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College Physics 2e

Problems & Exercises

College Physics 2eProblems & Exercises

21.1 Resistors in Series and Parallel

Note: Data taken from figures can be assumed to be accurate to three significant digits.

1.

(a) What is the resistance of ten 275-Ω275-Ω resistors connected in series? (b) In parallel?

2.

(a) What is the resistance of a 1.00×1021.00×102, a 2.50-kΩ2.50-kΩ, and a 4.00-kΩ4.00-kΩ resistor connected in series? (b) In parallel?

3.

What are the largest and smallest resistances you can obtain by connecting a 36.0-Ω36.0-Ω, a 50.0-Ω50.0-Ω, and a 700-Ω700-Ω resistor together?

4.

An 1800-W toaster, a 1400-W electric frying pan, and a 75-W lamp are plugged into the same outlet in a 15-A, 120-V circuit. (The three devices are in parallel when plugged into the same socket.). (a) What current is drawn by each device? (b) Will this combination blow the 15-A fuse?

5.

Your car’s 30.0-W headlight and 2.40-kW starter are ordinarily connected in parallel in a 12.0-V system. What power would one headlight and the starter consume if connected in series to a 12.0-V battery? (Neglect any other resistance in the circuit and any change in resistance in the two devices.)

6.

(a) Given a 48.0-V battery and 24.0-Ω24.0-Ω and 96.0-Ω96.0-Ω resistors, find the current and power for each when connected in series. (b) Repeat when the resistances are in parallel.

7.

Referring to the example combining series and parallel circuits and Figure 21.6, calculate I3I3 in the following two different ways: (a) from the known values of II and I2I2; (b) using Ohm’s law for R3R3. In both parts explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

8.

Referring to Figure 21.6: (a) Calculate P3P3 and note how it compares with P3P3 found in the first two example problems in this module. (b) Find the total power supplied by the source and compare it with the sum of the powers dissipated by the resistors.

9.

Refer to Figure 21.7 and the discussion of lights dimming when a heavy appliance comes on. (a) Given the voltage source is 120 V, the wire resistance is 0.400Ω0.400Ω, and the bulb is nominally 75.0 W, what power will the bulb dissipate if a total of 15.0 A passes through the wires when the motor comes on? Assume negligible change in bulb resistance. (b) What power is consumed by the motor?

10.

A 240-kV power transmission line carrying 5.00×102A5.00×102A is hung from grounded metal towers by ceramic insulators, each having a 1.00×1091.00×109 resistance. Figure 21.49. (a) What is the resistance to ground of 100 of these insulators? (b) Calculate the power dissipated by 100 of them. (c) What fraction of the power carried by the line is this? Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

The diagram shows a grounded metal transmission tower. Two ground conductors on top of the tower point out like antennas. Hanging from the tower are a set of three bundled conductors, one on either end and one in the middle.
Figure 21.49 High-voltage (240-kV) transmission line carrying 5.00×102A5.00×102A is hung from a grounded metal transmission tower. The row of ceramic insulators provide 1.00×109Ω1.00×109Ω of resistance each.
11.

Show that if two resistors R1R1 and R2R2 are combined and one is much greater than the other (R1>>R2R1>>R2): (a) Their series resistance is very nearly equal to the greater resistance R1R1. (b) Their parallel resistance is very nearly equal to smaller resistance R2R2.

12.

Unreasonable Results

Two resistors, one having a resistance of 145 Ω145 Ω, are connected in parallel to produce a total resistance of 150Ω150Ω. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

13.

Unreasonable Results

Two resistors, one having a resistance of 900 kΩ900 kΩ, are connected in series to produce a total resistance of 0.500 MΩ0.500 MΩ. (a) What is the value of the second resistance? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

21.2 Electromotive Force: Terminal Voltage

14.

Standard automobile batteries have six lead-acid cells in series, creating a total emf of 12.0 V. What is the emf of an individual lead-acid cell?

15.

Carbon-zinc dry cells (sometimes referred to as non-alkaline cells) have an emf of 1.54 V, and they are produced as single cells or in various combinations to form other voltages. (a) How many 1.54-V cells are needed to make the common 9-V battery used in many small electronic devices? (b) What is the actual emf of the approximately 9-V battery? (c) Discuss how internal resistance in the series connection of cells will affect the terminal voltage of this approximately 9-V battery.

16.

What is the output voltage of a 3.0000-V lithium cell in a digital wristwatch that draws 0.300 mA, if the cell’s internal resistance is 2.00Ω2.00Ω?

17.

