Willis High School Physics Workbook Unit 8 Electricity and Circuits. This workbook belongs to. Mr. Raven's Version

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1 Willis High School Physics Workbook Unit 8 Electricity and Circuits This workbook belongs to Period Mr. Raven's Version

2 Electricity and Circuits Pacing Guide DAY DATE TEXTBOOK PREREADING HOMEWORK F 2/ to 8.4 M 2/ T 2/ W 2/ T 2/ F 2/ & M 2/11 7 T 2/12 8 W 2/13 T 2/ F 2/ M 2/18 T 2/ W 2/ T 2/21 F 2/22 Workbook Completion Evaluation Instructor Use Only Section Maximum Points Awarded Points Warm-Up Problems 10 Textbook Reading 25 Classwork 25 Homework 30 Lab Reports 10 TOTAL

3 Electricity and Circuits Reference Material q e = 1.6 x C NAME SYMBOL UNIT SYMBOL charge q coulomb C current I ampere A voltage V volt V resistance R ohm Ω power P watt W charge q current = I time t voltage V current = I resistance R electric power = current voltage P IV energy = power time E Pt power time Pt energy in kwh = EkWh cost = rate energy in kwh cost rekwh Item Series Parallel Schematic Diagram Current (I) Voltage (V) Only one path for current Multiple paths for current I I I I I I... 1 I2 I3 T Same for each resistor Sum of currents V V V V V V V V T Sum of voltages T T Same for each resistor Equivalent Resistance R R R R eq Sum of individual resistances R R R R eq Reciprocal sum of individual resistances Always greater than the largest resistor Always less than the smallest resistor Conducting Elements All must conduct At least one must conduct Open Circuit Stops current everywhere Single does not stop current everywhere

4 Warm-Up Problems Date: Givens and Unknowns Relationship Date: Givens and Unknowns Relationship Solution: Date: Givens and Unknowns Relationship Solution: Solution:

5 Warm-Up Problems Date: Givens and Unknowns Relationship Date: Givens and Unknowns Relationship Solution: Date: Givens and Unknowns Relationship Solution: Solution:

6 Warm-Up Problems Date: Givens and Unknowns Relationship Date: Givens and Unknowns Relationship Solution: Date: Givens and Unknowns Relationship Solution: Solution:

7 Electricity and Circuits Textbook Reading Assignments Answer All Items With Complete Sentences Reading 1 Chapter 17 Electric Forces and Fields Section 17-1 Electric Charge Pages 628 to 631 a) What are the two types of electric charge and how do they interact? b) What is an ion and how is one created? c) What is meant by the principle of conservation of electric charge? d) What did Millikan s oil-drop experiment reveal about the nature of electric charge? e) Describe a conductor and list some examples. f) Describe an insulator and list some examples. Electricity and Circuits T1

8 Electricity and Circuits Textbook Reading Assignments Answer All Items With Complete Sentences Reading 2 Chapter 18 Electrical Energy and Capacitance Section 18-2 Potential Difference Page 670 a) What is electric potential? b) How is the electrical potential at a point related to the charge at that point? c) What is potential difference and what is its SI unit? d) What is the range of potential differences for batteries? e) What is the typical potential difference between the two slots in a household electrical outlet? T2 Electricity and Circuits

9 Electricity and Circuits Textbook Reading Assignments Answer All Items With Complete Sentences Reading 3 Chapter 19 Current and Resistance Section 19-1 Electric Current Pages 694 to 699 a) What is current and what is its SI unit? b) How is conventional current defined? c) What are the functions of batteries and generators? d) What are the differences between the two types of current? e) In direct current, charge carriers have a drift velocity, but in alternating current, there is no net velocity of charge carriers. Explain why. Electricity and Circuits T3

10 Electricity and Circuits Textbook Reading Assignments Answer All Items With Complete Sentences Reading 4 Chapter 19 Current and Resistance Section 19-2 Resistance Pages 700 to 701 a) What is resistance and what is its SI unit? b) What must be true about a material s resistance over a wide range of voltages for Ohm s Law to be valid? c) Do all materials function according to Ohm s Law? If not, explain how they are classified and list some examples of each. d) List the four factors that resistance varies with and the effect of each on resistance. T4 Electricity and Circuits

11 Electricity and Circuits Textbook Reading Assignments Answer All Items With Complete Sentences Reading 5 Chapter 19 Current and Resistance Section 19-3 Electric Power Pages 708 to 713 a) What is the rate of conversion of electrical energy? b) What are the three different expressions of power using current, voltage, and resistance? c) Electric companies do not sell power, they sell energy; how is this energy expressed by electric companies? d) How do electric companies calculate your electric bill? e) Explain why it is more efficient to transport electrical energy at high voltage and low currents than at low voltages and high currents. Electricity and Circuits T5

12 Electricity and Circuits Textbook Reading Assignments Answer All Items With Complete Sentences Reading 6 Chapter 20 Circuits and Circuit Elements Section 20-1 Schematic Diagrams and Circuits Pages 730 to 733 a) What is a schematic diagram what are some of the commonly used symbols and their meaning? b) What is an electric circuit? c) Describe what a load is. d) Describe the differences between an open circuit and a closed circuit. e) Why are short circuits hazardous? T6 Electricity and Circuits

