Consider the potential differences between pairs of points

Problem 1P The following questions are related to the passage “Dark Matter and the Structure of the Universe” on the previous page. As noted in the passage, our solar system orbits the center of the Milky Way galaxy in about 200 million years. If there were no dark matter in our galaxy, this period would be A. Longer. B. The same. C. Shorter.

Problem 1CQ Problem Draw a circuit diagram for the circuit of Figure P23.1.

Problem 2P Draw a circuit diagram for the circuit of Figure P23.2.

Problem 2CQ A flashlight bulb is connected to a battery and is glowing; the circuit is shown in Figure Q23.2. Is current greater than, less than, or equal to current ? Explain.

Problem 3P Draw a circuit diagram for the circuit of Figure P23.3.

Problem 3CQ Current flows into three resistors connected together one after the other as shown in Figure Q23.3. The accompanying graph shows the value of the potential as a function of position.

Problem 4CQ The circuit in Figure Q23.4 has two resistors, with . Which resistor dissipates the larger amount of power? Explain.

Problem 4P In Figure P23.4, what is the current in the wire above the junction? Does charge flow toward or away from the junction?

Problem 5CQ The lightbulb in the circuit diagram of Figure P23.5 has a resistance of 1.0 ?. Consider the potential difference between pairs of points in the figure. a. What are the magnitudes of ? b. What are the magnitudes if the bulb is removed?

Problem 5P The lightbulb in the circuit diagram of Figure P23.5 has a resistance of 1.0 ?. Consider the potential difference between pairs of points in the figure. a. What are the magnitudes of ? b. What are the magnitudes if the bulb is removed?

Problem 6CQ In the circuit shown in Figure Q23.6, bulbs A and B are glowing. Then the switch is closed. What happens to each bulb? Does it get brighter, stay the same, get dimmer, or go out? Explain.

Problem 6P a. What are the magnitude and direction of the current in the 30 ? resistor in Figure P23.6? b. Draw a graph of the potential as a function of the distance traveled through the circuit, traveling clockwise from V = 0 V at the lower left corner. See Figure P23.9 for an example of such a graph.

Problem 7CQ Figure Q23.7 shows two circuits. The two batteries are identical and the four resistors all have exactly the same resistance.

Problem 8CQ Figure Q23.8 shows two circuits. The two batteries are identical and the four resistors all have exactly the same resistance. a. Compare . Are they all the same? If not, rank them in order from largest to smallest. Explain. b. Rank in order, from largest to smallest, the five currents . Explain.

Problem 7P a. What are the magnitude and direction of the current in the 18 ? resistor in Figure P23.7? b. Draw a graph of the potential as a function of the distance traveled through the circuit, traveling clockwise from V = 0 V at the lower left corner. See Figure P23.9 for an example of such a graph.

Problem 8P a. What is the potential difference across each resistor in Figure P23.8? b. Draw a graph of the potential as a function of the distance traveled through the circuit, traveling clockwise from V = 0 V at the lower left corner. See Figure P23.9 for an example of such a graph.

Problem 9CQ a. In Figure Q23.9, what fraction of current I goes through the 3 ? resistor? b. If the 9 ? resistor is replaced with a larger resistor, will the fraction of current going through the 3 ? resistor increase, decrease, or stay the same?

Problem 9P The current in a circuit with only one battery is 2.0 A. Figure P23.9 shows how the potential changes when going around the circuit in the clockwise direction, starting from the lower left corner. Draw the circuit diagram.

Problem 10CQ Two of the three resistors in Figure Q23.10 are unknown but equal. Is the total resistance between points a and b less than, greater than, or equal to 50 ?? Explain.

Problem 10P What is the equivalent resistance of each group of resistors shown in Figure P23.10?

Problem 11CQ Two of the three resistors in Figure Q23.11 are unknown but equal. Is the total resistance between points a and b less than, greater than, or equal to 200 ?? Explain.