(a) What is the terminal voltage of a large 1.54-V carbon-zinc dry cell used in a physics lab to supply 2.00 A to a circuit, if the cell’s internal resistance is 0.100 Ω0.100 Ω? (b) How much electrical power does the cell produce? (c) What power goes to its load?

18.

What is the internal resistance of an automobile battery that has an emf of 12.0 V and a terminal voltage of 15.0 V while a current of 8.00 A is charging it?

19.

(a) Find the terminal voltage of a 12.0-V motorcycle battery having a 0.600-Ω0.600-Ω internal resistance, if it is being charged by a current of 10.0 A. (b) What is the output voltage of the battery charger?

20.

A car battery with a 12-V emf and an internal resistance of 0.050Ω0.050Ω is being charged with a current of 60 A. Note that in this process the battery is being charged. (a) What is the potential difference across its terminals? (b) At what rate is thermal energy being dissipated in the battery? (c) At what rate is electric energy being converted to chemical energy? (d) What are the answers to (a) and (b) when the battery is used to supply 60 A to the starter motor?

21.

The hot resistance of a flashlight bulb is 2.30Ω2.30Ω, and it is run by a 1.58-V alkaline cell having a 0.100-Ω0.100-Ω internal resistance. (a) What current flows? (b) Calculate the power supplied to the bulb using I2RbulbI2Rbulb. (c) Is this power the same as calculated using V2RbulbV2Rbulb?

22.

The label on a portable radio recommends the use of rechargeable nickel-cadmium cells (nicads), although they have a 1.25-V emf while alkaline cells have a 1.58-V emf. The radio has a 3.20-Ω3.20-Ω resistance. (a) Draw a circuit diagram of the radio and its batteries. Now, calculate the power delivered to the radio. (b) When using Nicad cells each having an internal resistance of 0.0400 Ω0.0400 Ω. (c) When using alkaline cells each having an internal resistance of 0.200 Ω0.200 Ω. (d) Does this difference seem significant, considering that the radio’s effective resistance is lowered when its volume is turned up?

23.

An automobile starter motor has an equivalent resistance of 0.0500Ω0.0500Ω and is supplied by a 12.0-V battery with a 0.0100-Ω0.0100-Ω internal resistance. (a) What is the current to the motor? (b) What voltage is applied to it? (c) What power is supplied to the motor? (d) Repeat these calculations for when the battery connections are corroded and add 0.0900Ω0.0900Ω to the circuit. (Significant problems are caused by even small amounts of unwanted resistance in low-voltage, high-current applications.)

24.

A child’s electronic toy is supplied by three 1.58-V alkaline cells having internal resistances of 0.0200Ω0.0200Ω in series with a 1.53-V carbon-zinc dry cell having a 0.100-Ω0.100-Ω internal resistance. The load resistance is 10.0Ω10.0Ω. (a) Draw a circuit diagram of the toy and its batteries. (b) What current flows? (c) How much power is supplied to the load? (d) What is the internal resistance of the dry cell if it goes bad, resulting in only 0.500 W being supplied to the load?

25.

(a) What is the internal resistance of a voltage source if its terminal voltage drops by 2.00 V when the current supplied increases by 5.00 A? (b) Can the emf of the voltage source be found with the information supplied?

26.

A person with body resistance between his hands of 10.0 kΩ10.0 kΩ accidentally grasps the terminals of a 20.0-kV power supply. (Do NOT do this!) (a) Draw a circuit diagram to represent the situation. (b) If the internal resistance of the power supply is 2000Ω2000Ω, what is the current through his body? (c) What is the power dissipated in his body? (d) If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in this situation to be 1.00 mA or less? (e) Will this modification compromise the effectiveness of the power supply for driving low-resistance devices? Explain your reasoning.

27.

Electric fish generate current with biological cells called electroplaques, which are physiological emf devices. The electroplaques in the South American eel are arranged in 140 rows, each row stretching horizontally along the body and each containing 5000 electroplaques. Each electroplaque has an emf of 0.15 V and internal resistance of 0.25Ω0.25Ω. If the water surrounding the fish has resistance of 800Ω800Ω, how much current can the eel produce in water from near its head to near its tail?

28.

Integrated Concepts

A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in ºC/minºC/min) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300 kcal/kgºC0.300 kcal/kgºC, assuming no heat escapes?

29.

Unreasonable Results

A 1.58-V alkaline cell with a 0.200-Ω0.200-Ω internal resistance is supplying 8.50 A to a load. (a) What is its terminal voltage? (b) What is the value of the load resistance? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable or inconsistent?

