When a nerve cell depolarizes, charge is transferred

Problem 1CQ Two wires connect a lightbulb to a battery, completing a circuit and causing the bulb to glow. Do the simple observations and measurements that you can make on this circuit prove that something is flowing through the wires? If so, state the observations and/or measurements that are relevant and the steps by which you can then infer that something must be flowing. If not, can you offer an alternative hypothesis about why the bulb glows that is at least plausible and that could be tested?

Problem 1P The current in an electric hair dryer is 10 A. How much charge and how many electrons flow through the hair dryer in 5.0 min?

Problem 2CQ Two wires connect a lightbulb to a battery, completing a circuit and causing the bulb to glow. Are the simple observations and measurements you can make on this circuit able to distinguish a current composed of positive charge carriers from a current composed of negative charge carriers? If so, describe how you can tell which it is. If not, why not?

Problem 2P electrons flow through a transistor in 1.0 ms. What is the current through the transistor?

Problem 3CQ What causes electrons to move through a wire as a current?

Problem 3P A wire carries a 1.0 A current for 30 s. How many electrons move past a point in the wire?

Problem 4CQ A lightbulb is connected to a battery by two copper wires of equal lengths but different thicknesses. A thick wire connects one side of the lightbulb to the positive terminal of the battery and a thin wire connects the other side of the bulb to the negative terminal. a. Which wire carries a greater current? Or is the current the same in both? Explain. b. If the two wires are switched, will the bulb get brighter, dimmer, or stay the same? Explain.

Problem 5CQ All wires in Figure Q22.5 are made of the same material and have the same diameter. Rank in order, from largest to smallest, the currents . Explain.

Problem 4P When a nerve cell depolarizes, charge is transferred across the cell membrane, changing the potential difference. For a typical nerve cell, 9.0 pC of charge flows in a time of 0.50 ms. What is the average current?

Problem 5P A wire carries a 15 mA current. How many electrons pass a given point on the wire in 1.0 s?

Problem 6CQ A wire carries a 4 A current. What is the current in a second wire that delivers twice as much charge in half the time?

Problem 6P In a typical lightning strike, 2.5 C flows from cloud to ground in 0.20 ?s. What is the current during the strike?

Problem 7CQ Metal 1 and metal 2 are each formed into 1-mm-diameter wires. The electric field needed to cause a 1 A current in metal 1 is larger than the electric field needed to cause a 1 A current in metal 2. Which metal has the larger resistivity? Explain.

Problem 7P A capacitor is charged to , then discharged by connecting a wire between the two plates. 40 ?s after the discharge begins, the capacitor still holds 13% of its original charge. What was the average current during the first 40 ms of the discharge?

Problem 8CQ Cells in the nervous system have a potential difference of 70 mV across the cell membrane separating the interior of the cell from the extracellular fluid. This potential difference is maintained by ion pumps that move charged ions across the membrane. Is this an emf?

Problem 8P In an ionic solution, positive ions with charge +2e pass to the right each second while negative ions with charge -e pass to the left. What are the magnitude and direction of current in the solution?

Problem 9P The starter motor of a car engine draws a current of 150 A from the battery. The copper wire to the motor is 5.0 mm in diameter and 1.2 m long. The starter motor runs for 0.80 s until the car engine starts. How much charge passes through the starter motor?

Problem 9CQ a. Which direction—clockwise or counterclockwise—does an electron travel through the wire in Figure Q22.9 ? Explain. b. Does an electron’s electric potential energy increase, decrease, or stay the same as it moves through the wire? Explain. c. If you answered “decrease” in part b, where does the energy go? If you answered “increase” in part b, where does the energy come from? d. Which way—up or down—does an electron move through the battery? Explain. e. Does an electron’s electric potential energy increase, decrease, or stay the same as it moves through the battery? Explain. f. If you answered “decrease” in part e, where does the energy go? If you answered “increase” in part e, where does the energy come from?

Problem 10CQ If you change the temperature of a segment of metal wire, the dimensions change and the resistivity changes. How does each of these changes affect the resistance of the wire?

Problem 10P A car battery is rated at 90 A . h, meaning that it can supply a 90 A current for 1 h before being completely discharged. If you leave your headlights on until the battery is completely dead, how much charge leaves the positive terminal of the battery?

Problem 12CQ The two circuits in Figure Q22.12 use identical batteries and wires made of the same material and of equal diameters. Rank in order, from largest to smallest, the currents at points 1 to 4.

