential of —2.00 V at a distance of 1.00 mm?If the potential due to a point charge is 5.00 102 V at a distance of 15.0 m, what are the sign and magnitude of the charge?In nuclear fission. a nucleus splits roughly in half. (a) What is the potential 2.00 10-14 m from a fragment that has 46 protons in it? (b) What is the potential energy in MeV of a similarly charged fragment at this distance?A research Van de Graaff generator has a 2.00-rn- diameter metal sphere with a charge of 5.00 mC on it. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (C) An oxygen atom with three missing electrons is released near the Van de Graatf generator. What is its energy in MeV at this distance?An electrostatic paint sprayer has a 0.200-m-diameter metal sphere at a potential of 25.0 kV that repels paint droplets onto a grounded object. (a) What charge is on the sphere? (b) What charge must a 0.100-mg drop of paint have to arrive at the object with a speed of 10.0 m/s?In one of the classic nuclear physics experiments at the beginning of the 20th century. an alpha particle was accelerated toward a gold nucleus, and its path was substantially deflected by the Coulomb interaction, If the energy of the doubly charged alpha nucleus was 5.00 MeV, how close to the gold nucleus (79 protons) could it come before being deflected?(a) What is the potential between two points situated 10 cm and 20 cm from a 3.0 C point charge? (b) To what location should the point at 20 cm be moved to increase this potential difference by a factor of two?Unreasonable Results (a) What is the final speed of an electron accelerated from rest through a voltage of 25.0 MV by a negatively charged Van de Graaff terminal? (b) What is unreasonable about this result? (C) Which assumptions are responsible?(a) Sketch the equipotential lines near a point charge + q. Indicate the direction of increasing potential. (b) Do the same for a point charge -3 q.Sketch the equipotential lines for the two equal positive charges shown in Figure 19.27. Indicate the direction of increasing potential. Figure 19.27 The electric field near two equal positive charges is directed away from each of the charges.Figure 19.28 shows the electric field lines near two charges q1and q2the first having a magnitude four times that of the second. Sketch the equipotential lines for these two charges, and indicate the direction of increasing potential.Sketch the equipotential lines a long distance from the charges shown in Figure 19.28. Indicate the direction of increasing potential. Figure 19.28 The electric field near two charges.Sketch the equipotential lines in the vicinity of two opposite charges, where the negative charge is three times as great in magnitude as the positive. See Figure 19.28 for a similar situation. Indicate the direction of increasing potential.Sketch the equipotential lines in the vicinity of the negatively charged conductor in Figure 19.29. How will these equipotentials look a long distance from the object? Figure 19.29 A negatively charged conductor.Sketch the equipotential lines surrounding the two conducting plates shown in Figure 19.30, given the top plate is positive and the bottom plate has an equal amount of negative charge. Be certain to indicate the distribution of charge on the plates. Is the field strongest where the plates are closest? Why should it be? Figure 19.30(a) Sketch the electric field lines in the vicinity of the charged insulator in Figure 19.31. Note its non-uniform charge distribution. (b) Sketch equipotential lines surrounding the insulator. Indicate the direction of increasing potential. Figure 19.31 A charged insulating rod such as might be used in a classroom demonstration.The naturally occurring charge on the ground on a fine day out in the open country is -1.00nC/m2. (a) What is the electric field relative to ground at a height of 3.00 m? (b) Calculate the electric potential at this height. (C) Sketch electric field and equipotential lines for this scenario.The lesser electric ray (Narcine bancroftii) maintains an incredible charge on its head and a charge equal in magnitude but opposite in sign on its tail (Figure 19.32). (a) Sketch the equipotential lines surrounding the ray. (b) Sketch the equipotentials when the ray is near a ship with a conducting surface. (C) How could this charge distribution be of use to the ray? Figure 19.32 Lesser electric ray (Narcine bancroftii) (credit: National Oceanic and Atmospheric Administration, NOAAs Fisheries Collection).What charge is stored in a 180 F capacitor when 120 V is applied to it?Find the charge stored when 5.50 V is applied to an 8.00 pF capacitor.What charge is stored in the capacitor in Example 19.8?Calculate the voltage applied to a 2.00 F capacitor when it holds 3.10 C of charge.What voltage must be applied to an 8.00 nF capacitor to store 0.160 mC of charge?What capacitance is needed to store 3.00 C of charge at a voltage of 120 V?What is the capacitance of a large Van de Graaff generator’s terminal, given that it stores 8.00 mC of charge at a voltage of 12.0 MV?Find the capacitance of a parallel plate capacitor having plates of area 5.00 m2 that are separated by 0.100 mm of Teflon.