13 Electricity and Circuits Textbook Reading Assignments Answer All Items With Complete Sentences Reading 7 Chapter 20 Circuits and Circuit Elements Section 20-2 Resistors in Series or in Parallel Pages 736 to 740 a) Describe the configuration of circuit elements that form a series circuit. b) What do all the circuit elements in a series circuit have in common? c) Equivalent resistance (R eq ) can be used to find the overall circuit current. What is the equivalent resistance of a multiple resistors wired in series? d) Describe how the series equivalent resistance relates to the individual resistors. e) What do series circuits require to create a complete circuit? Electricity and Circuits T7

14 Electricity and Circuits Textbook Reading Assignments Answer All Items With Complete Sentences Reading 8 Chapter 20 Circuits and Circuit Elements Section 20-2 Resistors in Series or in Parallel Pages 740 to 745 a) Describe the configuration of circuit elements that form a parallel circuit. b) What do all the circuit elements in a parallel circuit have in common? c) Equivalent resistance (R eq ) can be used to find the overall circuit current. What is the equivalent resistance of a multiple resistors wired in parallel? d) Describe how the parallel equivalent resistance relates to the individual resistors. e) What do parallel circuits not require to create a complete circuit? T8 Electricity and Circuits

15 ELECTRICITY & CIRCUITS Unit HISTORY OF ATOMIC STRUCTURE The search for the atom began as a philosophical question. The natural philosophers of ancient Greece began the search for the atom by asking such questions as: What is stuff composed of? What is the structure of material objects? Is there a basic unit from which all objects are made? As early as 400 B.C., some Greek philosophers proposed that matter is made of indivisible building blocks known as atomos. (Atomos in Greek means indivisible.) To these early Greeks, matter could not be continuously broken down and divided indefinitely. This indivisible building block from which all matter was composed became known as the atom. From the 1600s to the present century, the search for the atom became an experimental pursuit. Several scientists are notable. Among them are Robert Boyle, John Dalton, J.J. Thomson, Ernest Rutherford, and Neils Bohr. The conclusions regarding atomic structure are: All material objects are composed of atoms. There are different kinds of atoms known as elements; these elements can combine to form compounds. Different compounds have distinctly different properties. Material objects are composed of atoms and molecules of these elements and compounds, thus providing different materials with different electrical properties. An atom consists of a nucleus and a vast region of space outside the nucleus. Electrons are present in the region of space outside the nucleus. They are negatively charged and weakly bound to the atom. Electrons are often removed from and added to an atom by normal everyday occurrences. The nucleus of the atom contains positively charged protons and neutral neutrons. These protons and neutrons are not removable by usual everyday methods. It would require some form of high-energy nuclear occurrence to disturb the nucleus and subsequently dislodge its positivelycharged protons. 8.2 ELECTRIC CHARGE Electric charge, like mass, is one of the basic properties of elementary particles from which all matter is composed. The unit of charge is the Coulomb, C. The magnitude of the charge of an electron is: upon other objects following this rule: Like charges repel, unlike charges attract. q e = C Both electrons and protons are capable of exerting an electrical force. In fact, any charged object can exert a force Any charged object, whether positively or negatively charged, will attract a neutral object. 8.3 ELECTRIC CURRENT A flow of charge from one place to another is called an electric current. An electric circuit is a closed path in which an electric current carries energy from a source (such as a battery or generator), to a load (such as a motor or a lamp). In such a circuit, electric current is assumed to go from the positive terminal of the battery (or generator) through the circuit and back to the negative terminal of the battery. The direction of a current is conventionally considered to be that in which positive charge would have to move to produce the same effects as the actual current. A conductor is a substance through which charge can flow easily, and an insulator is one through which charge can flow only with great difficulty. Metals, many liquids, and plasmas (gases whose molecules are charged) are conductors; nonmetallic solids, certain liquids, and gases whose molecules are electrically neutral are insulators. A number of substances, called semiconductors, are intermediate in their ability to conduct charge. If an amount of charge, q, passes a given point in a conductor in the time interval, t, the current in the conductor is I = q t where the units of current is the ampere, A. UNIT 8: ELECTRICITY & CIRCUITS 165

16 8.4 OHM S LAW For a current to exist in a conductor, there must be a potential difference between its ends, just as a difference in height between source and outlet is necessary for a river current to exist. In the case of a metallic conductor, the current is directly proportional to the applied potential difference. This relationship is known as Ohm s law and is expressed in the form: I = V R where I is the current in amperes, A. V is the voltage or potential difference in volts, V. And R is the resistance in ohms, Ω. CLASSWORK 1. A wire carries a current of 1 A. How many electrons pass any point in the wire each second? ( electrons) 2. Find the current in a 200 Ω resistor when the potential difference across it is 40 V. (0.2 A) 3. An electric water heater draws 10 A of current from a 240 V power line. What is its resistance? (24 Ω) UNIT 8: ELECTRICITY & CIRCUITS 166

17 4. How many electrons per second must pass a given point in order to have a current of 2.0 A? ( electrons/s) 5. The battery of a car delivers 50 A for 2 s to start a car. (a) How many coulombs of charge move through the starter during this 2 s? (100 C) (b) How many electrons make up this amount of charge? ( electrons) 6. A car s starter motor draws 50 A. How much charge flows if the motor runs for 0.75 s? (37.5 C) 7. How long does it take for 52 C to pass through a wire carrying a current of 8.0 A? (6.5 s) UNIT 8: ELECTRICITY & CIRCUITS 167