Problem 11CQ The wires in Figure Q22.11 are all made of the same material; the length and radius of each wire are noted. Rank in order, from largest to smallest, the resistances of these wires. Explain.

Problem 11P What are the values of currents in Figure P22.11 ? The directions of the currents are as noted.

Problem 12P The currents through several segments of a wire object are shown in Figure P22.12 . What are the magnitudes and directions of the currents in segments B and C?

Problem 13 CQ The two circuits in Figure Q22.13 use identical batteries and wires made of the same material and of equal diameters. Rank in order, from largest to smallest, the currents at points 1 to 7. Explain.

Problem 13P A battery supplies a steady 1.5 A current to a circuit. If the charges moving in the battery are positive ions with charge e, how many ions per second are transported from the negative terminal to the positive terminal?

Problem 14CQ Which, if any, of these statements are true? (More than one may be true.) Explain your choice or choices. a. A battery supplies energy to a circuit. b. A battery is a source of potential difference. The potential difference between the terminals of the battery is always the same. c. A battery is a source of current. The current leaving the battery is always the same.

Problem 14P How much work is done to move 1.0 µCof charge from the negative terminal to the positive terminal of a 1.5 V battery?

Problem 15CQ Rank in order, from largest to smallest, the currents through the four resistors in Figure Q22.15. Explain.

Problem 15P What is the emf of a battery that does 0.60 J of work to transfer 0.050 C of charge from the negative to the positive terminal?

Problem 16CQ The circuit in Figure Q22.16 has three batteries of emf ? in series. Assuming the wires are ideal, sketch a graph of the potential as a function of distance traveled around the circuit, starting from V = 0 V at the negative terminal of the bottom battery. Note all important points on your graph.

Problem 16P A 9.0 V battery supplies a 2.5 mA current to a circuit for 5.0 hr. a. How much charge has been transferred from the negative to the positive terminal? ________________ b. How much work has been done on the charges that passed through the battery?

Problem 17CQ When lightning strikes the ground, it generates a large electric field along the surface of the ground directed toward the point of the strike. People near a lightning strike are often injured not by the lightning itself but by a large current that flows up one leg and down the other due to this electric field. To minimize this possibility, you are advised to stand with your feet close together if you are trapped outside during a lightning storm. Explain why this is beneficial. Hint: The current path through your body, up one leg and down the other, has a certain resistance. The larger the current along this path, the greater the damage.

Problem 17P An individual hydrogen-oxygen fuel cell has an output of 0.75 V. How many cells must be connected in series to drive a 24.0 V motor?

Problem18CQ One way to find out if a wire has corroded is to measure its resistance. Explain why the resistance of a wire increases if it becomes corroded.

Problem 18P An electric catfish can generate a significant potential difference using stacks of special cells called electrocytes . Each electrocyte develops a potential difference of 110 mV. How many cells must be connected in series to give the 350 V a large catfish can produce?

Problem 19CQ Over time, atoms “boil off” the hot filament in an incandescent bulb and the filament becomes thinner. How does this affect the brightness of the lightbulb?

Problem 19P A wire with resistance R is connected to the terminals of a 6.0 V battery. What is the potential difference ?Vends between the ends of the wire and the current I through it if the wire has the following resistances? (a) 1.0 ? (b) 2.0 ? (c) 3.0 ?.

Problem 20CQ Rank in order, from largest to smallest, the powers dissipated by the four resistors in Figure Q22.20.

Problem 20P Wires 1 and 2 are made of the same metal. Wire 2 has twice the length and twice the diameter of wire 1. What are the ratios of the resistances of the two wires?

Problem 21CQ We can model the rear window defroster in a car as a resistor that is connected to the car’s 12 V battery. The defroster is made of a material whose resistance increases rapidly as the temperature increases. When the defroster is cold , its resistance is low; when the defroster is warm, its resistance is high. Why is it better to make a defroster with a material like this than with a material whose resistance is independent of temperature? Think about how the resistance, the current, and the power will change as the window warms.

Problem 21P A wire has a resistance of 0.010 ?. What will the wire’s resistance be if it is stretched to twice its original length without changing the volume of the wire?