(a) What is the capacitance of a parallel plate capacitor having plates of area 1.50 m2 that are separated by 0.0200 mm of neoprene rubber? (b) What charge does it hold when 9.00 V is applied to it?Integrated Concepts A prankster applies 450 V to an 80.0 F capacitor and then tosses it to an unsuspecting victim. The victims finger is burned by the discharge of the capacitor through 0.200 g of flesh. What is the temperature increase of the flesh? Is it reasonable to assume no phase change?Unreasonable Results (a) A certain parallel plate capacitor has plates of area 4.00 m2 separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?Find the total capacitance of the combination of capacitors in Figure 19.33. Figure 19.33 A combination of series and parallel connections of capacitors.Suppose you want a capacitor bank with a total capacitance of 0.750 F and you possess numerous 1.50 mF capacitors. What is the smallest number you could hook together to achieve your goal. and how would you connect them?What total capacitances can you make by connecting a 5.00 F and an 8.00 F capacitor together?Find the total capacitance of the combination of capacitors shown in Figure 19.34. Figure 19.34 A combination of series and parallel connections of capacitors.Find the total capacitance of the combination of capacitors shown in Figure 19.35. Figure 19.35 A combination of series and parallel connections of capacitors.Unreasonable Results (a) An 8.00 F capacitor is connected in parallel to another capacitor, producing a total capacitance of 5.00 F. What is the capacitance of the second capacitor? (b) What is unreasonable about this result? (C) Which assumptions are unreasonable or inconsistent?(a) What is the energy stored in the 10.0 F capacitor of a heart defibrillator charged to 9.00103 V ? (b) Find the amount of stored charge.In open heart surgery. a much smaller amount of energy will defibrillate the heart. (a) What voltage is applied to the 8.00 F capacitor of a heart defibrillator that stores 40.0 J of energy? (b) Find the amount of stored charge.A 165 F capacitor is used in conjunction with a motor. How much energy is stored in it when 119 V is applied?Suppose you have a 9.00 V battery, a 2.00 F capacitor, and a 7.40 F capacitor. (a) Find the charge and energy stored if the capacitors are connected to the battery in series. (b) Do the same for a parallel connection.A nervous physicist worries that the two metal shelves of his wood frame bookcase might obtain a high voltage if charged by static electricity, perhaps produced by friction. (a) What is the capacitance of the empty shelves if they have area 1.00102 m2 and are 0.200 m apart? (b) What is the voltage between them it opposite charges of magnitude 2.00 nC are placed on them? (C) To show that this voltage poses a small hazard, calculate the energy stored.Show that for a given dielectric material the maximum energy a parallel plate capacitor can store is directly proportional to the volume of dielectric (Volume = A. d). Note that the applied voltage is limited by the dielectric strength.Construct Your Own Problem Consider a heart defibrillator similar to that discussed in Example 19.11. Construct a problem in which you examine the charge stored in the capacitor of a defibrillator as a function of stored energy. Among the things to be considered are the applied voltage and whether it should vary with energy to be delivered, the range of energies involved, and the capacitance of the defibrillator. You may also wish to consider the much smaller energy needed for defibrillation during open-heart surgery as a variation on this problem.Unreasonable Results (a) On a particular day, it takes 9.60 103 J of electric energy to start a truck’s engine. Calculate the capacitance of a capacitor that could store that amount of energy at 12.0 V. (b) What is unreasonable about this result? (c) Which assumptions are responsible?Can a wire carry a current and still be neutral-that is, have a total charge of zero? Explain.Car batteries are rated in ampere-hours (A h ). To what physical quantity do ampere-hours correspond (voltage, charge, ...), and what relationship do ampere-hours have to energy content?If two different wires having identical cross-sectional areas carry the same current, will the drift velocity be higher or lower in the better conductor? Explain in terms of the equation vd=1nqA by considering how the density of charge carriers n srelates to whether or not a material is a good conductor.Why are two conducting paths from a voltage source to an electrical device needed to operate the device?In cars, one battery