18 8. How much current passes through a person whose resistance is 100,000 Ω and to whom 120 V is applied? ( A) 9. A current of 4 A flows when a resistor is connected across a 12 V battery. Find the resistance of this resistor? (3 Ω) 10. What is the resistance of a clothes iron that draws 8 A when connected to 120 V? (15 Ω) 11. A current of 0.50 A flows through a lamp bulb when it is connected to a 120 V power source. What is the resistance of the bulb under these conditions? (240 Ω) 8.5 ELECTRIC POWER The rate at which work is done to maintain an electric current is given by the product of the current I and the potential difference V : P = IV where the unit of power is the Watt, W. The electric energy transferred to a resistor in a time interval t is converted to thermal energy (heat). Therefore, E = P t where the unit of energy is the Joule, J. UNIT 8: ELECTRICITY & CIRCUITS 168

19 CLASSWORK 12. A 6 V battery delivers 0.5 A of current to an electric motor connected across its terminals. (a) What is the power rating of the motor? (3 W ) (b) How much energy does the motor use in 5.0 min? (900 J) 13. What current flows through a 75 W light bulb connected to a 120 V outlet? (0.625 A) 14. A heater has a resistance of 10 Ω. It operates on 120 V. (a) What is the current through the resistance? (12 A) UNIT 8: ELECTRICITY & CIRCUITS 169

20 (b) What is the energy supplied by the heater in 10 s? (14,400 J) 15. A 100 W light bulb is 20% efficient. That means that 20% of the electric energy is converted to light energy. (a) How much energy does the light bulb convert into light each minute it is in operation? (1,200 J) (b) How much heat does the light bulb produce each minute? (4,800 J) 16. (a) How much energy does a 60 W bulb use in half an hour? (108,000 J) (b) If the light bulb is 12% efficient, how much heat does it generate during the half hour? (95,040 J) UNIT 8: ELECTRICITY & CIRCUITS 170

21 17. A motor connected to 120 V draws a current of 10 A. (a) What power is being consumed? (1200 W ) (b) How much energy does the motor use in 8 hr of operation? ( J) 18. (a) What current flows in a 60 W bulb in a 120 V circuit? (0.5 A) (b) What is the resistance of the filament? (240 Ω) 19. How much current is drawn by a 100 W stereo system connected to a 120 V outlet? (0.83 A) UNIT 8: ELECTRICITY & CIRCUITS 171

22 20. A 75.0 W light bulb is used in a lamp connected to a 120 V power source. (a) What current flows through the bulb? (0.625 A) (b) If the light bulb is 75% efficient, how much energy per minute is given of as light and as heat? (3375 J and 1125 J) 21. The resistance of an electric stove element at operating temperature is 11 Ω. (a) If 220 V are applied across it, what is the current through the element? (20 A) (b) How much energy does the element use in 30 s? ( J) UNIT 8: ELECTRICITY & CIRCUITS 172

23 8.6 THE KILOWATT-HOUR The kilowatt-hour (kw h) is an energy unit equal to the energy delivered by a source whose power is 1 kw in 1 h of operation: E kw h = P t 1000 where time is calculated in hours. Often, it is useful to calculate the cost of operating an appliance for a determined amount of time. Given the rate per killowatt-hour, r, and the power usage: C = re kw h where C is the operating cost. CLASSWORK 22. A new color TV set draws 2 A when operated on 120 V. (a) How much power does the set use? (240 W ) (b) If the set is operated for an average of 7 hours per day, what energy in kw h does it consume per month (30 days)? (50.4 kw h) (c) At $0.080 per kw h, what is the cost of operating the set per month? ($4.03) 23. A digital clock has an operating resistance of 12,000 Ω and is plugged into a 115 V outlet. (a) How much current does it draw? ( A) UNIT 8: ELECTRICITY & CIRCUITS 173

24 (b) How much power does it use? (1.1 W ) (c) If the owner of the clock pays $0.09 per kw h, what does it cost to operate the clock for 30 days? ($0.07) 24. What is the power consumption of a household heater that draws a current of 9 A when connected to a 120 V line? (1.08 kw ) 25. How much does it cost to operate a 100 W lamp continuously for one week if the power utility rate is 10 cents per kilowatt-hour? ($1.68) UNIT 8: ELECTRICITY & CIRCUITS 174

25 26. An old electrical device is found in the closet of an abandoned barn. Its label indicates that it uses 8.5 W of power and 1.7 A of current. Part of the label is missing and the voltage rating cannot be seen. What was the operating voltage of the device? (5 V ) 27. A 1500 W hair dryer connected to a 120 V outlet runs for 3 minutes. (a) How much current does the hair dryer draw? (12.5 A) (b) How much energy does it use? ( J) (c) How many kw h of energy were used? (0.075 kw h) UNIT 8: ELECTRICITY & CIRCUITS 175