Problem 22MCQ Lightbulbs are typically rated by their power dissipation when operated at a given voltage. Which of the following lightbulbs has the largest current through it when operated at the voltage for which it’s rated? A. 0.8 W, 1.5 V B. 6 W, 3 V C. 4 W, 4.5 V D. 8 W, 6 V

Problem 22P Resistivity measurements on the leaves of corn plants are a good way to assess stress and overall health. The leaf of a corn plant has a resistance of 2.0 M? measured between two electrodes placed 20 cm apart along the leaf. The leaf has a width of 2.5 cm and is 0.20 mm thick. What is the resistivity of the leaf tissue? Is this greater than or less than the resistivity of muscle tissue in the human body?

Problem 23MCQ Lightbulbs are typically rated by their power dissipation when operated at a given voltage. Which of the following lightbulbs has the largest resistance when operated at the voltage for which it’s rated? A. 0.8 W, 1.5 V B. 6 W, 3 V C. 4 W, 4.5 V D. 8 W, 6 V

Problem 23P What is the resistance of a. A 1.0-m-long copper wire that is 0.50 mm in diameter? b. A 10-cm-long piece of iron with a 1.0 mm × 1.0 mm square cross section?

Problem 24MCQ A copper wire is stretched so that its length increases and its diameter decreases. As a result, A. The wire’s resistance decreases, but its resistivity stays the same. B. The wire’s resistivity decreases, but its resistance stays the same. C. The wire’s resistance increases, but its resistivity stays the same. D. The wire’s resistivity increases, but its resistance stays the same.

Problem 24P A motorcyclist is making an electric vest that, when connected to the motorcycle’s 12 V battery, will warm her on cold rides. She is using 0.25-mm-diameter copper wire, and she wants a current of 4.0 A in the wire. What length wire must she use?

Problem 25MCQ The potential difference across a length of wire is increased. Which of the following does not increase as well? A. The electric field in the wire B. The power dissipated in the wire C. The resistance of the wire D. The current in the wire

Problem 25P The femoral artery is the large artery that carries blood to the leg. A person’s femoral artery has an inner diameter of 1.0 cm. What is the resistance of a 20-cm-long column of blood in this artery?

Problem 26MCQ A stereo amplifier creates a 5.0 V A. 7.1 V B. 10 V C. 14 V D. 25 V

Problem 26P A 3.0 V potential difference is applied between the ends of a 0.80-mm-diameter, 50-cm-long nichrome wire. What is the current in the wire?

Problem 27MCQ If a 1.5 V battery stores 5.0 kJ of energy (a reasonable value for an inexpensive C cell), for how many minutes could it sustain a current of 1.2 A? A. 2.7 B. 6.9 C. 9.0 D. 46

Problem 27P A 1.0-mm-diameter, 20-cm-long copper wire carries a 3.0 A current. What is the potential difference between the ends of the wire?

Problem 28MCQ Figure Q22.29 shows a side view of a wire of varying circular cross section. Rank in order the currents flowing in the three sections.

Problem 28P The relatively high resistivity of dry skin, about 1 × 106 ? . m, can safely limit the flow of current into deeper tissues of the body. Suppose an electrical worker places his palm on an instrument whose metal case is accidentally connected to a high voltage. The skin of the palm is about 1.5 mm thick. Estimate the area of skin on the worker’s palm that would contact a flat panel, then calculate the approximate resistance of the skin of the palm.

Problem 29MCQ A person gains weight by adding fat—and therefore adding girth—to his body and his limbs, with the amount of muscle remaining constant. How will this affect the electrical resistance of his limbs? A. The resistance will increase. B. The resistance will stay the same. C. The resistance will decrease.

Problem 29P a. How long must a 0.60-mm-diameter copper wire be to carry a 0.50 A current when connected to the terminals of a 1.5 V flashlight battery?

Problem 30P Figure P22.29 shows the current-versus-potential-difference graph for a resistor. a. What is the resistance of this resistor? b. Suppose the length of the resistor is doubled while keeping its cross section the same. (This requires doubling the amount of material the resistor is made of.) Copy the figure and add to it the current-versus-potential-difference graph for the longer resistor.

Problem 31P Figure P22.30 is a current-versus-potential-difference graph for a cylinder. What is the cylinder’s resistance?

Problem 32P In Example 22.6 the length of a 60 W, 240 ? lightbulb filament was calculated to be 60 cm. a. If the potential difference across the filament is 120 V, what is the strength of the electric field inside the filament? b. Suppose the length of the bulb’s filament were doubled without changing its diameter or the potential difference across it. What would the electric field strength be in this case? c. Remembering that the current in the filament is proportional to the electric field, what is the current in the filament following the doubling of its length? d. What is the resistance of the filament following the doubling of its length? Reference: Example 22.6 :

Problem 33P The electric field inside a 30-cm-long copper wire is 0.010 V/m. What is the potential difference between the ends of the wire?