Problem 11P What is the equivalent resistance of each group of resistors shown in Figure P23.11?

Problem 12CQ Rank in order, from largest to smallest, the currents in the circuit diagram in Figure Q23.12.

Problem 12P An 80-cm-long wire is made by welding a 1.0-mm-diameter, 20-cm-long copper wire to a 1.0-mm-diameter, 60-cm-long iron wire. What is the resistance of the composite wire?

Problem 13CQ The three bulbs in Figure 13 are identical. Rank the bulbs from brightest to dimmest. Explain. FIGURE 13

Problem 13P You have a collection of 1.0 k? resistors. How can you connect four of them to produce an equivalent resistance of 0.25 k??

Problem 14CQ The four bulbs in Figure Q23.14 are identical. Rank the bulbs from brightest to dimmest. Explain.

Problem 14P You have a collection of six 1.0 k? resistors. What is the smallest resistance you can make by combining them?

Problem 15CQ Figure Q23.15 shows five identical bulbs connected to a battery. All the bulbs are glowing. Rank the bulbs from brightest to dimmest. Explain.

Problem 15P You have three 6.0 ? resistors and one 3.0 ? resistor. How can you connect them to produce an equivalent resistance of 5.0 ??

Problem 16CQ a. The three bulbs in Figure Q23.16 are identical. Rank the bulbs from brightest to dimmest. Explain. b. Suppose a wire is connected between points 1 and 2. What happens to each bulb? Does it get brighter, stay the same, get dimmer, or go out? Explain.

Problem 16P You have six 1.0 k? resistors. How can you connect them to produce a total equivalent resistance of 1.5 k??

Problem 17CQ Initially, bulbs A and B in Figure Q23.17 are both glowing. Bulb B is then removed from its socket. Does removing bulb B cause the potential difference between points 1 and 2 to increase, decrease, stay the same, or become zero? Explain.

Problem 17P What is the equivalent resistance between points a and b in Figure P23.17?

Problem 18CQ a. Consider the points a and b in Figure Q23.18. Is the potential difference between points a and b zero? If so, why? If not, which point is more positive? b. If a wire is connected between points a and b, does it carry a current? If so, in which direction—to the right or to the left? Explain.

Problem 18P What is the equivalent resistance between points a and b in Figure P23.18?

Problem 19CQ Initially the lightbulb in Figure 19 is glowing. It is then removed from its socket. a. What happens to the current I when the bulb is removed? Does it increase, stay the same, or decrease? Explain. ________________ b. What happens to the potential difference ?V12 between points 1 and 2? Does it increase, stay the same, decrease or become zero? Explain.

Problem 19P The currents in two resistors in a circuit are shown in Figure P23.19. What is the value of resistor R?

Problem 20CQ A voltmeter is (incorrectly) inserted into a circuit as shown in Figure Q23.20. a. What is the current in the circuit? b. What does the voltmeter read? c. How would you change the circuit to correctly connect the voltmeter to measure the potential difference across the resistor?

Problem 20P Two batteries supply current to the circuit in Figure P23.20. The figure shows the potential difference across two of the resistors and the value of the third resistor. What current is supplied by the batteries?

Problem 21P Part of a circuit is shown in Figure P23.21. a. What is the current through the 3.0 ? resistor? b. What is the value of the current I?

Problem 21P Part of a circuit is shown in Figure P23.21. a. What is the current through the 3.0 ? resistor? b. What is the value of the current I?

Problem 22CQ Rank in order, from largest to smallest, the equivalent capacitances of the four groups of capacitors shown in Figure Q23.22.

Problem 22P What is the value of resistor R in Figure P23.22?

Problem 23CQ Figure Q23.23 shows a circuit consisting of a battery, a switch, two identical lightbulbs, and a capacitor that is initially uncharged. a. Immediately after the switch is closed, are either or both bulbs glowing? Explain. b. If both bulbs are glowing, which is brighter? Or are they equally bright? Explain. c. For any bulb (A or B or both) that lights up immediately after the switch is closed, does its brightness increase with time, decrease with time, or remain unchanged? Explain.