26 28. A household appliance was inadvertently left on for an entire week (7 days) while a family was away on vacation. A steady current of 5 A was drawn from the 120 V line. The cost of electricity in the area is 13 cents per kw h. (a) How much power is needed by the appliance? (600 W ) (b) How much energy was used? ( J) (c) How much did it cost to run the appliance? ($13.10) 29. A girl blows her hair dry every morning using a 1200 W electric hair dryer. On the average, it takes her 5 minutes each time she uses it. The cost of electricity in her area is 5 cents per kw h. What is the annual cost for running the hair dryer? ($1.83) UNIT 8: ELECTRICITY & CIRCUITS 176

27 8.7 ELECTRIC CIRCUITS This class will commonly use the following symbols: COMPONENT DESCRIPTION SYMBOL Resistor A resistor impedes the flow of current. Battery A battery supplies an increase in voltage potential across its terminals. Switch A switch connects and disconnects the flow of current. Ammeter An ammeter, connected in series, measures the magnitude of the current. Voltmeter A voltmeter, connected in parallel, measures the magnitude of the voltage drop. Series Circuit The picture to the right demonstrates components connected in series. Parallel Circuit The picture to the right demonstrates components connected in parallel. 8.8 SERIES CIRCUITS In a series circuit, the current is the same at all points along the wire. I T = I 1 = I 2 = I 3 An equivalent resistance is the resistance of a single resistor that could replace all the resistors in a circuit. The single resistor would have the same current through it as the resistors it replaced. R E = R 1 + R 2 + R 3 In a series circuit, the sum of the voltage drops equal the voltage drop across the entire circuit. V T = V 1 + V 2 + V 3 CLASSWORK 30. Draw a circuit diagram to include a 60 V battery, an ammeter and a resistance of 12.5 Ω. Indicate the ammeter reading. (4.8 A) UNIT 8: ELECTRICITY & CIRCUITS 177

28 31. Four 15 Ω resistors are connected in series to a 30 V battery. What is the current of the circuit? (0.5 A) 32. A 5 Ω resistor and a 10 Ω resistor are connected in series and placed across a 45 V potential difference. Draw the circuit. (a) What is the equivalent resistance of the circuit? (15 Ω) (b) What is the current through the circuit? (3 A) (c) What is the voltage drop across each resistor? (15 V, 30 V ) UNIT 8: ELECTRICITY & CIRCUITS 178

29 (d) What is the total voltage of the circuit? (45 V ) 33. A 10 Ω resistor, a 15 Ω resistor and a 5 Ω resistor are connected in series and placed across a 90 V potential difference. Draw the circuit. (a) What is the equivalent resistance of the circuit? (30 Ω) (b) What is the current through the circuit? (3 A) (c) What is the voltage drop across each resistor? (30 V, 45 V, 15 V ) UNIT 8: ELECTRICITY & CIRCUITS 179

30 (d) What is the total voltage of the circuit? (90 V ) 34. What is the equivalent resistance of two 12 Ω resistors connected in series? (24 Ω) 35. What is the equivalent resistance of a 6 Ω and 9 Ω resistor connected in series? (15 Ω) 36. Three 10 Ω resistors are connected in series to a 12 V battery. (a) Draw a diagram of the circuit. UNIT 8: ELECTRICITY & CIRCUITS 180

31 (b) What is the equivalent resistance of the circuit? (30 Ω) (c) What is the total current in the circuit? (0.4 A) (d) What is the potential drop across each resistor? (4 V ) (e) What is the current in each resistor? (0.4 A each) (f) What is the power dissipated by each resistor? (1.6 W ) UNIT 8: ELECTRICITY & CIRCUITS 181

32 8.9 PARALLEL CIRCUITS In a parallel circuit, each resistor provides a new path for electrons to flow. The total current is the sum of the currents through each resistor. I T = I 1 + I 2 + I 3 The equivalent resistance of a parallel circuit decreases as each new resistor is added. 1 R E = 1 R R R 3 The voltage drop across each branch is equal to the voltage of the source. V T = V 1 = V 2 = V 3 CLASSWORK 37. Three 15 Ω resistors are connected in parallel across a 90 V voltage. Draw the circuit. (a) Find the equivalent resistance of the circuit. (5 Ω) (b) Find the current in the entire circuit. (18 A) (c) Find the current through each branch of the circuit. (6 A) UNIT 8: ELECTRICITY & CIRCUITS 182

33 38. A 120 Ω resistor, a 60 Ω resistor and a 40 Ω resistor are connected in parallel and placed across a 120 V potential difference. Draw a diagram of the circuit. (a) Find the equivalent resistance of the circuit. (20 Ω) (b) Find the current in the entire circuit. (6 A) (c) Find the current through each branch of the circuit. (1 A, 2 A, 3 A) UNIT 8: ELECTRICITY & CIRCUITS 183

34 39. What is the equivalent resistance of two 124 Ω resistors connected in parallel? (62 Ω) 40. What is the equivalent resistance of a 6 Ω and 9 Ω resistor connected in parallel? (3.6 Ω) 41. Three 10 Ω resistors are connected in parallel to a 12 V battery. (a) Draw a diagram of the circuit. (b) What is the equivalent resistance of the circuit? (3.33 Ω) (c) What is the total current in the circuit? (3.6 A) UNIT 8: ELECTRICITY & CIRCUITS 184