Problem 34P A small electric lap blanket contains a 40-foot-long wire wrapped back and forth inside. An 18 V supply creates a current in this wire, warming it and thus the blanket. What is the electric field strength inside this wire?

Problem 35P Two identical lightbulbs are connected in series to a single 9.0 V battery. a. Sketch the circuit. b. Sketch a graph showing the potential as a function of distance through the circuit, starting with V = 0 V at the negative terminal of the battery.

Problem 36P a. What is the resistance of a 1500 W (120 V) hair dryer? b. What is the current in the hair dryer when it is used?

Problem 37P You’ve brought your 1000 W (120 V) hair dryer on vacation to Europe, where the standard outlet voltages are 230 V. Assuming the hair dryer can operate safely at the higher voltage, can you actually use it if the outlet can provide at most 15 A, or will it draw more current than this?

Problem 38P A 70 W electric blanket runs at 18 V. a. What is the resistance of the wire in the blanket? b. How much current does the wire carry?

Problem 39P A 60-cm-long heating wire is connected to a 120 V outlet. If the wire dissipates 45 W, what are (a) the current in and (b) the resistance of the wire?

Problem 40P An electric eel develops a potential difference of 450 V, driving a current of 0.80 A for a 1.0 ms pulse. For this pulse, find (a) the power, (b) the total energy, and (c) the total charge that flows.

Problem 41P The total charge a household battery can supply is given in units of mA . h. For example, a 9.0 V alkaline battery is rated 450 mA . h, meaning that such a battery could supply a 1 mA current for 450 h, a 2 mA current for 225 h, etc. How much energy, in joules, is this battery capable of supplying?

Problem 42GP A 3.0 V battery powers a flashlight bulb that has a resistance of 6.0 ?. How much charge moves through the battery in 10 min?

Problem 43GP A sculptor has asked you to help electroplate gold onto a brass statue. You know that the charge carriers in the ionic solution are monovalent (charge e)gold ions, and you’ve calculated that you must deposit 0.50 g of gold to reach the necessary thickness. How much current do you need, in mA, to plate the statue in 3.0 hr?

Problem 44 GP Older freezers developed a coating of ice inside that had to be melted periodically; an electric heater could speed this defrosting process. Suppose you’re melting ice from your freezer using a heating wire that carries a current of 5.0 A when connected to 120 V. a. What is the resistance of the wire? b. How long will it take the heater to melt 720 g of accumulated ice at ?10°C? Assume that all of the heat goes into warming and melting

Problem 46GP The hot dog cooker described in the chapter heats hot dogs by connecting them to 120 V household electricity. A typical hot dog has a mass of 60 g and a resistance of 150 ?. How long will it take for the cooker to raise the temperature of the hot dog from 20°C to 80°C? The specific heat of a hot dog is approximately 2500 J/kg . K.

Problem 45GP For a science experiment you need to electroplate a 100-nmthick zinc coating onto both sides of a very thin, 2.0 cm × 2.0 cm copper sheet. You know that the charge carriers in the ionic solution are divalent (charge 2e) zinc ions. The density of zinc is . If the electroplating apparatus operates at 1.0 mA, how long will it take the zinc to reach the desired thickness?

Problem 47GP Air isn’t a perfect electric insulator, but it has a very high resistivity. Dry air has a resistivity of approximately . A capacitor has square plates 10 cm on a side separated by 1.2 mm of dry air. If the capacitor is charged to 250 V, what fraction of the charge will flow across the air gap in 1 minute? Make the approximation that the potential difference doesn’t change as the charge flows.

Problem 48GP The biochemistry that takes place inside cells depends on various elements, such as sodium, potassium, and calcium, that are dissolved in water as ions. These ions enter cells through narrow pores in the cell membrane known as ion channels. Each ion channel, which is formed from a specialized protein molecule, is selective for one type of ion. Measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion channel carries a current of 1.8 pA. How many potassium ions pass through if the ion channel opens for 1.0 ms?

