Problems

Note to Instructors: Most of the homework problems in this chapter are available for assignment via an online homework management program such as WileyPLUS or WebAssign, and those marked with the icon are presented in a guided tutorial format that provides enhanced interactivity. See Preface for additional details.
Note: For problems that involve ac conditions, the current and voltage are rms values and the power is an average value, unless indicated otherwise.
ssm Solution is in the Student Solutions Manual.
WWW Solution is available on the World Wide Web at
This icon represents a biomedical application.
Section 20.1 Electromotive Force and Current,
Section 20.2 Ohm’s Law

| 1 | A lightning bolt delivers a charge of 35 C to the ground in a time of . What is the current?

| 2 | A defibrillator is used during a heart attack to restore the heart to its normal beating pattern (see Section 19.5). A defibrillator passes 18 A of current through the torso of a person in 2.0 ms. (a) How much charge moves during this time? (b) How many electrons pass through the wires connected to the patient?

| 3 | A battery charger is connected to a dead battery and delivers a current of 6.0 A for 5.0 hours, keeping the voltage across the battery terminals at 12 V in the process. How much energy is delivered to the battery?

| 4 | Suppose that the resistance between the walls of a biological cell is . (a) What is the current when the potential difference between the walls is 75 mV? (b) If the current is composed of Na+ ions (q = +e), how many such ions flow in 0.50 s?

| 5 | ssm The heating element of a clothes dryer has a resistance of 11 Ω and is connected across a 240-V electrical outlet. What is the current in the heating element?

* | 6 | A resistor is connected across the terminals of a 9.0-V battery, which delivers of energy to the resistor in six hours. What is the resistance of the resistor?

* | 7 | The resistance of a bagel toaster is . To prepare a bagel, the toaster is operated for one minute from a 120-V outlet. How much energy is delivered to the toaster?

* | 8 | A car battery has a rating of 220 ampere · hours (A · h). This rating is one indication of the total charge that the battery can provide to a circuit before failing. (a) What is the total charge (in coulombs) that this battery can provide? (b) Determine the maximum current that the battery can provide for 38 minutes.

** | 9 | ssm A beam of protons is moving toward a target in a particle accelerator. This beam constitutes a current whose value is . (a) How many protons strike the target in 15 s? (b) Each proton has a kinetic energy of . Suppose the target is a 15-gram block of aluminum, and all the kinetic energy of the protons goes into heating it up. What is the change in temperature of the block that results from the 15-s bombardment of protons?
Section 20.3 Resistance and Resistivity

| 10 | Two wires are identical, except that one is aluminum and one is copper. The aluminum wire has a resistance of . What is the resistance of the copper wire?

| 11 | A cylindrical copper cable carries a current of 1200 A. There is a potential difference of between two points on the cable that are 0.24 m apart. What is the radius of the cable?

| 12 | High-voltage power lines are a familiar sight throughout the country. The aluminum wire used for some of these lines has a cross-sectional area of . What is the resistance of ten kilometers of this wire?

| 13 | ssm www Two wires have the same length and the same resistance. One is made from aluminum and the other from copper. Obtain the ratio of the cross-sectional area of the aluminum wire to that of the copper wire.

| 14 | A coil of wire has a resistance of at 25°C and at 55°C. What is the temperature coefficient of resistivity?

| 15 | A wire of unknown composition has a resistance of when immersed in water at 20.0°C. When the wire is placed in boiling water, its resistance rises to . What is the temperature on a hot summer day when the wire has a resistance of ?

* | 16 | The temperature coefficient of resistivity for the metal gold is 0.0034 (C°)−1, and for tungsten it is 0.0045 (C°)−1. The resistance of a gold wire increases by 7.0% due to an increase in temperature. For the same increase in temperature, what is the percentage increase in the resistance of a tungsten wire?

* | 17 | A toaster uses a Nichrome heating wire. When the toaster is turned on at 20°C, the initial current is 1.50 A. A few seconds later, the toaster warms up and the current now has a value of 1.30 A. The average temperature coefficient of resistivity for Nichrome wire is . What is the temperature of the heating wire?

* | 18 | The filament in an incandescent light bulb is made from tungsten. The light bulb is plugged into a 120-V outlet and draws a current of 1.24 A. If the radius of the tungsten wire is 0.0030 mm, how long must the wire be?