35 (d) What is the voltage across each resistor? (12 V ) (e) What is the current in each resistor? (1.2 A) (f) What is the power dissipated by each resistor? (14.4 W ) 8.10 SERIES-PARALLEL CIRCUITS The current in a complex circuit can be found by first calculating the effective resistance of the parallel circuits. Then the effective resistance of the parallel circuits and all the series resistances can be combined into one total effective resistance and the total current can be determined. CLASSWORK 42. Find each of the following. Write N.I. if not enough information is provided. I 1= I 2= I 3= V 1= V 2= V 3= UNIT 8: ELECTRICITY & CIRCUITS 185

36 43. Find each of the following. Write N.I. if not enough information is provided. I 1= I 2= I 3= V 1= V 2= V 3= 44. Find each of the following. Write N.I. if not enough information is provided. I 1= I 2= I 3= I 4= V 1= V 2= V 3= V 4= 45. Find each of the following. Write N.I. if not enough information is provided. I 1= I 2= I 3= V 1= V 2= V 3= 46. Find each of the following. Write N.I. if not enough information is provided. I 1= I 2= I 3= I 4= I 5= V 1= V 2= V 3= V 4= V 5= UNIT 8: ELECTRICITY & CIRCUITS 186

37 ELECTRICITY & CIRCUITS Homework 1. An object has a charge of -18 nc. Calculate the net number of electrons it contains. ( electrons) 2. If the billions of freely moving electrons in a penny repel one another, why don t they fly out of the penny? 3. Balloons X, Y and Z are suspended from strings as shown at the right. Negatively-charged balloon X attracts balloon Y and balloon Y repells balloon Z. Balloon Z. Circle all that apply. (a) may be positively-charged (b) may be negatively-charged (c) may be neutral (d) must be positively-charged (e) must be negatively-charged (f) must be neutral 4. A 3 A current passes through a 200 Ω resistor. What is the voltage drop across the resistor? (600 V ) UNIT 8: HOMEWORK A122

38 5. A household appliance draws 15 A of current from a 240 V power line. What is its resistance? (16 Ω) 6. (a) How long will it take for 100 C to pass through a wire carrying a current of 3 A? (33.3 s) (b) If the wire has an internal resistance of 250 µω, what is the voltage drop across the wire? (750 µv ) 7. Ronnie puts batteries in his flashlight. Until the batteries die, it draws 0.5 A of current, allowing a total of 5400 C of charge to flow through the circuit. How long will Arthur be able to use the flashlight before the batteries energy is depleted? (10,800 s) UNIT 8: HOMEWORK A123

39 8. Justine s hair dryer has a resistance of 9 Ω when first turned on. How much current does the hair dryer draw from the 110 V line in Justine s house? (12.2 A) 9. Camille takes her pocket calculator out of her bookbag as she gets ready to do her physics homework. In the calculator, a C charge encounters 19.0 Ω of resistance every 2.0 seconds. What is the potential difference of the battery? (1.52 V ) 10. What is the resistance of an iron that draws 10 A when connected to a 120 V power source? (12 Ω) 11. A small motor draws 3 A. How much charge flows into the motor if it runs for 2 minutes? (360 C) UNIT 8: HOMEWORK A124

40 12. Derive an equation for the energy, E, consumed by an appliance using only current, time, and resistance. (E = I 2 Rt) 13. A 9 V battery delivers 0.25 A of current to a motor. (a) What is the power rating of the motor? (2.25 W ) (b) How much energy is used in 68 s (153 J) 14. A 1200 W iron is connected to a 120 V power outlet? (a) How much current flows through the iron? (10 A) (b) If the iron remains plugged into the wall for 4 hours, how much energy is used? ( J) UNIT 8: HOMEWORK A125

41 15. (a) Johnny s 12 V car battery delivers 0.8 A of current to his stereo. How much power is used by the stereo? (9.6 W ) (b) If the stereo continues to run for 1 hour, how much energy is consumed? (34.6 kj) 16. A 60 W light bulb is connected to a 120 V power source. (a) What current flows through the bulb? (0.5 A) (b) If the bulb is 75% efficient, how much energy per minute is geven off as light? As heat? (E L=2.7 kj; E H=900 J) 17. Which has more resistance when plugged into a 120 V line, A 1400 W microwave oven or a 150 W electric can opener? (R M =10.3 Ω; R C.O.=96 Ω) UNIT 8: HOMEWORK A126

42 18. While writing these notes, Mr. Hampshire spent about 20 hours working on his computer that has a power input of 60 W. How much did it cost for the energy use if it costs $0.10 per kw h? ($ 0.12) 19. A hand-drier in a public restroom operates with a 1,000 Ω resistance and is connected to a 120 V line. (a) How much current does it draw? (0.12 A) (b) How much power does it use? (14.4 W ) (c) If the restroom owner pays $0.08 per kw h, what does it cost to operate the hand-drier continually for one entire day? ($ 0.03) 20. How much will it cost to keep a 10 W cell phone charger operating continuously for one week if the power utility rate is 8 cents per kw h? ($ 0.13) UNIT 8: HOMEWORK A127