30.

Unreasonable Results

(a) What is the internal resistance of a 1.54-V dry cell that supplies 1.00 W of power to a 15.0-Ω15.0-Ω bulb? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

21.3 Kirchhoff’s Rules

31.

Apply the loop rule to loop abcdefgha in Figure 21.25.

32.

Apply the loop rule to loop aedcba in Figure 21.25.

33.

Verify the second equation in Example 21.5 by substituting the values found for the currents I1I1 and I2I2.

34.

Verify the third equation in Example 21.5 by substituting the values found for the currents I1I1 and I3I3.

35.

Apply the junction rule at point a in Figure 21.50.

The diagram shows a complex circuit with four voltage sources E sub one, E sub two, E sub three, E sub four and several resistive loads, wired in two loops and many junctions. Several points on the diagram are marked with letters a through j. The current in each branch is labeled separately.
Figure 21.50
36.

Apply the loop rule to loop abcdefghija in Figure 21.50.

37.

Apply the loop rule to loop akledcba in Figure 21.50.

38.

Find the currents flowing in the circuit in Figure 21.50. Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

39.

Solve Example 21.5, but use loop abcdefgha instead of loop akledcba. Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors.

40.

Find the currents flowing in the circuit in Figure 21.45.

41.

Unreasonable Results

Consider the circuit in Figure 21.51, and suppose that the emfs are unknown and the currents are given to be I1=5.00 AI1=5.00 A, I2=3.0 AI2=3.0 A, and I3=–2.00 AI3=–2.00 A. (a) Could you find the emfs? (b) What is wrong with the assumptions?

The diagram shows a complex circuit with two voltage sources E sub one and E sub two, and three resistive loads, wired in two loops and two junctions. Several points on the diagram are marked with letters a through h. The current in each branch is labeled separately.
Figure 21.51

21.4 DC Voltmeters and Ammeters

42.

What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 1.00-MΩ1.00-MΩ resistance on its 30.0-V scale?

43.

What is the sensitivity of the galvanometer (that is, what current gives a full-scale deflection) inside a voltmeter that has a 25.0-kΩ25.0-kΩ resistance on its 100-V scale?

44.

Find the resistance that must be placed in series with a 25.0-Ω25.0-Ω galvanometer having a 50.0-μA50.0-μA sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 0.100-V full-scale reading.

45.

Find the resistance that must be placed in series with a 25.0-Ω25.0-Ω galvanometer having a 50.0-μA50.0-μA sensitivity (the same as the one discussed in the text) to allow it to be used as a voltmeter with a 3000-V full-scale reading. Include a circuit diagram with your solution.

46.

Find the resistance that must be placed in parallel with a 25.0-Ω25.0-Ω galvanometer having a 50.0-μA50.0-μA sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 10.0-A full-scale reading. Include a circuit diagram with your solution.

47.

Find the resistance that must be placed in parallel with a 25.0-Ω25.0-Ω galvanometer having a 50.0-μA50.0-μA sensitivity (the same as the one discussed in the text) to allow it to be used as an ammeter with a 300-mA full-scale reading.

48.

Find the resistance that must be placed in series with a 10.0-Ω10.0-Ω galvanometer having a 100-μA100-μA sensitivity to allow it to be used as a voltmeter with: (a) a 300-V full-scale reading, and (b) a 0.300-V full-scale reading.

49.

Find the resistance that must be placed in parallel with a 10.0-Ω10.0-Ω galvanometer having a 100-μA100-μA sensitivity to allow it to be used as an ammeter with: (a) a 20.0-A full-scale reading, and (b) a 100-mA full-scale reading.

50.

Suppose you measure the terminal voltage of a 1.585-V alkaline cell having an internal resistance of 0.100Ω0.100Ω by placing a 1.00-kΩ1.00-kΩ voltmeter across its terminals. (See Figure 21.52.) (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

The figure shows a circuit diagram that includes a battery with an internal resistance r and a voltmeter connected across its terminals. The current I is shown by an arrow pointing in a clockwise direction.
Figure 21.52
51.

Suppose you measure the terminal voltage of a 3.200-V lithium cell having an internal resistance of 5.00Ω5.00Ω by placing a 1.00-kΩ1.00-kΩ voltmeter across its terminals. (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

52.

A certain ammeter has a resistance of 5.00×105Ω5.00×105Ω on its 3.00-A scale and contains a 10.0-Ω10.0-Ω galvanometer. What is the sensitivity of the galvanometer?

53.

