Unit 15: Electrical Circuits

Transcription

1 INQUIRY PHYSICS A Modified Learning Cycle Curriculum by Granger Meador Unit 15: Electrical Circuits Student Papers 2010 by Granger Meador inquiryphysics.org

2 15 Electrical Circuits Nam e Lab A: BASIC CIRCUITRY A continuous flow of electric charge creates an electric "current". The study of moving charges is called electrodynamics. You already know some important information about electricity in motion. You know that electric motors are used in electric appliances such as mixers, vacuum cleaners, pumps, drills, sanders, and saws. Each of those appliances exerts a force over a distance. Any object that exerts a force over distance is capable of doing. You can now deduce that electricity must be a form of. EXPLORATION answer questions with complete sentences To begin our study of current electricity, we must start with the basics. At your lab station you will find some electric leads (wires with clips on each end for easy attachment), a dry cell, light bulbs, and light bulb holders. Step 1: Arrange one bulb (without a holder), one dry cell, and wire in as many ways as you can to make the bulb emit light. Sketch each of your arrangements in the space below, including failures as well as successes. Label the sketches of the successes. Include a drawing of how to light a bulb using only ONE wire. 1. Describe the similarities among your successful trials. Be specific about where the wires must touch both the bulb and the dry cell. Step 2: Use a bulb in a bulb holder (instead of a bare bulb), the dry cell, and wire. Arrange these in as many ways as you can to make the bulb light. 2. What two parts of the bulb does the holder make contact with? Step 3: Using one dry cell, light as many bulbs in holders as you can. Sketch each of your successful arrangements in the space below. Unit 15: Electrical Circuits, Lab A: Basic Circuitry 2009 by G. Meador

3 3. Compare your results to those of other lab groups. You should note that the brightness of a given number of bulbs is affected by the way the wires are connected. Specify below what sort of setup yields the most bright bulbs. The dry cell is the source of electric energy and the light bulb is the user. When an electric energy source and an electrical energy user are connected so that electrical energy is used, that hookup is called an electrical circuit. Every electrical circuit must have at least one energy source and one energy user. It must also have a way to connect the energy source and the energy user. The connectors, the energy source, and the energy user are the circuit elements. You know that until the circuit elements were connected there was no evidence that energy was being used. The interaction among the elements of an electrical circuit causes an electric current. The electric current moves through the circuit elements. Step 4: Diagrams for electric circuits use symbols like the ones shown at right to represent the circuit elements. Connect the bulbs in holders, the dry cell, and wire as shown in each circuit diagram shown below. Circuits like these are examples of series circuits. 4. How does the brightness of the bulbs in the two circuits differ? Step 5: In the circuit with two bulbs, unscrew one of the bulbs. 5. What happens to the other bulb? Step 6: Set up the circuit diagramed at right. A circuit like this is called a parallel circuit. 6. Do both bulbs light? Step 7: Unscrew one of the bulbs in the parallel circuit. 7. What happens to the other bulb? 8. In your own words, describe the differences between series and parallel circuits. Discuss both their physical differences as well as their behavior when a bulb fails. Unit 15: Electrical Circuits, Lab A: Basic Circuitry 2009 by G. Meador