Problem 23P What are the resistances R and the emf of the battery in Figure P23.23?

Problem 24CQ Figure Q23.24 shows the voltage as a function of time across a capacitor as it is discharged (separately) through three different resistors. Rank in order, from largest to smallest, the values of the resistances .

Problem 25 CQ A charged capacitor could be connected to two identical resistors in either of the two ways shown in Figure Q23.25. Which configuration will discharge the capacitor in the shortest time once the switch is closed? Explain.

Problem 24P The ammeter in Figure P23.24 reads 3.0 A. Find .

Problem 26CQ A flashing light is controlled by the charging and discharging of an RC circuit. If the light is flashing too rapidly, describe two changes that you could make to the circuit to reduce the flash rate.

Problem 26P Find the current through and the potential difference across each resistor in Figure P23.26.

Problem 28CQ Consider the model of nerve conduction in myelinated axons presented in the chapter. Suppose the distance between the nodes of Ranvier was halved for a particular axon. a. How would this affect the resistance and the capacitance of one segment of the axon? b. How would this affect the time constant for the charging of one segment? c. How would this affect the signal propagation speed for the axon?

Problem 28P Consider the potential differences between pairs of points in Figure P23.28. What are the magnitudes of the potential differences ?

Problem 29CQ Adding a myelin sheath to an axon results in faster signal propagation. It also means that less energy is required for a signal to propagate down the axon. Explain why this is so.

Problem 29P For the circuit shown in Figure P23.29, find the current through and the potential difference across each resistor. Place your results in a table for ease of reading.

Problem 30MCQ What is the current in the circuit of Figure Q23.30? A. 1.0 A B. 1.7 A C. 2.5 A D. 4.2 A

Problem 31MCQ Which resistor in Figure Q23.30 dissipates the most power? A. The 4.0 ? resistor. B. The 6.0 ? resistor. C. Both dissipate the same power.

Problem 30P A photoresistor, whose resistance decreases with light intensity, is connected in the circuit of Figure P23.30. On a sunny day, the photoresistor has a resistance of 0.56 k?. On a cloudy day, the resistance rises to 4.0 k?. At night, the resistance is 20 k?. a. What does the voltmeter read for each of these conditions? b. Does the voltmeter reading increase or decrease as the light intensity increases?

Problem 31P A photoresistor, whose resistance decreases with light intensity, is connected in the circuit of Figure 31. a. Draw a circuit diagram to illustrate how you would use a voltmeter and an ammeter to determine the resistance of the photoresistor in this circuit. ________________ b. What do the two meters read when the resistance of the photoresistor is 2.5 k??

Problem 32MCQ Normally, household lightbulbs are connected in parallel to a power supply. Suppose a 40 W and a 60 W lightbulb are, instead, connected in series, as shown in Figure Q23.32. Which bulb is brighter? A. The 60 W bulb. B. The 40 W bulb. C. The bulbs are equally bright.

Problem 33MCQ A metal wire of resistance R is cut into two pieces of equal length. The two pieces are connected together side by side. What is the resistance of the two connected wires?

Problem 33P A 6.0 ?F capacitor, a 10 ?F capacitor, and a 16 ?F capacitor are connected in series. What is their equivalent capacitance?

Problem 35MCQ Two capacitors are connected in series. They are then reconnected to be in parallel. The capacitance of the parallel combination A. Is less than that of the series combination. B. Is more than that of the series combination. C. Is the same as that of the series combination. D. Could be more or less than that of the series combination depending on the values of the capacitances.

Problem 35P You need a capacitance of 50 ?F, but you don’t happen to have a 50 ?F capacitor. You do have a 75 ?F capacitor. What additional capacitor do you need to produce a total capacitance of 50 ?F? Should you join the two capacitors in parallel or in series?