A 1.00-MΩ1.00-MΩ voltmeter is placed in parallel with a 75.0-kΩ75.0-kΩ resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) What is the resistance of the combination? (c) If the voltage across the combination is kept the same as it was across the 75.0-kΩ75.0-kΩ resistor alone, what is the percent increase in current? (d) If the current through the combination is kept the same as it was through the 75.0-kΩ75.0-kΩ resistor alone, what is the percentage decrease in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

54.

A 0.0200-Ω0.0200-Ω ammeter is placed in series with a 10.00-Ω10.00-Ω resistor in a circuit. (a) Draw a circuit diagram of the connection. (b) Calculate the resistance of the combination. (c) If the voltage is kept the same across the combination as it was through the 10.00-Ω10.00-Ω resistor alone, what is the percent decrease in current? (d) If the current is kept the same through the combination as it was through the 10.00-Ω10.00-Ω resistor alone, what is the percent increase in voltage? (e) Are the changes found in parts (c) and (d) significant? Discuss.

55.

Unreasonable Results

Suppose you have a 40.0-Ω40.0-Ω galvanometer with a 25.0-μA25.0-μA sensitivity. (a) What resistance would you put in series with it to allow it to be used as a voltmeter that has a full-scale deflection for 0.500 mV? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

56.

Unreasonable Results

(a) What resistance would you put in parallel with a 40.0-Ω40.0-Ω galvanometer having a 25.0-μA25.0-μA sensitivity to allow it to be used as an ammeter that has a full-scale deflection for 10.0-μA 10.0-μA? (b) What is unreasonable about this result? (c) Which assumptions are responsible?

21.5 Null Measurements

57.

What is the emfxemfx of a cell being measured in a potentiometer, if the standard cell’s emf is 12.0 V and the potentiometer balances for Rx=5.000ΩRx=5.000Ω and Rs=2.500ΩRs=2.500Ω?

58.

Calculate the emfxemfx of a dry cell for which a potentiometer is balanced when Rx=1.200ΩRx=1.200Ω, while an alkaline standard cell with an emf of 1.600 V requires Rs=1.247ΩRs=1.247Ω to balance the potentiometer.

59.

When an unknown resistance RxRx is placed in a Wheatstone bridge, it is possible to balance the bridge by adjusting R3R3 to be 2500Ω2500Ω. What is RxRx if R2R1=0.625R2R1=0.625?

60.

To what value must you adjust R3R3 to balance a Wheatstone bridge, if the unknown resistance RxRx is 100Ω100Ω, R1R1 is 50.0Ω50.0Ω, and R2R2 is 175Ω175Ω?

61.

(a) What is the unknown emfxemfx in a potentiometer that balances when RxRx is 10.0Ω10.0Ω, and balances when RsRs is 15.0Ω15.0Ω for a standard 3.000-V emf? (b) The same emfxemfx is placed in the same potentiometer, which now balances when RsRs is 15.0Ω15.0Ω for a standard emf of 3.100 V. At what resistance RxRx will the potentiometer balance?

62.

Suppose you want to measure resistances in the range from 10.0Ω10.0Ω to 10.0 kΩ10.0 kΩ using a Wheatstone bridge that has R2R1=2.000R2R1=2.000. Over what range should R3R3 be adjustable?

21.6 DC Circuits Containing Resistors and Capacitors

63.

The timing device in an automobile’s intermittent wiper system is based on an RCRC time constant and utilizes a 0.500-μF0.500-μF capacitor and a variable resistor. Over what range must RR be made to vary to achieve time constants from 2.00 to 15.0 s?

64.

A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?

65.

The duration of a photographic flash is related to an RCRC time constant, which is 0.100 μs0.100 μs for a certain camera. (a) If the resistance of the flash lamp is 0.0400Ω0.0400Ω during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is 800800?

66.

A 2.00- and a 7.50-μF7.50-μF capacitor can be connected in series or parallel, as can a 25.0- and a 100-kΩ100-kΩ resistor. Calculate the four RCRC time constants possible from connecting the resulting capacitance and resistance in series.

67.

After two time constants, what percentage of the final voltage, emf, is on an initially uncharged capacitor CC, charged through a resistance RR?

68.

A 500-Ω500-Ω resistor, an uncharged 1.50-μF1.50-μF capacitor, and a 6.16-V emf are connected in series. (a) What is the initial current? (b) What is the RCRC time constant? (c) What is the current after one time constant? (d) What is the voltage on the capacitor after one time constant?

69.