4 15 Electrical Circuits Nam e Lab B: CURRENT You have constructed both series and parallel circuits, and noted some of the differences between them. We will now concentrate on series circuits to develop the concepts of current, voltage, and resistance. We will also eventually discover a relationship between the current, voltage, and resistance of a circuit. The first concept we must master is current. The Exploration stated that circuit elements, when properly connected, have a current that moves through them. The current can be thought of as the amount of charge flowing through the circuit each second. Current is measured in units called amperes (A) with a device called an ammeter. The ammeter is put into a circuit so that electricity flows through it. Hooking up the ammeter properly is very important. Improper hookup can destroy an ammeter. Ammeter Hookup Connect the positive (+) terminal of the ammeter to the part of the circuit leading to the positive (+) terminal of the battery. Connect the negative (-) terminal of the ammeter to the part of the circuit leading to the negative (-) terminal of the battery. Never hook an ammeter into a circuit that does not have a resistor (such as a light bulb) in it. Analog Meters An analog ammeter may have two or more red positive terminals. You must read the terminal s label to determine which scale on the meter is to be used. Always hook the circuit up with largest range terminal first. If the measured current is less than the maximum value for the next lower terminal, you should switch to it for greater precision. If the ammeter needle ever "pegs out" by shooting up beyond the scale limits, disconnect it immediately and ask the instructor for assistance. Digital Multimeters Digital multimeters have multiple plugs and settings to measure current, voltage, and resistance and may operate with both direct current (DC) and alternating current (AC) circuits. Your instructor will guide you in setting it up for use as a DC ammeter. MEASURING CURRENT IN SERIES CIRCUITS Ammeters are represented in circuit diagrams by a capital "A" with a circle around it. Connect dry cells, light bulbs, and an ammeter as shown in the diagrams on the back. Record each ammeter reading under the appropriate diagram. Unit 15: Electrical Circuits, Lab B: Current

5 Circuit #1 Current = A Circuit #2 Current = A Circuit #3 Current = A Circuit #4 Current = A 1. Which circuit had the brightest bulb(s)? Which had the dimmest bulb(s)? 2. State the relationship between the measured current and the observed brightness of the bulbs. ANSWER THIS AND ALL REMAINING QUESTIONS WITH COMPLETE SENTENCES 3. Which pair(s) of circuits would allow you to see how the number of sources affects current? 4. State how the number of energy sources affects the current in a circuit. 5. Which pair(s) of circuits would allow you to see how the number of users affects current? 6. State how the number of energy users affects the current in a circuit. Unit 15: Electrical Circuits, Lab B: Current

6 15 Electrical Circuits Nam e Alternate Lab A/B: AMMETERS AND VOLTMETERS You have completed electrostatics, the study of electrical charges at rest. Mankind's earliest knowledge of electrostatics dates back many centuries. We are now entering the study of electrical charges that are in motion - electrodynamics. Electric circuits, with currents to run lamps and motors, did not develop until batteries were invented around the year The growth of the use of electricity was then so rapid that it produced not just a part of physics but a new electrical civilization in less than a century. An electric energy source and an electric energy user can be connected in a way that furnishes evidence that electrical energy is being used. That hookup is called an electrical circuit. Every electrical circuit must have at least one energy source and one energy user. It must also have a way to connect the energy source and the energy user. The connectors, the energy source, and the energy user are the circuit elements. In this lab, you will be hooking up various simple circuits and measuring quantities known as voltage and current. One can compare the flow of electrons through a circuit to the flow of water through a stream. Current in an electrical circuit is much like current in a stream - it is a measurement of flow. Electrons flow in circuits, of course, not water. As for voltage, synonyms for voltage include "potential difference" and "electromotive force". Voltage is literally the potential energy difference per unit charge in a circuit. In the analogy to a stream, voltage would be like a waterfall that provides the impetus for the current. In constructing electrical circuits, one follows (or creates) diagrams to signify the various elements and how they are connected. At right are some common symbols used for circuit elements. Please note that in physics parlance, a "battery" is a connection of several wet or dry cells, not a single dry cell as is used colloquially. Your car "battery" is a true battery because it consists of several connected wet cells. An ammeter is a device that measures how much current is moving through a circuit. Current is measured in amperes. That is why the current measurer is called an ammeter. A voltmeter is a device that measures how much voltage is generated or used by a circuit element. Voltage is measured in volts. Ammeters and voltmeters are designed to be hooked into a circuit in very specific ways. Improper connection of these meters to a circuit can destroy them. Be very careful when hooking meters into circuits! Ammeter Procedure When you measure the current in a circuit, you connect the ammeter directly into the circuit, with one wire connecting the positive (+) terminal of the ammeter to the part of the circuit leading to the positive (+) terminal of the dry cell. The second wire connects the negative (-) terminal of the ammeter to the part of the circuit leading to the negative (-) terminal of the dry cell. Another rule is that you should never hook an ammeter into a circuit that does not have some sort of resistor (such as a light bulb) in it. Otherwise, you will be setting up a short circuit and may overload the ammeter. Voltmeter Procedure When you measure a dry cell's voltage, one wire is connected from the positive (+) terminal of the dry cell to the positive (+) terminal of the voltmeter. The second wire connects the negative (-) terminals of the dry cell and the voltmeter. The voltmeter is then hooked across the dry cell. Whenever a voltmeter is used to measure (in volts) the voltage of any electrical circuit element, the voltmeter is always hooked across that element, such that the side of the element corresponding to the positive side of the circuit is attached to the positive terminal of the meter, and the negative side of the element is attached to the negative terminal of the meter. Unlike ammeters, voltmeters can be hooked into circuits that have no resistors in them. If there are resistors, however, voltmeters should be hooked across the circuit, not directly into it. Before you begin the main experiment, let s try lighting a bulb using only one wire and one battery. Unscrew a light bulb from its socket and figure out how to connect the parts. Sketch in the space below how you make the connections. Then deduce how the light bulb is wired, and complete the wires in the diagram at right to show how they must connect to the base of the bulb. Unit 15: Electrical Circuits, Alternate Lab A/B: Ammeters and Voltmeters