Problem 36MCQ If a cell’s membrane thickness doubles but the cell stays the same size, how do the resistance and the capacitance of the cell membrane change? A. The resistance and the capacitance increase. B. The resistance increases, the capacitance decreases. C. The resistance decreases, the capacitance increases. D. The resistance and the capacitance decrease.

Problem 36P What is the equivalent capacitance of the three capacitors in Figure P23.36?

Problem 37MCQ If a cell’s diameter is reduced by 50% without changing the membrane thickness, how do the resistance and capacitance of the cell membrane change? A. The resistance and the capacitance increase. B. The resistance increases, the capacitance decreases. C. The resistance decreases, the capacitance increases. D. The resistance and the capacitance decrease.

Problem 37P What is the equivalent capacitance of the three capacitors in Figure P23.37?

Problem 38P For the circuit of Figure P23.38, a. What is the equivalent capacitance? b. How much charge flows through the battery as the capacitors are being charged?

Problem 40P What is the time constant for the discharge of the capacitor in Figure P23.40?

Problem 41P What is the time constant for the discharge of the capacitor in Figure P23.41?

Problem 42P Capacitors won’t hold a charge indefinitely; as time goes on. charge gradually migrates from the positive to the negative plate. We can model this as a discharge of the capacitor through an internal “leakage resistance.” A 0.47 F capacitor charged to 2.5 V will initially discharge with a leakage current of 0.25 mA. a. What is the leakage resistance? ________________ b. How long will it take for the capacitor voltage to drop to 1.0 V?

Problem 43P A 10 ?F capacitor initially charged to 20 ?C is discharged through a 1.0 k? resistor. How long does it take to reduce the capacitor’s charge to 10 ?C?

Problem 44P The switch in Figure P23.45 has been in position a for a long time. It is changed to position b at t = 0 s. What are the charge Q on the capacitor and the current I through the resistor (a) immediately after the switch is closed? (b) At t = 50 ?s? (c) At t = 200 ?s?

Problem 45P A 9.0-nm-thick cell membrane undergoes an action potential that follows the curve in the table on page 748. What is the strength of the electric field inside the membrane just before the action potential and at the peak of the depolarization?

Problem 46P A cell membrane has a resistance and a capacitance and thus a characteristic time constant. What is the time constant of a 9.0-nmthick membrane surrounding a 0.040-mm-diameter spherical cell?

Problem 47P Changing the thickness of the myelin sheath surrounding an axon changes its capacitance and thus the conduction speed. A myelinated nerve fiber has a conduction speed of 55 m/s. If the spacing between nodes is 1.0 mm and the resistance of segments between nodes is 25 M?, what is the capacitance of each segment?

Problem 48P A particular myelinated axon has nodes spaced 0.80 mm apart. The resistance between nodes is 20 M?; the capacitance of each insulated segment is 1.2 pF. What is the conduction speed of a nerve impulse along this axon?

Problem 49P To measure signal propagation in a nerve in the arm, the nerve is triggered near the armpit. The peak of the action potential is measured at the elbow and then, 4.0 ms later, 24 cm away from the elbow at the wrist. a. What is the speed of propagation along this nerve? b. A determination of the speed made by measuring the time between the application of a stimulus at the armpit and the peak of an action potential at the elbow or the wrist would be inaccurate. Explain the problem with this approach, and why the noted technique is preferable.

Problem 50P A myelinated axon conducts nerve impulses at a speed of 40 m/s. What is the signal speed if the thickness of the myelin sheath is halved but no other changes are made to the axon?

Problem 51GP How much power is dissipated by each resistor in Figure P23.52?

Problem 52GP Two 75 W (120 V) lightbulbs are wired in series, then the combination is connected to a 120 V supply. How much power is dissipated by each bulb?

Problem 53GP The corroded contacts in a lightbulb socket have 5.0 ? total resistance. How much actual power is dissipated by a 100 W (120V) lightbulb screwed into this socket?