Problem 49GP High-resolution measurements have shown that an ion channel (see Problem 48) is a 0.30-nm-diameter cylinder with length of 5.0 nm. The intracellular fluid filling the ion channel has resistivity 0.60 ? . m. What is the resistance of the ion channel? Reference: Problem 48: The biochemistry that takes place inside cells depends on various elements, such as sodium, potassium, and calcium, that are dissolved in water as ions. These ions enter cells through narrow pores in the cell membrane known as ion channels. Each ion channel, which is formed from a specialized protein molecule, is selective for one type of ion. Measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion channel carries a current of 1.8 pA. How many potassium ions pass through if the ion channel opens for 1.0 ms?

Problem 50GP When an ion channel opens in a cell wall (see Problem 48), monovalent (charge e) ions flow through the channel at a rate of . a. What is the current through the channel? b. The potential difference across the ion channel is 70 mV. What is the power dissipation in the channel?

Problem 51GP The total charge a battery can supply is rated in mA . h, the product of the current (in mA) and the time (in h) that the battery can provide this current. A battery rated at 1000 mA . h can supply a current of 1000 mA for 1.0 h, 500 mA current for 2.0 h, and so on. A typical AA rechargeable battery has a voltage of 1.2 V and a rating of 1800 mA . h. For how long could this battery drive current through a long, thin wire of resistance 22 ??

Problem 52GP The heating element of a simple heater consists of a 2.0-mlong, 0.60-mm-diameter nichrome wire. When plugged into a 120 V outlet, the heater draws 8.0 A of current when hot. a. What is the wire’s resistance when it is hot? b. Use your answer to part a to calculate the resistivity of nichrome in this situation. Why is it not the same as the value of ? given for nichrome in Table 22.1?

Problem 53GP Variations in the resistivity of blood can give valuable clues to changes in the blood’s viscosity and other properties. The resistivity is measured by applying a small potential difference and measuring the current. Suppose a medical device attaches electrodes into a 1.5-mm-diameter vein at two points 5.0 cm apart. What is the blood resistivity if a 9.0 V potential difference causes a 230 ?A current through the blood in the vein?

Problem 54GP A 40 W (120 V) lightbulb has a tungsten filament of diameter 0.040 mm. The filament’s operating temperature is 1500°C. a. How long is the filament? b. What is the resistance of the filament at 20°C?

Problem 55GP Wires aren’t really ideal. The voltage drop across a currentcarrying wire can be significant unless the resistance of the wire is quite low. Suppose a 50 ft extension cord is being used to provide power to an electric lawn mower. The cord carries a 10 A current. The copper wire in a typical extension cord has a 1.3 mm diameter. What is the voltage drop across a 50 ft length of wire at this current?

Problem 56GP When the starter motor on a car is engaged, there is a 300 A current in the wires between the battery and the motor. Suppose the wires are made of copper and have a total length of 1.0 m. What minimum diameter can the wires have if the voltage drop along the wires is to be less than 0.50 V?

Problem 57GP The electron beam inside a television picture tube is 0.40 mm in diameter and carries a current of 50 ?A. This electron beam impinges on the inside of the picture tube screen. a. How many electrons strike the screen each second? b. The electrons move with a velocity of . What electric field strength is needed to accelerate electrons from rest to this velocity in a distance of 5.0 mm? c. Each electron transfers its kinetic energy to the picture tube screen upon impact. What is the power delivered to the screen by the electron beam? Hint: What potential difference produced the field that accelerated electrons? This is an emf.

Problem 58GP The two segments of the wire in Figure P22.59 have equal diameters and equal lengths but different resistivities . Current I passes through this wire. If the resistivities have the ratio , what is the ratio of the potential differences across the two segments of the wire?

Problem 60GP A wire is 2.3 m long and has a diameter of 0.38 mm. When connected to a 1.2 V battery, there is a current of 0.61 A. What material is the wire likely made of?

Problem 59GP A 15-cm-long nichrome wire is connected between the terminals of a 1.5 V battery. If the current in the wire is 2.0 A, what is the wire’s diameter?

Problem 61 P The filament of a 100 W (120 V) lightbulb is a tungsten wire 0.035 mm in diameter. At the filament’s operating temperature, the resistivity is . How long is the filament?

Problem 62GP You’ve made the finals of the Science Olympics! As one of your tasks, you’re given 1.0 g of copper and asked to make a wire, using all the metal, with a resistance of 1.0 ?. Copper has a density of . What length and diameter will you choose for your wire?