43 21. A 100 W light bulb is plugged into a 120 V line. (a) What is the resistance of the light bulb? (144 Ω) (b) How much current flows through the bulb? (0.83 A) (c) If the power utility rate is 10 cents per kw h, how much will it cost to operate the light bulb for 25 days? ($6.00) 22. What happens to the total circuit resistance when more devices are added to a series circuit? 23. Are the electrons flowing in a circuit provided by the battery? Why or why not? UNIT 8: HOMEWORK A128

44 24. If one of three bulbs blows out in a series circuit, what happens to the current in the other two bulbs? 25. Draw a circuit to include a 12 V battery, a resistor of 1.25 Ω, and a voltmeter to measure the voltage drop across the resistor. (a) Determine the current in the circuit. (9.6 A) (b) What is the voltmeter reading. (12 V ) UNIT 8: HOMEWORK A129

45 26. A 3 Ω and a 10 Ω resistor are connected in series and placed across a 24 V potential difference. (a) Draw the circuit. (b) What is the equivalent resistance of the circuit? (13 Ω) (c) What is the current through the circuit? (1.85 A) (d) What is the voltage drop across each resistor? (V 1=5.5 V ; V 2=18.5 V ) (e) What is the total voltage drop of the circuit? (24 V ) UNIT 8: HOMEWORK A130

46 27. A 10 Ω, a 20 Ω, and a 30 Ω resistor are connected in series and placed across a 60 V potential difference. (a) Draw the circuit. (b) What is the equivalent resistance of the circuit? (60 Ω) (c) What is the current through the circuit? (1 A) (d) What is the voltage drop across each resistor? (V 1=10 V ; V 2=20 V ; V 3=30 V ) (e) What is the total voltage drop of the circuit? (60 V ) UNIT 8: HOMEWORK A131

47 28. Four 1.25 Ω resistors are connected across a 9 V battery. (a) Draw a diagram of the circuit. (b) What is the equivalent resistance of the circuit? (5 Ω) (c) What is the total current through the circuit? (1.8 A) (d) What is the current in each resistor? (I 1=I 2=I 3=I 4=1.8 A) (e) What is the power dissipated by each resistor? (4.05 W ) UNIT 8: HOMEWORK A132

48 29. What happens to the total circuit resistance when more devices are added to a parallel circuit? 30. If one of three lamps blows out when connected in parallel, what happens to the current in the other two? 31. Describe the differences between a series circuit and a parallel circuit. 32. Five 10 Ω resistors are connected in parallel. Solve for the total resistance. (2 Ω) 33. What happens to the total circuit resistance when more devices are added to a parallel circuit? UNIT 8: HOMEWORK A133

49 34. Four 15 Ω resistors are connected in parallel across a 60 V source. (a) Draw the circuit. (b) Find the equivalent resistance in the circuit. (3.75 Ω) (c) Find the current in the entire circuit. (16 A) (d) Solve for the current through each branch of the circuit. (I 1=I 2=I 3=I 4=4 A) 35. Solve for the equivalent resistance of a 15 Ω, 20 Ω, and 25 Ω resistor connected in parallel. (6.38 Ω) UNIT 8: HOMEWORK A134

50 36. A 20 Ω, a 40 Ω, and a 50 Ω resistor are connected in parallel across a 30 V potential difference. (a) Draw a circuit diagram. (b) Find the equivalent resistance of the circuit. (10.5 Ω) (c) Find the current in the entire circuit. (2.85 A) (d) Find the current through each branch of the circuit. (I 1=1.5 A; I 2=0.75 A; I 3=0.6 A) UNIT 8: HOMEWORK A135

51 37. A 100 Ω and a 50 Ω resistor are connected in parallel across a 120 V potential difference. (a) Draw a circuit diagram. (b) Find the equivalent resistance of the circuit. (33.3 Ω) (c) Find the current in the entire circuit. (3.6 A) (d) Find the current through each branch of the circuit. I 1=1.2 A; I 2=2.4 A) 38. Three 10 Ω resistors are connected in parallel. This arrangement is connected in series with a 12 Ω resistor. Determine the equivalent resistance. (15.3 Ω) UNIT 8: HOMEWORK A136

52 Ohm s Law The fundamental relationship among the three important electrical quantities current, voltage, and resistance was discovered by Georg Simon Ohm. The relationship and the unit of electrical resistance were both named for him to commemorate this contribution to physics. OBJECTIVES V IR Voltage = Current Resistance Determine the mathematical relationship between current, potential difference, and resistance in a simple circuit. SETUP 1. Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel 2 of the computer interface. 2. Open Logger Pro. Open the file 22 Ohms Law in the Physics with Vernier folder. A graph of potential vs. current will be displayed. The meter displays potential and current readings. 3. With the power supply turned off, connect the power supply, 100 resistor, current probe, differential voltage probe, wires, and clips into a circuit. Attach the red connectors electrically closer to the positive side of the power supply. 4. With the power supply off, click. A dialog box will appear. Click to zero both sensors. This sets the zero for both probes with no current flowing and with no voltage applied. PROCEDURE 1. Set the power supply to 0 V and turn it on. Click to begin data collection. Click. 2. Increase the voltage on the power supply to approximately 0.5 V. Click. 3. Increase voltage by about 0.5 V. Click. Repeat this process until you reach a voltage of 5.0 V. 4. Click, set the power supply back to 0 V, and turn it off. 5. Click the Linear Fit button,. The slope is the actual resistor value. Record the actual resistor value in the Data Table. 6. Repeat for all three resistors. DATA TABLE TRIAL ACTUAL RESISTOR VALUE 1 Ω 2 Ω 3 Ω