* | 19 | ssm www Two wires have the same cross-sectional area and are joined end to end to form a single wire. One is tungsten, which has a temperature coefficient of resistivity of . The other is carbon, for which . The total resistance of the composite wire is the sum of the resistances of the pieces. The total resistance of the composite does not change with temperature. What is the ratio of the lengths of the tungsten and carbon sections? Ignore any changes in length due to thermal expansion.

** | 20 | A digital thermometer employs a thermistor as the temperature-sensing element. A thermistor is a kind of semiconductor and has a large negative temperature coefficient of resistivity . Suppose for the thermistor in a digital thermometer used to measure the temperature of a patient. The resistance of the thermistor decreases to 85% of its value at the normal body temperature of 37.0°C. What is the patient’s temperature?
Section 20.4 Electric Power

| 21 | The heating element in an iron has a resistance of . The iron is plugged into a 120-V outlet. What is the power delivered to the iron?

| 22 | A portable CD player operates with a voltage of 4.5 V, and its power usage is 0.11 W. Find the current in the player.

| 23 | A blow-dryer and a vacuum cleaner each operate with a voltage of 120 V. The current rating of the blow-dryer is 11 A, and that of the vacuum cleaner is 4.0 A. Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 15 minutes to the energy used by the vacuum cleaner in one-half hour.

| 24 | There are approximately 110 million TVs in the United States. Each uses, on average, 75 W of power and is turned on for 6.0 hours a day. If electrical energy costs $0.12 per kWh, how much money is spent every day in keeping the TVs turned on?

| 25 | ssm In doing a load of clothes, a clothes dryer uses 16 A of current at 240 V for 45 min. A personal computer, in contrast, uses 2.7 A of current at 120 V. With the energy used by the clothes dryer, how long (in hours) could you use this computer to “surf” the Internet?

* | 26 | A piece of Nichrome wire has a radius of . It is used in a laboratory to make a heater that uses of power when connected to a voltage source of 120 V. Ignoring the effect of temperature on resistance, estimate the necessary length of wire.

* | 27 | ssm Tungsten has a temperature coefficient of resistivity of 0.0045 (C°)−1. A tungsten wire is connected to a source of constant voltage via a switch. At the instant the switch is closed, the temperature of the wire is 28°C, and the initial power delivered to the wire is P0. At what wire temperature will the power that is delivered to the wire be decreased to ?

* | 28 | An electric heater is used to boil small amounts of water and consists of a coil that is immersed directly in the water. It operates from a 120-V socket. How much time is required for this heater to raise the temperature of 0.50 kg of water from 13°C to the normal boiling point?

* | 29 | An iron wire has a resistance of at 20.0°C and a mass of . A current of 0.10 A is sent through the wire for one minute and causes the wire to become hot. Assuming that all the electrical energy is delivered to the wire and remains there, find the final temperature of the wire. [Hint: Use the average resistance of the wire during the heating process, and see Table 12.2 for the specific heat capacity of iron. Note that .]
Section 20.5 Alternating Current

| 30 | According to Equation 20.7, an ac voltage V is given as a function of time t by , where V0 is the peak voltage and f is the frequency (in hertz). For a frequency of 60.0 Hz, what is the smallest value of the time at which the voltage equals one-half of the peak value?

| 31 | The current in a circuit is ac and has a peak value of 2.50 A. Determine the rms current.

| 32 | The rms current in a copy machine is 6.50 A, and the resistance of the machine is . What is (a) the average power and (b) the peak power delivered to the machine?

| 33 | ssm The average power used by a stereo speaker is 55 W. Assuming that the speaker can be treated as a resistance, find the peak value of the ac voltage applied to the speaker.

| 34 | Review Conceptual Example 7 as an aid in solving this problem. A portable electric heater uses 18 A of current. The manufacturer recommends that an extension cord attached to the heater receive no more than 2.0 W of power per meter of length. What is the smallest radius of copper wire that can be used in the extension cord? (Note: An extension cord contains two wires.)

| 35 | An electric furnace runs nine hours a day to heat a house during January (31 days). The heating element has a resistance of and carries a current of 25 A. The cost of electricity is $0.12/kWh. Find the cost of running the furnace for the month of January.

* | 36 | A light bulb is connected to a 120.0-V wall socket. The current in the bulb depends on the time t according to the relation I = (0.707 A) sin [(314 Hz)t]. (a) What is the frequency of the alternating current? (b) Determine the resistance of the bulb’s filament. (c) What is the average power delivered to the light bulb?