Problem 54GP A real battery is not just an emf. We can model a real 1.5 V battery as a 1.5 V emf in series with a resistor known as the “internal resistance,” as shown in Figure P23.55. A typical battery has 1.0 ? internal resistance due to imperfections that limit current through the battery. When there’s no current through the battery, and thus no voltage drop across the internal resistance, the potential difference between its terminals is 1.5 V, the value of the emf. Suppose the terminals of this battery are connected to a 2.0 ? resistor. a. What is the potential difference between the terminals of the battery? b. What fraction of the battery’s power is dissipated by the internal resistance?

Problem 55GP For the real battery shown in Figure P23.55, calculate the power dissipated by a resistor R connected to the battery when (a) R = 0.25 ?, (b) R = 0.50 ?, (c) R = 1.0 ?, (d) R = 2.0 ?, and (e) R = 4.0 ?. (Your results should suggest that maximum power dissipation is achieved when the external resistance R equals the internal resistance. This is true in general.)

Problem 56GP Batteries are recharged by connecting them to a power supply (i.e., another battery) of greater emf in such a way that the current flows into the positive terminal of the battery being recharged, as was shown in Example 23.1. This reverse current through the battery replenishes its chemicals. The current is kept fairly low so as not to overheat the battery being recharged by dissipating energy in its internal resistance. a. Suppose the real battery of Figure P23.55 is rechargeable. What emf power supply should be used for a 0.75 A recharging current? b. If this power supply charges the battery for 10 minutes, how much energy goes into the battery? How much is dissipated as thermal energy in the internal resistance?

Problem 57GP When two resistors are connected in parallel across a battery of unknown voltage, one resistor carries a current of 3.2 A while the second carries a current of 1.8 A. What current will be supplied by the same battery if these two resistors are connected to it in series?

Problem 58GP The 10 ? resistor in Figure P23.59 is dissipating 40 W of power. How much power are the other two resistors dissipating?

Problem 59GP At this instant, the current in the circuit of Figure P23.60 is 20 mA in the direction shown and the capacitor charge is 200 ?C. What is the resistance R?

Problem 60GP What is the equivalent resistance between points a and b in Figure P23.61?

Problem 61GP You have three 12 ? resistors. Draw diagrams showing how you could arrange all three so that their equivalent resistance is (a) 4.0 ?, (b) 8.0 ?, (c) 18 ?, and (d) 36 ?.

Problem 62GP A 9.0 V battery is connected to a wire made of three segments of different metals connected one after another: 10 cm of copper wire, then 12 cm of iron wire, then 18 cm of tungsten wire. All of the wires are 0.26 mm in diameter. Find the potential difference across each piece of wire.

Problem 63GP You have a device that needs a voltage reference of 3.0 V, but you have only a 9.0 V battery. Fortunately, you also have several 10 k? resistors. Show how you can use the resistors and the battery to make a circuit that provides a potential difference of 3.0 V.

Problem 64GP There is a current of 0.25 A in the circuit of Figure P23.65. a. What is the direction of the current? Explain. b. What is the value of the resistance R? c. What is the power dissipated by R? d. Make a graph of potential versus position, starting from V = 0 V in the lower left corner and proceeding clockwise. See Figure P23.9 for an example.

Problem 65GP A circuit you’re building needs an ammeter that goes from 0 mA to a full-scale reading of 50.0 mA. Unfortunately, the only ammeter in the storeroom goes from 0 ?A to a fullscale reading of only 500 ?A. Fortunately, you can make this ammeter work by putting it in a measuring circuit, as shown in Figure P23.66. This lets a certain fraction of the current pass through the meter; knowing this value, you can deduce the total current. Assume that the ammeter is ideal. a. What value of R must you use so that the meter will go to full scale when the current I is 50.0 mA? Hint: When I = 50.0 mA, the ammeter should be reading its maximum value. b. What is the equivalent resistance of your measuring circuit?