53 ELECTRICAL RESISTANCE Discussion Different substances offer different amounts of resistance to an electric current. Physicists have found that length, cross-sectional area, and the material the conductor is made of determine the resistance of a conductor. In this experiment, you will observe the effects of length, cross-sectional area, and material on the resistance of conductors. You will use a set of mounted resistance coils, which will provide wire coils of different lengths, diameters, and metals. The resistance provided by each resistance coil will affect the current in the resistor. You will measure the potential difference across the resistance coil, and you will find the current in the conductor. Then you will use these values to calculate the resistance of each resistance coil using the definition of resistance. Voltage Resistance = Current V R I Procedure 1. Start each measurement with the Power Supply off, the voltage adjusted to zero volts, and the current adjusted to maximum. 2. The end of each resistance coil is connected to a bolt which may be shared with the next coil. Connect the power supply output to the bolts at the ends of a coil. Observations and Data Collection 3. Turn on the Power Supply and slowly increase the Power Supply Voltage Output until the current output reaches around 0.1 to 0.2 amps. 4. In the Data Table, record the Voltage across the resistance coil and the current through the resistance coil. 5. Turn off the Power Supply DO NOT LEAVE POWER SUPPLY ON 6. Repeat for all five resistance coils. Calculations 7. Using the definition of resistance above, calculate each coil s Resistance and record it in the Data Table. Page 1 of 2

54 Data Table Coil Metal Gauge Number Area (10-8 m 2 ) Length (m) Resistivity (10-8 Ω m) Voltage (V) Current (A) Resistance (Ω) 1 copper copper copper copper coppernickel Questions and Interpretations 1. As wire length increases (Coils 1 & 3 and 2 & 4), wire resistance (circle one): increases decreases stays the same 2. As wire area increases (Coils 1 & 2 and 3 & 4), wire resistance (circle one): increases decreases stays the same 3. As wire resistivity increases(coils 1 & 5), wire resistance (circle one): increases decreases stays the same Page 2 of 2

55 Series Resistor Circuits Components in an electrical circuit are in series when they are connected one after the other, so that the same current flows through both of them. Components are in parallel when they are in alternate branches of a circuit. Series and parallel circuits function differently. You may have noticed the differences in electrical circuits you use. When using some decorative holiday light circuits, if one lamp burns out, the whole string of lamps goes off. These lamps are in series. When a light bulb burns out in your house, the other lights stay on. Household wiring is normally in parallel. You can monitor these circuits using a Current Probe and a Voltage Probe and see how they operate. One goal of this experiment is to study circuits made up of two resistors in series or parallel. You can then use Ohm s law to determine the equivalent resistance of the two resistors. OBJECTIVES To study current flow in series circuits. To study voltages in series circuits. Use Ohm s law to calculate equivalent resistance of series circuits. Series Resistors MATERIALS Computer Vernier computer interface Logger Pro two Vernier Current Probes one Vernier Differential Voltage Probe Vernier Circuit Board with batteries and jumpers PROCEDURE Preliminary 1. Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel 2 of the interface. 2. Open the file 23a Series Parallel Circ in the Physics with Vernier folder. Current and voltage readings will be displayed in a meter. 3. Connect together the two voltage leads (red and black) of the Voltage Probe. Click, and then click to zero both sensors. This sets the zero for both probes with no current flowing and with no voltage applied. Page 1 of 4

56 Part I Voltage in Series Circuits 4. Connect the series circuit shown in Figure 2 using the 10 resistors for resistor 1 and resistor 2. Notice the Voltage Probe is used to measure the total voltage applied to both resistors. The red terminal of the Current Probe should be toward the + terminal of the power supply. Voltage Probe Current Probe Figure 2 5. For this part of the experiment, you do not even have to click on the button. You can take readings from the meter at any time. To test your circuit, briefly press on the switch to complete the circuit. Both current and voltage readings should increase. If they do not, recheck your circuit. 6. Press on the switch to complete the circuit again and read the current (I) and total voltage (V TOT ). Record the values in the data table. 7. Connect the leads of the Voltage Probe across resistor 1. Press on the switch to complete the circuit and read this voltage (V 1 ). Record this value in the data table. 8. Connect the leads of the Voltage Probe across resistor 2. Press on the switch to complete the circuit and read this voltage (V 2 ). Record this value in the data table. Page 2 of 4

57 Part II Currents in Series Circuits 9. For this part of the experiment, you will use two Current Probes. Open the experiment file 23b Series Parallel Circ. Two graphs of current vs. time are displayed. 10. Disconnect the Voltage Probe and, into the same channel, connect a second Current Probe. 11. With nothing connected to either probe, click, then click to zero both sensors. This adjusts the current reading to zero with no current flowing. 12. Connect the series circuit shown in Figure 4 using the 10 resistor and the 51 resistor. The Current Probes will measure the current flowing into and out of the two resistors. The red terminal of each Current Probe should be toward the + terminal of the power supply. Figure For this part of the experiment, you will make a graph of the current measured by each probe as a function of time. You will start the graphs with the switch open, close the switch for a few seconds, and then release the switch Click on the button, wait a second or two, then press on the switch to complete the circuit. Release the switch just before the graph is completed. 15. Select the region of the graph where the switch was on by dragging the cursor over it. Click on the Statistics button,, and record the mean current in the data table. Determine the mean current in the second graph following the same procedure. Page 3 of 4