* | 37 | ssm The recovery time of a hot water heater is the time required to heat all the water in the unit to the desired temperature. Suppose that a 52-gal unit starts with cold water at 11°C and delivers hot water at 53°C. The unit is electric and utilizes a resistance heater (120 V ac, ) to heat the water. Assuming that no heat is lost to the environment, determine the recovery time (in hours) of the unit.

** | 38 | To save on heating costs, the owner of a greenhouse keeps 660 kg of water around in barrels. During a winter day, the water is heated by the sun to 10.0°C. During the night the water freezes into ice at 0.0 °C in nine hours. What is the minimum ampere rating of an electric heating system (240 V) that would provide the same heating effect as the water does?
Section 20.6 Series Wiring

| 39 | ssm The current in a series circuit is 15.0 A. When an additional resistor is inserted in series, the current drops to 12.0 A. What is the resistance in the original circuit?

| 40 | A 60.0-W lamp is placed in series with a resistor and a 120.0-V source. If the voltage across the lamp is 25 V, what is the resistance R of the resistor?

| 41 | A resistor and an resistor are connected in series across a 15.0-V battery. What is the voltage across (a) the resistor and (b) the resistor?

| 42 | The current in a resistor is 0.12 A. This resistor is in series with a resistor, and the series combination is connected across a battery. What is the battery voltage?

| 43 | ssm Three resistors, 25, 45, and , are connected in series, and a 0.51-A current passes through them. What is (a) the equivalent resistance and (b) the potential difference across the three resistors?

* | 44 | Multiple-Concept Example 9 reviews the concepts that are important to this problem. A light bulb is wired in series with a resistor, and they are connected across a 120.0-V source. The power delivered to the light bulb is 23.4 W. What is the resistance of the light bulb? Note that there are two possible answers.

* | 45 | ssm An extension cord is used with an electric weed trimmer that has a resistance of . The extension cord is made of copper wire that has a cross-sectional area of . The combined length of the two wires in the extension cord is 92 m. (a) Determine the resistance of the extension cord. (b) The extension cord is plugged into a 120-V socket. What voltage is applied to the trimmer itself?

* | 46 | Two cylindrical rods, one copper and the other iron, are identical in lengths and cross-sectional areas. They are joined end to end to form one long rod. A 12-V battery is connected across the free ends of the copper–iron rod. What is the voltage between the ends of the copper rod?

** | 47 | Two resistances, R1 and R2, are connected in series across a 12-V battery. The current increases by 0.20 A when R2 is removed, leaving R1 connected across the battery. However, the current increases by just 0.10 A when R1 is removed, leaving R2 connected across the battery. Find (a) R1 and (b) R2.
Section 20.7 Parallel Wiring

| 48 | What resistance must be placed in parallel with a 155-Ω resistor to make the equivalent resistance 115 Ω?

| 49 | ssm A loudspeaker and an loudspeaker are connected in parallel across the terminals of an amplifier. Assuming the speakers behave as resistors, determine the equivalent resistance of the two speakers.

| 50 | For the three-way bulb (50 W, 100 W, 150 W) discussed in Conceptual Example 11, find the resistance of each of the two filaments. Assume that the wattage ratings are not limited by significant figures and ignore any heating effects on the resistances.

| 51 | Help with problems of this kind is available in Interactive Solution 20.51 20.51 at . A coffee cup heater and a lamp are connected in parallel to the same 120-V outlet. Together, they use a total of 111 W of power. The resistance of the heater is . Find the resistance of the lamp.

| 52 | The drawing shows a circuit that contains a battery, two resistors, and a switch. What is the equivalent resistance of the circuit when the switch is (a) open and (b) closed? What is the total power delivered to the resistors when the switch is (c) open and (d) closed?

| 53 | ssm Two resistors, 42.0 and , are connected in parallel. The current through the resistor is 3.00 A. (a) Determine the current in the other resistor. (b) What is the total power supplied to the two resistors?

| 54 | A wire whose resistance is R is cut into three equally long pieces, which are then connected in parallel. In terms of R, what is the resistance of the parallel combination?

* | 55 | ssm The total current delivered to a number of devices connected in parallel is the sum of the individual currents in each device. Circuit breakers are resettable automatic switches that protect against a dangerously large total current by “opening” to stop the current at a specified safe value. A 1650-W toaster, a 1090-W iron, and a 1250-W microwave oven are turned on in a kitchen. As the drawing shows, they are all connected through a 20-A circuit breaker to an ac voltage of 120 V. (a) Find the equivalent resistance of the three devices. (b) Obtain the total current delivered by the source and determine whether the breaker will “open” to prevent an accident.