terminal is connected to the metal body. How does this allow a single wire to supply current to electrical devices rather than two wires?Why isn't a bird sitting on a high-voltage power line electrocuted? Contrast this with the situation in which a large bird hits two wires simultaneously with its wings.The IR drop across a resistor means that there is a change in potential or voltage across the resistor. Is there any change in current as it passes through a resistor? Explain.How is the I R drop in a resistor similar to the pressure drop in a fluid flowing through a pipe?In which of the three semiconducting materials listed in Table 20.1 do impurities supply free charges? (Hint: Examine the range of resistivity for each and determine whether the pure semiconductor has the higher or lower conductivity.)Does the resistance of an object depend on the path current takes through it? Consider, for example, a rectangular bar-is its resistance the same along its length as across its width? (See Figure 20.37.)If aluminum and copper wires of the same length have the same resistance, which has the larger diameter?Explain why R=R0(1 + a?T) for the temperature variation of the resistance R of an object is not as accurate as P=P0(1 + a?T) which gives the temperature variation of resistivity P.Why do incandescent lightbulbs grow dim late in their lives, particularly just before their filaments break?The power dissipated in a resistor is given by P = V2/R, which means power decreases if resistance increases. Yet this power is also given by P = I2R, which means power increases if resistance increases. Explain why there is no contradiction here.Give an example of a use of AC power other than in the household. Similarly, give an example of a use of DC power other than that supplied by batteries.Why do voltage, current, and power go through zero 120 times per second for 60-Hz AC electricity?You are riding in a train, gazing into the distance through its window. As close objects streak by, you notice that the nearby fluorescent lights make dashed streaks. Explain.Using an ohmmeter, a student measures the resistance between various points on his body. He finds that the resistance between two points on the same finger is about the same as the resistance between two points on opposite hands-both are several hundred thousand ohms. Furthermore, the resistance decreases when more skin is brought into contact with the probes of the ohmmeter. Finally, there is a dramatic drop in resistance (to a few thousand ohms) when the skin is wet. Explain these observations and their implications regarding skin and internal resistance of the human body.What are the two major hazards of electricity?Why isn’t a short circuit a shock hazard?What determines the severity of a shock? Can you say that a certain voltage is hazardous without further information?An electrified needle is used to burn off warts, with the circuit being completed by having the patient sit on a large butt plate. Why is this plate large?Some surgery is performed with high-voltage electricity passing from a metal scalpel through the tissue being cut. Considering the nature of electric fields at the surface of conductors, why would you expect most of the current to flow from the sharp edge of the scalpel? Do you think high- or low-frequency AC is used?Some devices often used in bathrooms, such as hairdryers, often have safety messages saying “Do not use when the bathtub or basin is full of water." Why is this so?We are often advised to not flick electric switches with wet hands, dry your hand first. We are also advised to never throw water on an electric fire. Why is this so?Before working on a power transmission line, linemen will touch the line with the back of the hand as a final check that the voltage is zero. Why the back of the hand?Why is the resistance of wet skin so much smaller than dry, and why do blood and other bodily fluids have low resistances?Could a person on intravenous infusion (an IV) be microshock sensitive?In view of the small currents that cause shock hazards and the larger currents that circuit breakers and fuses interrupt, how do they play a role in preventing shock hazards?Note that in Figure 20.28, both the concentration gradient and the Coulomb force tend to move Na+ ions into the cell. What prevents this? Figure 20.28 The semipermeable membrane of a cell has different concentrations of ions inside and out. Diffusion moves the K+ and Cl ions in the direction shown, until the Coulomb force halts further transfer. This results in a layer of positive charge on the outside, a layer of negative charge on the inside, and thus a voltage across the cell membrane. The membrane is normally impermeable to Na+.Define depolarization, repolarization, and the action potential.Explain the properties of myelinated nerves in terms of the insulating properties of myelin.What is the current in milliamperes produced by the solar cells of a pocket calculator through which 4.00 C of charge passes in 4.00 h?A total of 600 C of charge passes through a flashlight in 0.500 h. What is the average current?What is the current when a typical static charge of 0.250 C moves from your finger to a metal doorknob in 1.00 C?Find the current when 2.00 nC jumps between your comb and hair over a 0.500-s time interval.A large lightning bolt had a 20,000-A current and moved 30.0 C of charge. What was its duration?The 200-A current through a spark plug moves 0.300 mC of charge. How long does the spark last?