A heart defibrillator being used on a patient has an RCRC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an 8.00-μF8.00-μF capacitance, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to 6.00×102V6.00×102V?

70.

An ECG monitor must have an RCRC time constant less than 1.00×102μs1.00×102μs to be able to measure variations in voltage over small time intervals. (a) If the resistance of the circuit (due mostly to that of the patient’s chest) is 1.00 kΩ1.00 kΩ, what is the maximum capacitance of the circuit? (b) Would it be difficult in practice to limit the capacitance to less than the value found in (a)?

71.

Figure 21.53 shows how a bleeder resistor is used to discharge a capacitor after an electronic device is shut off, allowing a person to work on the electronics with less risk of shock. (a) What is the time constant? (b) How long will it take to reduce the voltage on the capacitor to 0.250% (5% of 5%) of its full value once discharge begins? (c) If the capacitor is charged to a voltage V0V0 through a 100-Ω100-Ω resistance, calculate the time it takes to rise to 0.865V00.865V0 (This is about two time constants.)

A parallel circuit with a switch, an embedded electronic circuit, a capacitor, and a resistor is shown. The embedded circuit, capacitor, and resistor are connected in parallel with each other: the electronic circuit on the left, the capacitor in the middle, and the resistor on the right. The capacitor has a capacitance of eighty micro farads. The resistor has a resistance of two hundred fifty kilohms. The switch is on the top, between the electronic circuit and the capacitor leg.
Figure 21.53
72.

Using the exact exponential treatment, find how much time is required to discharge a 250-μF250-μF capacitor through a 500-Ω500-Ω resistor down to 1.00% of its original voltage.

73.

Using the exact exponential treatment, find how much time is required to charge an initially uncharged 100-pF capacitor through a 75.0-MΩ75.0-MΩ resistor to 90.0% of its final voltage.

74.

Integrated Concepts

If you wish to take a picture of a bullet traveling at 500 m/s, then a very brief flash of light produced by an RCRC discharge through a flash tube can limit blurring. Assuming 1.00 mm of motion during one RCRC constant is acceptable, and given that the flash is driven by a 600-μF600-μF capacitor, what is the resistance in the flash tube?

75.

Integrated Concepts

A flashing lamp in a Christmas earring is based on an RCRC discharge of a capacitor through its resistance. The effective duration of the flash is 0.250 s, during which it produces an average 0.500 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? (c) Find the capacitance. (d) What is the resistance of the lamp?

76.

Integrated Concepts

A 160-μF160-μF capacitor charged to 450 V is discharged through a 31.2-kΩ31.2-kΩ resistor. (a) Find the time constant. (b) Calculate the temperature increase of the resistor, given that its mass is 2.50 g and its specific heat is 1.67kJkgºC1.67kJkgºC, noting that most of the thermal energy is retained in the short time of the discharge. (c) Calculate the new resistance, assuming it is pure carbon. (d) Does this change in resistance seem significant?

77.

Unreasonable Results

(a) Calculate the capacitance needed to get an RCRC time constant of 1.00×103s1.00×103s with a 0.100-Ω0.100-Ω resistor. (b) What is unreasonable about this result? (c) Which assumptions are responsible?

78.

Construct Your Own Problem

Consider a camera’s flash unit. Construct a problem in which you calculate the size of the capacitor that stores energy for the flash lamp. Among the things to be considered are the voltage applied to the capacitor, the energy needed in the flash and the associated charge needed on the capacitor, the resistance of the flash lamp during discharge, and the desired RCRC time constant.

79.

Construct Your Own Problem

Consider a rechargeable lithium cell that is to be used to power a camcorder. Construct a problem in which you calculate the internal resistance of the cell during normal operation. Also, calculate the minimum voltage output of a battery charger to be used to recharge your lithium cell. Among the things to be considered are the emf and useful terminal voltage of a lithium cell and the current it should be able to supply to a camcorder.

80.

Critical Thinking A circuit has a voltage source producing 1.00×102V1.00×102V and a 2.50×103Ω2.50×103Ω resistor. (a) If the circuit contains nothing else, how much power is dissipated by the resistor? (b) A second 2.50×103Ω2.50×103Ω resistor is added in parallel to the first resistor. Now how much power is dissipated by the resistors? (c) Now place the two resistors in series. How much power is dissipated by the resistors? (d) Why would a parallel arrangement of resistors dissipate more power than a series arrangement of resistors of the same value? (e) Which delivers more energy in a given time period, the parallel combination of resistors, the series combination of resistors, or is the energy delivered in a given time period the same?

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