* | 56 | A cylindrical aluminum pipe of length 1.50 m has an inner radius of and an outer radius of . The interior of the pipe is completely filled with copper. What is the resistance of this unit? (Hint: Imagine that the pipe is connected between the terminals of a battery and decide whether the aluminum and copper parts of the pipe are in series or in parallel.)

** | 57 | The rear window defogger of a car consists of thirteen thin wires embedded in the glass. The wires are connected in parallel to the 12.0-V battery, and each has a length of 1.30 m. The defogger can melt of ice at 0 °C into water at 0 °C in two minutes. Assume that all the power delivered to the wires is used immediately to melt the ice. Find the cross-sectional area of each wire.
Section 20.8 Circuits Wired Partially in Series and Partially in Parallel

| 58 | Find the equivalent resistance between points A and B in the drawing.

| 59 | ssm A coffee maker and a frying pan are connected in series across a 120-V source of voltage. A bread maker is also connected across the 120-V source and is in parallel with the series combination. Find the total current supplied by the source of voltage.

| 60 | Find the equivalent resistance between the points A and B in the drawing.

| 61 | ssm Determine the equivalent resistance between the points A and B for the group of resistors in the drawing.

| 62 | A resistor is connected in parallel with a resistor. This parallel group is connected in series with a resistor. The total combination is connected across a 15.0-V battery. Find (a) the current and (b) the power delivered to the resistor.

* | 63 | The circuit in the drawing contains five identical resistors. The 45-V battery delivers 58 W of power to the circuit. What is the resistance R of each resistor?

* | 64 | Concept Simulation 20.5 at provides some background pertinent to this problem. Determine the power supplied to each of the resistors in the drawing.

* | 65 | ssm www The current in the resistor in the drawing is 0.500 A. Find the current in (a) the resistor and in (b) the resistor.

** | 66 | Three identical resistors are connected in parallel. The equivalent resistance increases by when one resistor is removed and connected in series with the remaining two, which are still in parallel. Find the resistance of each resistor. Section 20.9 Internal Resistance

| 67 | ssm A battery has an internal resistance of . A number of identical light bulbs, each with a resistance of , are connected in parallel across the battery terminals. The terminal voltage of the battery is observed to be one-half the emf of the battery. How many bulbs are connected?

| 68 | A battery has an internal resistance of and an emf of 9.00 V. What is the maximum current that can be drawn from the battery without the terminal voltage dropping below 8.90 V?

| 69 | A new “D” battery has an emf of 1.5 V. When a wire of negligible resistance is connected between the terminals of the battery, a current of 28 A is produced. Find the internal resistance of the battery.

| 70 | When a light bulb is connected across the terminals of a battery, the battery delivers 24 W of power to the bulb. A voltage of 11.8 V exists between the terminals of the battery, which has an internal resistance of . What is the emf of the battery?

* | 71 | A battery delivering a current of 55.0 A to a circuit has a terminal voltage of 23.4 V. The electric power being dissipated by the internal resistance of the battery is 34.0 W. Find the emf of the battery.

* | 72 | A resistor has a resistance R, and a battery has an internal resistance r. When the resistor is connected across the battery, ten percent less power is dissipated in R than would be dissipated if the battery had no internal resistance. Find the ratio r/R.
Section 20.10 Kirchhoff’s Rules

| 73 | Two batteries, each with an internal resistance of , are connected as in the drawing. In effect, the 9.0-V battery is being used to charge the 8.0-V battery. What is the current in the circuit?

| 74 | Interactive LearningWare 20.1 at provides background for this problem. Find the magnitude and direction of the current in the resistor in the drawing.

| 75 | ssm Consider the circuit in the drawing. Determine (a) the magnitude of the current in the circuit and (b) the magnitude of the voltage between the points labeled A and B. (c) State which point, A or B, is at the higher potential.

| 76 | Determine the current (magnitude and direction) in the 8.0- and resistors in the drawing.

* | 77 | ssm Determine the voltage across the resistor in the drawing. Which end of the resistor is at the higher potential?

* | 78 | Concept Simulation 20.3 at allows you to verify your answer for this problem. Find the current in the resistor in the drawing. Specify the direction of the current.

Problem 78

** | 79 | The circuit in the drawing is known as a Wheatstone bridge circuit. Find the voltage between points B and D, and state which point is at the higher potential.