Problem 66GP A circuit you’re building needs a voltmeter that goes from 0 V to a full-scale reading of 5.0 V. Unfortunately, the only meter in the storeroom is an ammeter that goes from 0 ?A to a full-scale reading of 500 ?A. It is possible to use this meter to measure voltages by putting it in a measuring circuit as shown in Figure P23.67. What value of R must you use so that the meter will go to full scale when the potential difference ?V is 5.0 V? Assume that the ammeter is ideal.

Problem 67GP A circuit you’re building needs a voltmeter that goes from 0 V to a full-scale reading of 5.0 V. Unfortunately, the only meter in the storeroom is an ammeter that goes from 0 ?A to a full-scale reading of 500 ?A. It is possible to use this meter to measure voltages by putting it in a measuring circuit as shown in Figure P23.67. What value of R must you use so that the meter will go to full scale when the potential difference ?V is 5.0 V? Assume that the ammeter is ideal.

Problem 68GP You have three 12 ?F capacitors. Draw diagrams showing how you could arrange all three so that their equivalent capacitance is (a) 4.0 ?F, (b) 8.0 ?F, (c) 18 ?F, and (d) 36 ?F.

Problem 69GP Initially, the switch in Figure P23.70 is in position a and capacitors are uncharged. Then the switch is flipped to position b. Afterward, what are the charge on and the potential difference across each capacitor?

Problem 70GP The capacitor in an RC circuit with a time constant of 15 ms is charged to 10 V. The capacitor begins to discharge at t = 0 s. a. At what time will the charge on the capacitor be reduced to half its initial value? b. At what time will the energy stored in the capacitor be reduced to half its initial value?

Problem 71GP What value resistor will discharge a 1.0 ?F capacitor to 10% of its initial charge in 2.0 ms?

Problem 72GP The charging circuit for the flash system of a camera uses a 100 ?F capacitor that is charged from a 250 V power supply. What is the most resistance that can be in series with the capacitor if the capacitor is to charge to at least 87% of its final voltage in no more than 8.0 s?

Problem 73GP A capacitor is discharged through a 100 ? resistor. The discharge current decreases to 25% of its initial value in 2.5 ms. What is the value of the capacitor?

Problem 74GP A 50 ?F capacitor that had been charged to 30 V is discharged through a resistor. Figure P23.76 shows the capacitor voltage as a function of time. What is the value of the resistance?

Problem 75GP The switch in Figure P23.77 has been closed for a very long time. a. What is the charge on the capacitor? b. The switch is opened at t = 0 s. At what time has the charge on the capacitor decreased to 10% of its initial value?

Problem 76GP Intermittent windshield wipers use a variable resistor in an RC circuit to set the delay between successive passes of the wipers. A typical circuit is shown in Figure P23.78. When the switch closes, the capacitor (initially uncharged) begins to charge and the potential at point b begins to increase. A sensor measures the potential difference between points a and b, triggering a pass of the wipers when . (Another part of the circuit, not shown, discharges the capacitor at this time so that the cycle can start again.) a. What value of the variable resistor will give 12 seconds from the start of a cycle to a pass of the wipers? b. To decrease the time, should the variable resistance be increased or decreased?

Problem 77GP In Example 23.14 we estimated the capacitance of the cell membrane to be 89 pF, and in Example 23.15 we found that approximately 10,000 ions flow through an ion channel when it opens. Based on this information and what you learned in this chapter about the action potential, estimate the total number of sodium ion channels in the membrane of a nerve cell.

Problem 78GP The giant axon of a squid is 0.5 mm in diameter, 10 cm long, and not myelinated. Unmyelinated cell membranes behave as capacitors with 1 ?F of capacitance per square centimeter of membrane area. When the axon is charged to the -70 mV resting potential, what is the energy stored in this capacitance?

Problem 79GP A cell has a 7.0-nm-thick membrane with a total membrane area of . a. We can model the cell as a capacitor, as we have seen. What is the magnitude of the charge on each “plate” when the membrane is at its resting potential of -70 mV? b. How many sodium ions does this charge correspond to?