(a) A defibrillator sends a 6.00-A current through the chest of a patient by applying a 10,000-V potential as in the figure below. What is the resistance of the path? (b) The defibrillator paddles make contact with the patient through a conducting gel that greatly reduces the path resistance. Discuss the difficulties that would ensue if a larger voltage were used to produce the same current through the patient, but with the path having perhaps 50 times the resistance. (Hint: The current must be about the same, so a higher voltage would imply greater power. Use this equation for power: P=I2 RP = .)During open-heart surgery, a defibrillator can be used to bring a patient out of cardiac arrest. The resistance of the path is 500 and a 10.0-mA current is needed. What voltage should be applied?(a) A defibrillator passes 12.0 A of current through the torso of a person for 0.0100 s. How much charge moves? (b) How many electrons pass through the wires connected to the patient? (See figure two problems earlier.)A clock battery wears out after moving 10,000 C of charge through the clock at a rate of 0.500 mA. (a) How long did the clock run? (b) How many electrons per second flowed?The batteries of a submerged non-nuclear submarine supply 1000 A at full speed ahead. How long does it take to move Avogadro’s number (6.02 1023) of electrons at this rate?Electron guns are used in X-ray tubes. The electrons are accelerated through a relatively large voltage and directed onto a metal target, producing X-rays. (a) How many electrons per second strike the target if the current is 0.500 mA? (b) What charge strikes the target in 0.750 s?A large cyclotron directs a beam of He ++ nuclei onto a target with a beam current of 0.250 mA. (a) How many He++ nuclei per second is this? (b) How long does it take for 1.00 C to strike the target? (c) How long before 1.00 mol of He++ nuclei strike the target?Repeat the above example on Example 20.3, but for a wire made of silver and given there is one free electron per silver atom.Using the results of the above example on Example 20.3, find the drift velocity in a copper wire of twice the diameter and carrying 20.0A.A 14-gauge copper wire has a diameter of 1.628 mm. What magnitude current flows when the drift velocity is 1.00 mm/s? (See above example on Example 20.3 for useful information.)SPEAR, a storage ring about 72.0 m in diameter at the Stanford Linear Accelerator (closed in 2009), has a 20.0-A circulating beam of electrons that are moving at nearly the speed of light. (See Figure 20.39.) How many electrons are in the beam? Figure 20.39 Electrons circulating in the storage ring called SPEAR constitute a 20.0-A current. Because they travel close to the speed of light, each electron completes many orbits in each second.What current flows through the bulb of a 3.00-V flashlight when its hot resistance is 3.60 O ?Calculate the effective resistance of a pocket calculator that has a 1.35-V battery and through which 0.200 mA flows.What is the effective resistance of a car’s starter motor when 150 A flows through it as the car battery applies 11.0 V to the motor?How many volts are supplied to operate an indicator light on a DVD player that has a resistance of 140, given that 25.0 mA passes through it?(a) F ind the voltage drop in an extension cord having a 0.0600-O resistance and through which 5.00 A is flowing. (b) A cheaper cord utilizes thinner wire and has a resistance of 0.300 O. What is the voltage drop in it when 5.00 A flows? (c) Why is the voltage to whatever appliance is being used reduced by this amount? What is the effect on the appliance?A power transmission line is hung from metal towers with glass insulators having a resistance of 1.00109 O. What current flows through the insulator if the voltage is 200 kV? (Some high-voltage lines are DC.)What is the resistance of a 20.0-m-long piece of 12-gauge copper wire having a 2.053-mm diameter?The diameter of 0-gauge copper wire is 8.252 mm. Find the resistance of a 1.00-km length of such wire used for power transmission.If the 0.100-mm diameter tungsten filament in a light bulb is to have a resistance of 0.200at 20.0°C, how long should it be?Find the ratio of the diameter of aluminum to copper wire, if they have the same resistance per unit length (as they might in household wiling).What current flows through a 2.54-cm-diameter rod of pure silicon that is 20.0 cm long, when 1,00 103 V is applied to it? (Such a rod may be used to make nuclear-particle detectors, for example.)