58 DATA TABLE Part I: Series Circuits R 1 ( ) R 2 ( ) I (A) V TOT (V) V 1 (V) V 2 (V) Req ( ) Part II: Currents R 1 ( ) R 2 ( ) I 1 (A) I 2 (A) ANALYSIS 1. Using the measurements recorded above and Ohm s law ( R VTOT I ), calculate the equivalent resistance (R eq ) of the circuit in Part I. 2. Examine the results of Part I. What is the relationship between the three voltage readings: V 1, V 2, and V TOT? 3. What did you discover about the current flow in a series circuit in Part II? Page 4 of 4

59 Parallel Resistor Circuits Components in an electrical circuit are in series when they are connected one after the other, so that the same current flows through both of them. Components are in parallel when they are in alternate branches of a circuit. Series and parallel circuits function differently. You may have noticed the differences in electrical circuits you use. When using some decorative holiday light circuits, if one lamp burns out, the whole string of lamps goes off. These lamps are in series. When a light bulb burns out in your house, the other lights stay on. Household wiring is normally in parallel. You can monitor these circuits using a Current Probe and a Voltage Probe and see how they operate. One goal of this experiment is to study circuits made up of two resistors in series or parallel. You can then use Ohm s law to determine the equivalent resistance of the two resistors. OBJECTIVES To study current flow in parallel circuits. To study voltages in parallel circuits. Use Ohm s law to calculate equivalent resistance of parallel circuits. Parallel Resistors MATERIALS Computer Vernier computer interface Logger Pro two Vernier Current Probes one Vernier Differential Voltage Probe Vernier Circuit Board with batteries and jumpers PROCEDURE Preliminary 1. Connect the Current Probe to Channel 1 and the Differential Voltage Probe to Channel 2 of the interface. 2. Open the file 23a Series Parallel Circ in the Physics with Vernier folder. Current and voltage readings will be displayed in a meter. 3. Connect together the two voltage leads (red and black) of the Voltage Probe. Click, then click to zero both sensors. This sets the zero for both probes with no current flowing and with no voltage applied. Page 1 of 4

60 Part I Voltage in Parallel Circuits 4. Connect the parallel circuit shown below using 51 resistors for both resistor 1 and resistor 2. The Voltage Probe is used to measure the voltage applied to both resistors. The red terminal of the Current Probe should be toward the + terminal of the power supply. The Current Probe is used to measure the total current in the circuit. Figure 3 5. For this part of the experiment, you do not even have to click on the button. You can take readings from the meter at any time. To test your circuit, briefly press on the switch to complete the circuit. Both current and voltage readings should increase. If they do not, recheck your circuit. 6. Press the switch to complete the circuit again and read the total current (I) and total voltage (V TOT ). Record the values in the data table. 7. Connect the leads of the Voltage Probe across resistor 1. Press on the switch to complete the circuit and read the voltage (V 1 ) across resistor 1. Record this value in the data table. 8. Connect the leads of the Voltage Probe across resistor 2. Press on the switch to complete the circuit and read the voltage (V 2 ) across resistor 2. Record this value in the data table. Page 2 of 4

61 Part II Currents in Parallel Circuits 9. For Part II of the experiment, you will use two Current Probes. Open the experiment file 23b Series Parallel Circ. Two graphs of current vs. time are displayed. 10. Disconnect the Voltage Probe and, into the same channel, connect a second Current Probe. 11. With nothing connected to either probe, click, then click to zero both sensors. This adjusts the current reading to zero with no current flowing. 12. Connect the parallel circuit as shown in Figure 5 using the 51 resistor and the 68 resistor. The two Current Probes will measure the current through each resistor individually. The red terminal of each Current Probe should be toward the + terminal of the power supply. Figure For this part of the experiment, you will make a graph of the current measured by each probe as a function of time. You will start the graphs with the switch open, close the switch for a few seconds, and then release the switch Click and wait a second or two. Then press on the switch to complete the circuit. Release the switch just before the graph is completed. 15. Select the region of the graph where the switch was on by dragging the cursor over it. Click the Statistics button,, and record the mean current in the data table. Determine the mean current in the second graph following the same procedure. Page 3 of 4

62 DATA TABLE Part I: Parallel circuits R 1 ( ) R 2 ( ) I (A) V TOT (V) V 1 (V) V 2 (V) Req ( ) Part II: Currents R 1 ( ) R 2 ( ) I 1 (A) I 2 (A) ANALYSIS 1. Using the measurements recorded above and Ohm s law ( Req VTOT I ), calculate the equivalent resistance (R eq ) of the circuit in Part I. 2. Examine the results of Part I. What do you notice about the relationship between the three voltage readings V 1, V 2, and V TOT in parallel circuits? 3. What did you discover about the current flow in a parallel circuit in Part II? 4. If the two measured currents in your parallel circuit were not the same, which resistor had the larger current going through it? Why? Page 4 of 4