Problem 80PP The Defibrillator A defibrillator is designed to pass a large current through a patient’s torso in order to stop dangerous heart rhythms. Its key part is a capacitor that is charged to a high voltage. The patient’s torso plays the role of a resistor in an RC circuit. When a switch is closed, the capacitor discharges through the patient’s torso. A jolt from a defibrillator is intended to be intense and rapid; the maximum current is very large, so the capacitor discharges quickly. This rapid pulse depolarizes the heart, stopping all electrical activity. This allows the heart’s internal nerve circuitry to reestablish a healthy rhythm. A typical defibrillator has a 32 ?F capacitor charged to 5000 V. The electrodes connected to the patient are coated with a conducting gel that reduces the resistance of the skin to where the effective resistance of the patient’s torso is 100 ?. Which pair of graphs in Figure P23.82 best represents the capacitor voltage and the current through the torso as a function of time after the switch is closed?

Problem 81PP The Defibrillator A defibrillator is designed to pass a large current through a patient’s torso in order to stop dangerous heart rhythms. Its key part is a capacitor that is charged to a high voltage. The patient’s torso plays the role of a resistor in an RC circuit. When a switch is closed, the capacitor discharges through the patient’s torso. A jolt from a defibrillator is intended to be intense and rapid; the maximum current is very large, so the capacitor discharges quickly. This rapid pulse depolarizes the heart, stopping all electrical activity. This allows the heart’s internal nerve circuitry to reestablish a healthy rhythm. A typical defibrillator has a 32 ?F capacitor charged to 5000 V. The electrodes connected to the patient are coated with a conducting gel that reduces the resistance of the skin to where the effective resistance of the patient’s torso is 100 ?. For the values noted in the passage above, what is the time constant for the discharge of the capacitor? A. 3.2 ms B. 160 ms C. 3.2 ms D. 160 ms

Problem 82PP The Defibrillator A defibrillator is designed to pass a large current through a patient’s torso in order to stop dangerous heart rhythms. Its key part is a capacitor that is charged to a high voltage. The patient’s torso plays the role of a resistor in an RC circuit. When a switch is closed, the capacitor discharges through the patient’s torso. A jolt from a defibrillator is intended to be intense and rapid; the maximum current is very large, so the capacitor discharges quickly. This rapid pulse depolarizes the heart, stopping all electrical activity. This allows the heart’s internal nerve circuitry to reestablish a healthy rhythm. A typical defibrillator has a 32 ?F capacitor charged to 5000 V. The electrodes connected to the patient are coated with a conducting gel that reduces the resistance of the skin to where the effective resistance of the patient’s torso is 100 ?. If a patient receives a series of jolts, the resistance of the torso may increase. How does such a change affect the initial current and the time constant of subsequent jolts? A. The initial current and the time constant both increase. B. The initial current decreases, the time constant increases. C. The initial current increases, the time constant decreases. D. The initial current and the time constant both decrease.

Problem 83PP The Defibrillator A defibrillator is designed to pass a large current through a patient’s torso in order to stop dangerous heart rhythms. Its key part is a capacitor that is charged to a high voltage. The patient’s torso plays the role of a resistor in an RC circuit. When a switch is closed, the capacitor discharges through the patient’s torso. A jolt from a defibrillator is intended to be intense and rapid; the maximum current is very large, so the capacitor discharges quickly. This rapid pulse depolarizes the heart, stopping all electrical activity. This allows the heart’s internal nerve circuitry to reestablish a healthy rhythm. A typical defibrillator has a 32 ?F capacitor charged to 5000 V. The electrodes connected to the patient are coated with a conducting gel that reduces the resistance of the skin to where the effective resistance of the patient’s torso is 100 ?. In some cases, the defibrillator may be charged to a lower voltage. How will this affect the time constant of the discharge? A. The time constant will increase. B. The time constant will not change. C. The time constant will decrease.