(a) To what temperature must you raise a copper wire, originally at 20.0°C, to double its resistance, neglecting any changes in dimensions? (b) Does this happen in household wiring under ordinary circumstances?A resistor made of Nichrome wire is used in an application where its resistance cannot change more than 1.00% from its value at 20.0°C. Over what temperature range can it be used?Of what material is a resistor made if its resistance is 40.0% greater at 100°C than at 20.0°C ?An electronic device designed to operate at any temperature in the range from -10.0°C to 55.0°C contains pure carbon resistors. By what factor does their resistance increase over this range?a) Of what material is a wire made, if it is 25.0 m long with a 0.100 mm diameter and has a resistance of 77.7at 20,0°C ? (b) What is its resistance at 150°C ?Assuming a constant temperature coefficient of resistivity, what is the maximum percent decrease in the resistance of a constantan wire starting at 20.0°C?A wire is drawn through a die, stretching it to four times its original length. By what factor does its resistance increase?A copper wire has a resistance of 0.500at 20.0°C, and an iron wire has a resistance of 0.525at the same temperature. At what temperature are their resistances equal?(a) Digital medical thermometers determine temperature by measuring the resistance of a semiconductor device called a thermistor (which has a= - 0.0600/°C ) when it is at the same temperature as the patient. What is a patient's temperature if the thermistor’s resistance at that temperature is 82.0% of its value at 37.0°C (normal body temperature)? (b) The negative value for a may not be maintained for very low temperatures. Discuss why and whether this is the case here. (Hint: Resistance can’t become negative.)Integrated Concepts (a) Redo Exercise 20.25 taking into account the thermal expansion of the tungsten filament. You may assume a thermal expansion coefficient of 12 10-6/°C. (b) By what percentage does your answer differ from that in the example?Unreasonable Results (a) To what temperature must you raise a resistor made of constantan to double its resistance, assuming a constant temperature coefficient of resistivity? (b) To cut it in half? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable, or which premises are inconsistent?What is the power of a 1.00 102 MV lightning boit having a current of 2.00 104 A ?What power is supplied to the starter motor of a large truck that draws 250 A of current from a 24.0-V battery hookup?A charge of 4.00 C of charge passes through a pocket calculator’s solar cells in 4.00 h. What is the power output, given the calculator’s voltage output is 3.00 V? (See Figure 20.40.) Figure 20.40 The strip of solar cells just above the keys of this calculator convert light to electricity to supply its energy needs. (credit: Evan-Amos, Wikimedia Commons)How many watts does a flashlight that has 6.00102C pass through it in 0.500 h use if its voltage is 3.00 V?Find the power dissipated in each of these extension cords: (a) an extension cord having a 0,0600 resistance and through which 5.00 A is flowing; (b) a cheaper cord utilizing thinner wire and with a resistance of 0.300 O.Verify that the units of a volt-ampere are watts, as implied by the equation P =IV.Show that the units 1 V2/=1W , as implied by the equation P=V2/R .Show that the units 1 A 2 = 1W, as implied by the equation P=I 2 R.Verify the energy unit equivalence that 1 kWh = 3.60106 J.Electrons in an X-ray tube are accelerated through 1 .00 102 kV and directed toward a target to produce X-rays. Calculate the power of the electron beam in this tube if it has a current of 15.0 mA.An electric water heater consumes 5.00 kW for 2.00 h per day. What is the cost of running it for one year if electricity costs 12.0 cents/kW h ? See Figure 20.41. Figure 20.41 On-demand electric hot water heater. Heat is supplied to water only when needed, (credit: aviddavid, Flickr)With a 1200-W toaster, how much electrical energy is needed to make a slice of toast (cooking time = 1 minute)? At 9.0 cents/kW h, how much does this cost?What would be the maximum cost of a CFL such that the total cost (investment plus operating) would be the same for both CFL and incandescent 60-W bulbs? Assume the cost of the incandescent bulb is 25 cents and that electricity costs 10 cents/kWh, Calculate the cost for 1000 hours, as in the cost effectiveness of CFL example.Some makes of older cars have 6.00-V electrical systems. (a) What is the hot resistance of a 30.0-W headlight in such a car? (b) What current flows through it?Alkaline batteries have the advantage of putting out constant voltage until very