7 Now hook up the four circuits shown below. (Each lab partner should independently build one of the circuits.) Record the current and voltage for each circuit in the table as well as the relative brightness of the bulbs. Circuit #1 Circuit #2 Circuit #3 Circuit #4 Circuit Current (amperes) Voltage (volts) Bulb Brightness (qualitative) Which circuit(s) had the brightest bulb(s)? answer all questions in complete sentences 2. What simple explanation (in terms of energy sources and energy users) can you give for your answer to question 1? 3. Which circuit(s) had the dimmest bulb(s)? 4. What simple explanation (in terms of energy sources and energy users) can you give for your answer to question 3? 5. In the scientific method, one should only change one variable to observe how it affects another variable. (You cannot change two variables simultaneously to see how only one of them affects a third variable.) Which pairs of circuits should you compare to see if the number of bulbs affects the voltage readings? What effect, if any, do you see? 6. Which pairs of circuits should you compare to see if the number of bulbs affects the current readings? What effect, if any, do you see? 7. Which pairs of circuits should you compare to see how voltage affects current? What effect, if any, do you see? Unit 15: Electrical Circuits, Alternate Lab A/B: Ammeters and Voltmeters

8 15 Electrical Circuits Nam e Lab C: OHM'S LAW You will recall from our electrostatics unit that voltage is energy change per unit charge. The instructor will demonstrate how to use a voltmeter, a device which measures the change in electrical energy per unit charge occurring across a circuit element. The instructions are summarized below: Voltmeter Procedure To measure the voltage across a circuit element, one wire is connected from the positive (+) terminal of the voltmeter to the positive (+) side of the circuit element. Another wire connects the negative (-) terminal of the voltmeter to the negative (-) side of the circuit element. Voltmeters are always hooked across an element, not in series with it. The voltmeter can be thought of as a small parallel circuit added onto the existing circuit. Never hook a voltmeter in series. You will experiment to discover the relationship between voltage (V), current (I), and resistance (R). We will begin by examining how voltage affects current when resistance is held constant. Connect circuits 1, 2, and 3. Set the power supply as indicated or hook up dry cells to create the required voltages. Measure and record in Table I the voltage and the current for each. (Measure the voltage - do not assume it is what you set on the supply or what you see on a dry cell s label.) Circuit #1: Voltage Set at 1.5V Circuit #2: Voltage Set at 3V Circuit #3: Voltage Set at 4.5V Table I - Voltage and Current Data read the meters to the limit of their precision Circuit Voltage = V (volts) Current = I (amperes) Resistance = R (ohms) Use the computer to construct a graph of the data with current on the x-axis and voltage on the y-axis. 1. The shape of your graph indicates the relationship between voltage and current. What is that relationship? 2. Use the program s regression line capability to fit a line to your graph. W rite out the complete linear equation relating voltage (V) and current (I), inserting properly rounded slope and y-intercept numbers. 3. The slope of the graph is related to what was held constant in the experiment. Identify the proper relationship and use it to re-write your equation in purely symbolic form. 4. We will consider your graph s slope to be a measured value. The supposed value of the resistors can provide a theoretical value for what the slope should have been. Compute the percentage error between those values. show your work Unit 15: Electrical Circuits, Lab C: Ohm s Law