Problem 63GP Not too long ago houses were protected from excessive currents by fuses rather than circuit breakers. Sometimes a fuse blew out and a replacement wasn’t at hand. Because a copper penny happens to have almost the same diameter as a fuse, some people replaced the fuse with a penny. Unfortunately, a penny never blows out, no matter how large the current, and the use of pennies in fuse boxes caused many house fires. Make the appropriate measurements on a penny, then calculate the resistance between the two faces of a solid-copper penny. (Modern pennies have the same dimensions, but are made of zinc with a copper coating.)

Problem 64GP An immersion heater used to boil water for a single cup of tea plugs into a 120 V outlet and is rated at 300 W. a. What is the resistance of the heater? b. Suppose your super-size, super-insulated tea mug contains 400 g of water at a temperature of 18°C. How long will this heater take to bring the water to a boil? You can ignore the energy needed to raise the temperature of the mug and the heater itself.

Problem 65GP The graph in Figure P22.66 shows the current through a 1.0 ? resistor as a function of time. a. How much charge flowed through the resistor during the 10 s interval shown? b. What was the total energy dissipated by the resistor during this time?

Problem 67GP If you touch the two terminals of a power supply with your two fingertips on opposite hands, the potential difference will produce a current through your torso. The maximum safe current is approximately 5 mA. a. If your hands are completely dry, the resistance of your body from fingertip to fingertip is approximately 500 k?. If you accidentally touch both terminals of your 120 V household electricity supply with dry fingers, will you receive a dangerous shock? b. If your hands are moist, your resistance drops to approximately 1 k?. If you accidentally touch both terminals of your 120 V household supply with moist fingers, will you receive a dangerous shock?

Problem 67GP If you touch the two terminals of a power supply with your two fingertips on opposite hands, the potential difference will produce a current through your torso. The maximum safe current is approximately 5 mA. a. If your hands are completely dry, the resistance of your body from fingertip to fingertip is approximately 500 k?. If you accidentally touch both terminals of your 120 V household electricity supply with dry fingers, will you receive a dangerous shock? b. If your hands are moist, your resistance drops to approximately 1 k?. If you accidentally touch both terminals of your 120 V household supply with moist fingers, will you receive a dangerous shock?

Problem 68GP The average resistivity of the human body (apart from surface resistance of the skin) is about 5.0 ? · m. The conducting path between the right and left hands can be approximated as a cylinder 1.6 m long and 0.10 m in diameter. The skin resistance can be made negligible by soaking the hands in salt water. a. What is the resistance between the hands if the skin resistance is negligible? b. If skin resistance is negligible, what potential difference between the hands is needed for a lethal shock current of 100 mA? Your result shows that even small potential differences can produce dangerous currents when skin is damp.

Problem 69PP Lightbulb Failure You’ve probably observed that the most common time for an incandescent lightbulb to fail is the moment when it is turned on. Let’s look at the properties of the bulb’s filament to see why this happens. The current in the tungsten filament of a lightbulb heats the filament until it glows. The filament is so hot that some of the atoms on its surface fly off and end up sticking on a cooler part of the bulb. Thus the filament gets progressively thinner as the bulb ages. There will certainly be one spot on the filament that is a bit thinner than elsewhere. This thin segment will have a higher resistance than the surrounding filament. More power will be dissipated at this spot, so it won’t only be a thin spot, it also will be a hot spot. Now, let’s look at the resistance of the filament. The graph in Figure P22.70 shows data for the current in a lightbulb as a function of the potential difference across it. The graph is not linear, so the filament is not an ohmic material with a constant resistance. However, we can define the resistance at any particular potential difference ?V to be R = ?V/I. This ratio, and hence the resistance, increases with ?V and thus with temperature. When the bulb is turned on, the filament is cold and its resistance is much lower than during normal, high-temperature operation. The low resistance causes a surge of higher-than-normal current lasting a fraction of a second until the filament heats up. Because power dissipation is , the power dissipated during this first fraction of a second is much larger than the bulb’s rated power. This current surge concentrates the power dissipation at the high-resistance thin spot, perhaps melting it and breaking the filament. For the bulb in Figure P22.70, what is the approximate resistance of the bulb at a potential difference of 6.0 V? A. 7.0 ? B. 17 ? C. 27 ? D. 37 ?