nearly the end of their life. How long will an alkaline battery rated at 1.00 A h and 1.58 V keep a 1.00-W flashlight bulb burning?A cauterizer, used to stop bleeding in surgery, puts out 2.00 mA at 15.0 kV. (a) What is its power output? (b) What is the resistance of the path?The average television is said to be on 6 hours per day. Estimate the yearly cost of electricity to operate 100 million TVs, assuming their power consumption averages 150 W and the cost of electricity averages 12.0 cents/kW h .An old lightbulb draws only 50.0 W, rather than its original 60.0 W, due to evaporative thinning of its filament. By what factor is its diameter reduced, assuming uniform thinning along its length? Neglect any effects caused by temperature differences.-gauge copper wire has a diameter of 9.266 mm. Calculate the power loss in a kilometer of such wire when it carries 1.00102 A.Integrated Concepts Cold vaporizers pass a current through water, evaporating it with only a small increase in temperature. One such home device is rated at 3.50 A and utilizes 120 V AC with 95.0% efficiency. (a) What is the vaporization rate in grams per minute? (b) How much water must you put into the vaporizer for 8.00 h of overnight operation? (See Figure 20.42.)*******Integrated Concepts (a) What energy is dissipated by a lightning bolt having a 20,000-A current, a voltage of 1.00102 MV, and a length of 1.00 ms? (b) What mass of tree sap could be raised from 18.0°C to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?Integrated Concepts What current must be produced by a 12.0-V battery-operated bottle warmer in order to heat 75.0 g of glass, 250 g of baby formula, and 3.00102 g of aluminum from 20.0°C to 90.0°C in 5.00 min?Integrated Concepts How much time is needed for a surgical cauterizer to raise the temperature of 1.00 g of tissue from 37.0°C to 100°C and then boil away 0.500 g of water, if it puts out 2.00 mA at 15.0 kV? Ignore heat transfer to the surroundings.Integrated Concepts Hydroelectric generators (see Figure 20.43) at Hoover Dam produce a maximum current of 8.00 103 A at 250 kV. (a) What is the power output? (b) The water that powers the generators enters and leaves the system at low speed (thus its kinetic energy does not change) but loses 160 m in altitude. How many cubic meters per second are needed, assuming 85.0% efficiency?Integrated Concepts (a) Assuming 95.0% efficiency for the conversion of electrical power by the motor, what current must the 12.0-V batteries of a 750-kg electric car be able to supply: (a) To accelerate from rest to 25.0 m/s in 1.00 min? (b) To climb a 2.00 102-m- high hill in 2.00 min at a constant 25.0-m/s speed while exerting 5.00 102 N of force to overcome air resistance and friction? (c) To travel at a constant 25.0-m/s speed, exerting a 5.00 102 N force to overcome air resistance and friction? See Figure 20.44.Integrated Concepts A light-rail commuter train draws 630 A of 650-V DC electricity when accelerating, (a) What is its power consumption rate in kilowatts? (b) How long does it take to reach 20.0 m/s stalling from rest if its loaded mass is 5.30 1()4 kg, assuming 95.0% efficiency and constant power? (c) Find its average acceleration. (d) Discuss how the acceleration you found for the light-rail train compares to what might be typical for an automobile.Integrated Concepts (a) An aluminum power transmission line has a resistance of 0.0580/km. What is its mass per kilometer? (b) What is the mass per kilometer of a copper line having the same resistance? A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.Integrated Concepts (a) An immersion heater utilizing 120 V can raise the temperature of a 1.00 102 -g aluminum cup containing 350 g of water from 20.0°C to 95.0°C in 2.00 min. Find its resistance, assuming it is constant during the process. (b) A lower resistance would shorten the heating time. Discuss the practical limits to speeding the heating by lowering the resistance.Integrated Concepts (a) What is the cost of heating a hot tub containing 1500 kg of water from 10.0°C to 40.0°C, assuming 75.0% efficiency to account for heat transfer to the surroundings? The cost of electricity is 9 cents/kW h. (b) What current was used by the 220-V AC electric heater, if this took 4.00 h?Unreasonable Results (a) What current is needed to transmit 1.00 102MW of power at 480 V? (b) What power is dissipated by the transmission lines if they have a 1.00 -resistance? (c) What is unreasonable about this result? (d) Which assumptions are unreasonable, or which premises are inconsistent?Unreasonable Results (a) What current is needed to transmit 1.00 102 MW of power at 10.0kV? (b) Find the resistance of 1.00 km of wire that would cause a 0.0100% power loss. (c) What is the diameter of a 1.00-km-long copper wire having this resistance? (d) What is unreasonable about these results? (e) Which assumptions are unreasonable, or which premises are inconsistent?Construct Your Own Problem Consider an electric immersion heater used to heat a cup of water to make tea. Construct a problem in which you calculate the needed resistance of the heater so that it increases the temperature of the water and cup in a reasonable amount of time. Also calculate the cost of the electrical energy used in your process. Among the things to be considered are the voltage used, the masses and heat capacities involved, heat losses, and the time over which the heating takes place. Your instructor may wish for you to consider a thermal safety switch (perhaps bimetallic) that will halt the process before damaging temperatures are reached in the immersion unit.