Problem 84PP Electric Fish The voltage produced by a single nerve or muscle cell is quite small, but there are many species of fish that use multiple action potentials in series to produce significant voltages. The electric organs in these fish are composed of specialized disk-shaped cells called electrocytes. The cell at rest has the usual potential difference between the inside and the outside, but the net potential difference across the cell is zero. An electrocyte is connected to nerve fibers that initially trigger a depolarization in one side of the cell but not the other. For the very short time of this depolarization, there is a net potential difference across the cell, as shown in Figure P23.86. Stacks of these cells connected in series can produce a large total voltage. Each stack can produce a small current; for more total current, more stacks are needed, connected in parallel. In an electric eel, each electrocyte can develop a voltage of 150 mV for a short time. For a total voltage of 450 V, how many electrocytes must be connected in series? A. 300 B. 450 C. 1500 D. 3000

Problem 85PP Electric Fish The voltage produced by a single nerve or muscle cell is quite small, but there are many species of fish that use multiple action potentials in series to produce significant voltages. The electric organs in these fish are composed of specialized disk-shaped cells called electrocytes. The cell at rest has the usual potential difference between the inside and the outside, but the net potential difference across the cell is zero. An electrocyte is connected to nerve fibers that initially trigger a depolarization in one side of the cell but not the other. For the very short time of this depolarization, there is a net potential difference across the cell, as shown in Figure P23.86. Stacks of these cells connected in series can produce a large total voltage. Each stack can produce a small current; for more total current, more stacks are needed, connected in parallel. An electric eel produces a pulse of current of 0.80 A at a voltage of 500 V. For the short time of the pulse, what is the instantaneous power? A. 400 W B. 500 W C. 625 W D. 800 W

Problem 86PP Electric Fish The voltage produced by a single nerve or muscle cell is quite small, but there are many species of fish that use multiple action potentials in series to produce significant voltages. The electric organs in these fish are composed of specialized disk-shaped cells called electrocytes. The cell at rest has the usual potential difference between the inside and the outside, but the net potential difference across the cell is zero. An electrocyte is connected to nerve fibers that initially trigger a depolarization in one side of the cell but not the other. For the very short time of this depolarization, there is a net potential difference across the cell, as shown in Figure P23.86. Stacks of these cells connected in series can produce a large total voltage. Each stack can produce a small current; for more total current, more stacks are needed, connected in parallel. Electric eels live in fresh water. The torpedo ray is an electric fish that lives in salt water. The electrocytes in the ray are grouped differently than in the eel; each stack of electrocytes has fewer cells, but there are more stacks in parallel. Which of the following best explains the ray’s electrocyte arrangement? A. The lower resistivity of salt water requires more current but lower voltage. B. The lower resistivity of salt water requires more voltage but lower current. C. The higher resistivity of salt water requires more current but lower voltage. D. The higher resistivity of salt water requires more voltage but lower current.

Problem 87PP Electric Fish The voltage produced by a single nerve or muscle cell is quite small, but there are many species of fish that use multiple action potentials in series to produce significant voltages. The electric organs in these fish are composed of specialized disk-shaped cells called electrocytes. The cell at rest has the usual potential difference between the inside and the outside, but the net potential difference across the cell is zero. An electrocyte is connected to nerve fibers that initially trigger a depolarization in one side of the cell but not the other. For the very short time of this depolarization, there is a net potential difference across the cell, as shown in Figure P23.86. Stacks of these cells connected in series can produce a large total voltage. Each stack can produce a small current; for more total current, more stacks are needed, connected in parallel. The electric catfish is another electric fish that produces a voltage pulse by means of stacks of electrocytes. As the fish grows in length, the magnitude of the voltage pulse the fish produces grows as well. The best explanation for this change is that, as the fish grows, A. The voltage produced by each electrocyte increases. B. More electrocytes are added to each stack. C. More stacks of electrocytes are added in parallel to the existing stacks. D. The thickness of the electrocytes increases.