Problem 70PP Lightbulb Failure You’ve probably observed that the most common time for an incandescent lightbulb to fail is the moment when it is turned on. Let’s look at the properties of the bulb’s filament to see why this happens. The current in the tungsten filament of a lightbulb heats the filament until it glows. The filament is so hot that some of the atoms on its surface fly off and end up sticking on a cooler part of the bulb. Thus the filament gets progressively thinner as the bulb ages. There will certainly be one spot on the filament that is a bit thinner than elsewhere. This thin segment will have a higher resistance than the surrounding filament. More power will be dissipated at this spot, so it won’t only be a thin spot, it also will be a hot spot. Now, let’s look at the resistance of the filament. The graph in Figure P22.70 shows data for the current in a lightbulb as a function of the potential difference across it. The graph is not linear, so the filament is not an ohmic material with a constant resistance. However, we can define the resistance at any particular potential difference ?V to be R = ?V/I. This ratio, and hence the resistance, increases with ?V and thus with temperature. When the bulb is turned on, the filament is cold and its resistance is much lower than during normal, high-temperature operation. The low resistance causes a surge of higher-than-normal current lasting a fraction of a second until the filament heats up. Because power dissipation is , the power dissipated during this first fraction of a second is much larger than the bulb’s rated power. This current surge concentrates the power dissipation at the high-resistance thin spot, perhaps melting it and breaking the filament. As the bulb ages, the resistance of the filament A. Increases. B. Decreases. C. Stays the same.

Problem 71PP Lightbulb Failure You’ve probably observed that the most common time for an incandescent lightbulb to fail is the moment when it is turned on. Let’s look at the properties of the bulb’s filament to see why this happens. The current in the tungsten filament of a lightbulb heats the filament until it glows. The filament is so hot that some of the atoms on its surface fly off and end up sticking on a cooler part of the bulb. Thus the filament gets progressively thinner as the bulb ages. There will certainly be one spot on the filament that is a bit thinner than elsewhere. This thin segment will have a higher resistance than the surrounding filament. More power will be dissipated at this spot, so it won’t only be a thin spot, it also will be a hot spot. Now, let’s look at the resistance of the filament. The graph in Figure P22.70 shows data for the current in a lightbulb as a function of the potential difference across it. The graph is not linear, so the filament is not an ohmic material with a constant resistance. However, we can define the resistance at any particular potential difference ?V to be R = ?V/I. This ratio, and hence the resistance, increases with ?V and thus with temperature. When the bulb is turned on, the filament is cold and its resistance is much lower than during normal, high-temperature operation. The low resistance causes a surge of higher-than-normal current lasting a fraction of a second until the filament heats up. Because power dissipation is , the power dissipated during this first fraction of a second is much larger than the bulb’s rated power. This current surge concentrates the power dissipation at the high-resistance thin spot, perhaps melting it and breaking the filament. Which of the curves in Figure P22.72 best represents the expected variation in current as a function of time in the short time interval immediately after the bulb is turned on?

Problem 72PP Lightbulb Failure You’ve probably observed that the most common time for an incandescent lightbulb to fail is the moment when it is turned on. Let’s look at the properties of the bulb’s filament to see why this happens. The current in the tungsten filament of a lightbulb heats the filament until it glows. The filament is so hot that some of the atoms on its surface fly off and end up sticking on a cooler part of the bulb. Thus the filament gets progressively thinner as the bulb ages. There will certainly be one spot on the filament that is a bit thinner than elsewhere. This thin segment will have a higher resistance than the surrounding filament. More power will be dissipated at this spot, so it won’t only be a thin spot, it also will be a hot spot. Now, let’s look at the resistance of the filament. The graph in Figure P22.70 shows data for the current in a lightbulb as a function of the potential difference across it. The graph is not linear, so the filament is not an ohmic material with a constant resistance. However, we can define the resistance at any particular potential difference ?V to be R = ?V/I. This ratio, and hence the resistance, increases with ?V and thus with temperature. When the bulb is turned on, the filament is cold and its resistance is much lower than during normal, high-temperature operation. The low resistance causes a surge of higher-than-normal current lasting a fraction of a second until the filament heats up. Because power dissipation is , the power dissipated during this first fraction of a second is much larger than the bulb’s rated power. This current surge concentrates the power dissipation at the high-resistance thin spot, perhaps melting it and breaking the filament. There are devices to put in a light socket that control the current through a lightbulb, thereby increasing its lifetime. Which of the following strategies would increase the lifetime of a bulb without making it dimmer? A. Reducing the average current through the bulb B. Limiting the maximum current through the bulb C. Increasing the average current through the bulb D. Limiting the minimum current through the bulb