(a) What is the hot resistance of a 25-W light bulb that runs on 120-V AC? (b) If the bulb’s operating temperature is 2700°C, what is its resistance at 2600°C?Certain heavy industrial equipment uses AC power that has a peak voltage of 679 V. What is the rms voltage?A certain circuit breaker trips when the rms current is 15.0 A. What is the corresponding peak current?Military aircraft use 400-Hz AC power, because it is possible to design lighter-weight equipment at this higher frequency. What is the time for one complete cycle of this power?A North American tourist takes his 25.0-W, 120-V AC razor to Europe, finds a special adapter, and plugs it into 240 V AC. Assuming constant resistance, what power does the razor consume as it is ruined?In this problem, you will verify statements made at the end of the power losses for Example 20.10. (a) What current is needed to transmit 100 MW of power at a voltage of 25.0 kV? (b) Find the power loss in a 1.00 transmission line. (c) What percent loss does this represent?A small office-building air conditioner operates or 408-V AC and consumes 50.0 kW. (a) What is its effective resistance? (b) What is the cost of running the air conditioner during a hot summer month when it is on 8.00 h per day for 30 days and electricity costs 9.00 cenls/kW h ?What is the peak power consumption of a 12G-V AC microwave over that draws 10.0A?What is the peak current through a 500-W room heater that operates on 120-V AC power?Two different electrical devices have the same power consumption, but one is meant to be operated on 12G-V AC and the other on 240-V AC. (a) What is the ratio of their resistances? (b) What is the ratio of their currents? (c) Assuming its resistance is unaffected, by what factor will the power increase if a 120-V AC device is connected to 240-V AC?Nichrome wire is used in some radiative heaters. (a) Find the resistance needed if the average power output is to be 1.00 kW utilizing 120-V AC. (b) What length of Nichrome wire, having a cross-sectional area of 5.00mm2, is needed if the operating temperature is 500°C ? (c) What power will it draw when first switched on?Find the time after t = 0 when the instantaneous voltage of 60-Hz AC first reaches the following values: (a) V0/2 (b) v0 (c) 0.(a) At what two times in the first period following t = 0 does the instantaneous voltage in 60-Hz AC equal Vrms ? (b) V rms?(a) Haw much power is dissipated in a short circuit of 240-V AC through a resistance of 0.250 ? (b) What current flows?What voltage is involved in a 1.44-kW short circuit through a 0.100- resistance?Find the current through a person and identify the likely effect on her if she touches a 120-V AC source: (a) if she is standing on a rubber mat and offers a total resistance of 300 k; (b) if she is standing barefoot on wet grass and has a resistance of only 4000 k .While taking a bath, a person touches the metal case of a radio. The path through the person to the drainpipe and ground has a resistance of 4000 . What is the smallest voltage on the case of the radio that could cause ventricular fibrillation?Foolishly trying to fish a burning piece of bread from a toaster with a metal butter knife, a man conies into contact with 120-V AC. He does not even feel it since, luckily, he is wearing rubber-soled shoes. What is the minimum resistance of the path the current follows through the person?(a) During surgery, a current as small as 20.0 ? applied directly to the heart may cause ventricular fibrillation. If the resistance of the exposed heart is 300 , what is the smallest voltage that poses this danger? (b) Does your answer imply that special electrical safety precautions are needed?(a) What is the resistance of a 220-V AC short circuit that generates a peak power of 96.8 kW? (b) What would the average power be if the average power be if the voltage was 120 V AC?A heart defibrillator passes 10.0 A through a patient’s torso for 5.00 ms in an attempt to restore normal beating. (a) How much charge passed? (b) What voltage was applied if 500 J of energy was dissipated? (c) What was the path's resistance? (d) Find the temperature increase caused in the 8.00 kg of affected tissue.