9 Next we will examine how resistance affects current when voltage is held constant. Connect circuits 4, 5, 6, and 7. BE SURE TO PROVIDE A VOLTAGE OF 1.5 V. Record all data in Table II. Circuit #4 Circuit #5 Circuit #6 Circuit #7 Table II - Resistance and Current Data read the meters to the limit of their precision Circuit Voltage (V) Current (A) Resistance (Ù) Use the computer to construct a graph of the data. Graph resistance on the x-axis and current on the y-axis 5. The shape of your graph indicates the relationship between resistance and current. What is that relationship? 6. You cannot perform a linear fit to a curve. Select your data points and then have the computer perform a curve fit. What type of fit did you select? 7. The computer will provide the necessary constant(s) for your curve. Write out the complete equation relating resistance (R) and current (I), inserting the appropriately rounded constant(s). 8. The constant in your equation is related to what was held constant in the experiment. Identify the relationship and rewrite your equation in purely symbolic form. Your answers to questions 3 and 8 should be mathematically equivalent. If they are not, ask the instructor for assistance. 9. Use the value from your graph as the measured value and the average voltage as the theoretical value to calculate a percentage error. show your work 10. You have discovered a relationship known as Ohm's Law. It states that the current in a circuit is to the and to the. Unit 15: Electrical Circuits, Lab C: Ohm s Law

10 15 Electrical Circuits Nam e Reading: ELECTRIC SHOCK Your body is controlled by electrical nerve impulses, so electric currents can disrupt normal bodily functions. It is the current that passes through your body, not the voltage across it, which determines the severity of the shock. The current can damage your organs, with the heart, brain, and spinal cord being particularly susceptible. Ohm's Law gives the amount of current actually passing through the body as I=V/R. The resistance used varies with the situation. Internally, your blood and fluids are good conductors with a resistance of about 200 Ù. Externally, current must first pass through the skin (unless it is cut) and it typically has a much higher resistance. A calm person's dry skin may have a resistance of 500,000 Ù, while sweaty palms may have a resistance 10 to 50 times lower. (This is why a lie detector measures skin resistance along with other physiological factors.) A person standing in saltwater has a skin resistance of only 500 Ù. Usually the electric current must pass through three series resistances: your skin (e.g. your nose), body fluids, and your skin again (e.g. your toes). Thus if your greasy nose has a resistance of 50,000 Ù, your blood has 200 Ù, and your sweaty feet have 10,000 Ù and you cross a 120 V household circuit, a current of (120 V) / (50,000 Ù Ù + 10,000 Ù) = A will pass through you. What would that do? A current greater than 1 ma (0.001 A) causes discomfort. Above 16 ma, you lose control of your muscles and they undergo contractions. Between 25 ma and 100 ma, you have difficulty breathing and eventually respiration stops. Between 100 ma and 200 ma, your heart stops pumping and undergoes uncoordinated contractions called ventricular fibrillation. Above 200 ma, irreversible heart damage occurs. So with a greasy nose and sweaty feet, the 2 ma current would cause discomfort. Special thanks to Dr. Stewart Ryan of the University of Oklahoma PROBLEMS show your work 1. Repairing his car in the rain, Victor Vector puts his hands on the terminals of its 12.0 V battery. If his total resistance is 10,000 Ù, what current and effects will he experience? 2. Despondent over the latest test results, Victor sharpens his fingers and puts them in the slots of a 120 V wall outlet while bathing in saltwater. If his total resistance is 1,300 Ù, what current and effects will he experience? Unit 15: Electrical Circuits: Readings on Electric Shock, Power, & Appliances