Section 20.11 The Measurement of Current and Voltage

| 80 | The coil of wire in a galvanometer has a resistance of . The galvanometer exhibits a full-scale deflection when the current through it is 0.400 mA. A resistor is connected in series with this combination so as to produce a voltmeter. The voltmeter is to have a full-scale deflection when it measures a potential difference of 10.0 V. What is the resistance of this resistor?

| 81 | ssm A galvanometer has a full-scale current of 0.100 mA and a coil resistance of . This instrument is used with a shunt resistor to form an ammeter that will register full scale for a current of 60.0 mA. Determine the resistance of the shunt resistor.

| 82 | Voltmeter A has an equivalent resistance of and a full-scale voltage of 50.0 V. Voltmeter B, using the same galvanometer as voltmeter A, has an equivalent resistance of . What is its full-scale voltage?

| 83 | The coil of a galvanometer has a resistance of , and its meter deflects full scale when a current of 6.20 mA passes through it. To make the galvanometer into an ammeter, a shunt resistor is added to it. What is the maximum current that this ammeter can read?

* | 84 | Two scales on a voltmeter measure voltages up to 20.0 and 30.0 V, respectively. The resistance connected in series with the galvanometer is for the 20.0-V scale and for the 30.0-V scale. Determine the coil resistance and the full-scale current of the galvanometer that is used in the voltmeter.

** | 85 | ssm In measuring a voltage, a voltmeter uses some current from the circuit. Consequently, the voltage measured is only an approximation to the voltage present when the voltmeter is not connected. Consider a circuit consisting of two resistors connected in series across a 60.0-V battery. (a) Find the voltage across one of the resistors. (b) A voltmeter has a full-scale voltage of 60.0 V and uses a galvanometer with a full-scale deflection of 5.00 mA. Determine the voltage that this voltmeter registers when it is connected across the resistor used in part (a).
Section 20.12 Capacitors in Series and in Parallel

| 86 | Three capacitors (4.0, 6.0, and ) are connected in series across a 50.0-V battery. Find the voltage across the capacitor.

| 87 | Determine the equivalent capacitance between A and B for the group of capacitors in the drawing.

| 88 | Two capacitors are connected in parallel across the terminals of a battery. One has a capacitance of and the other a capacitance of . These two capacitors together store of charge. What is the voltage of the battery?

| 89 | ssm Three capacitors have identical geometries. One is filled with a material whose dielectric constant is 2.50. Another is filled with a material whose dielectric constant is 4.00. The third capacitor is filled with a material whose dielectric constant is such that this single capacitor has the same capacitance as the series combination of the other two. Determine .

| 90 | A and a capacitor are connected to a 60.0-V battery. What is the total charge supplied to the capacitors when they are wired (a) in parallel and (b) in series with each other?

| 91 | Suppose two capacitors (C1 and C2) are connected in series. Show that the sum of the energies stored in these capacitors is equal to the energy stored in the equivalent capacitor. [Hint: The energy stored in a capacitor can be expressed as q2/(2C).]

* | 92 | A and a capacitor are connected in series across a 30.0-V battery. A capacitor is then connected in parallel across the capacitor. Determine the voltage across the capacitor.

* | 93 | ssm A and a capacitor are connected in series across a 24-V battery. What voltage is required to charge a parallel combination of the two capacitors to the same total energy?

** | 94 | The drawing shows two fully charged capacitors . The switch is closed, and charge flows until equilibrium is reestablished (i.e., until both capacitors have the same voltage across their plates). Find the resulting voltage across either capacitor.

Section 20.13 RC Circuits

| 95 | ssm In a heart pacemaker, a pulse is delivered to the heart 81 times per minute. The capacitor that controls this pulsing rate discharges through a resistance of . One pulse is delivered every time the fully charged capacitor loses 63.2% of its original charge. What is the capacitance of the capacitor?

| 96 | An electronic flash attachment for a camera produces a flash by using the energy stored in a capacitor. Between flashes, the capacitor recharges through a resistor whose resistance is chosen so the capacitor recharges with a time constant of 3.0 s. Determine the value of the resistance.

| 97 | The circuit in the drawing contains two resistors and two capacitors that are connected to a battery via a switch. When the switch is closed, the capacitors begin to charge up. What is the time constant for the charging process?

* | 98 | Concept Simulation 20.4 at provides background for this problem and gives you the opportunity to verify your answer graphically. How many time constants must elapse before a capacitor in a series RC circuit is charged to 80.0% of its equilibrium charge?

* | 99 | For one approach to problems like this one, consult Interactive Solution 20.99 at . Four identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.72 s. What is the time constant when they are connected with the same resistor as in part b?

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.