11 15 Electrical Circuits Nam e Reading: POW ER AND APPLIANCES Current is the rate of charge flow, so one ampere is equal to one of charge flowing past a point in the circuit each. So 1 A = 1 / 1. Voltage is the energy change per unit charge, so one volt is equal to one of energy change for each of charge that flows. So 1 V = 1 / 1. If you multiply current and voltage, the result is measured in AV, but using the above definitions of amperes and volts, that can be simplified to 1 / 1, which is the same thing as 1, indicating that the product of current and voltage is. Below is a table of common appliances and their current and power requirements. Appliance Current (A) Power (W) Stereo system W incandescent light bulb Desktop computer Televisions: Average CRT Average LCD Average rear projection Average plasma Drip coffee maker Garage-door opener Vacuum cleaner door refrigerator (18 ft ) Steam iron Toaster (2-slot) Dishwasher Microwave oven Clothes washer Clothes dryer * Water heater * Electric stove (4-burner) and oven * Forced-air heater * * this appliance runs on a 240 V circuit instead of 120 V Mostly taken from The Physics Teacher, Vol. 32, p. 511; TV data from CNET.com, 4/2007 Your home's electrical system is split into several parallel circuits. Each circuit is protected from shorts (where wires cross, causing low resistance and high current) or overloads (where too many appliances are turned on, causing high current) by a fuse or circuit breaker. The fuse melts or the circuit breaker switch turns off when the current exceeds a safe value. A typical kitchen might have an electric oven, microwave, dishwasher, refrigerator, drip coffee maker, and four 60 W light bulbs. If all were operating, the current would be: 45.4 A + 10 A A A A + 2 A = 76 A. That large a current would require very large wires, so the kitchen would likely run off two separate circuits. One 50 A, 240 V circuit would be for the oven. Another 35 A, 120 V circuit would serve the rest of the kitchen. PROBLEM: How much power could be output from a 35 A, 120 V circuit? show your work Unit 15: Electrical Circuits: Readings on Electric Shock, Power, & Appliances

12 15 Electrical Circuits Nam e Enrichm ent: RESISTORS You have found that greater resistance in a circuit results in lower current. Any material has some innate resistance to current, even such excellent conductors as copper wire. In wires, that resistance is a nuisance. In other situations, resistance is useful. Everyday appliances and electrical gadgets contain resistors to regulate the current. Too much current could easily overload the circuits in your calculator, for example. Specialized resistors have color-coded rings on their outer coverings that indicate exactly how much resistance in ohms (Ù) the resistor will theoretically give to a circuit. The 4-band resistor color-coding scheme, that yields 2 significant figures of precision, is shown below; some resistors use 5 bands for 3 sig figs. Band 1 First Digit: 0 Black 1 Brown 2 Red 3 Orange 4 Yellow 5 Green 6 Blue 7 Violet 8 Gray 9 White Band 2 Second Digit: 0 Black 1 Brown 2 Red 3 Orange 4 Yellow 5 Green 6 Blue 7 Violet 8 Gray 9 White Band 3 Put the first two digits together and then multiply by: Silver: multiply by.01 Gold: multiply by.1 Black: multiply by 1 Brown: multiply by 10 Red: multiply by 100 Orange: multiply by 1,000 Yellow: multiply by 10,000 Green: multiply by 100,000 Blue: multiply by 1,000,000 Band 4 Indicates Resistor Accuracy (below are a few examples) Black or no band: accurate to ± 20% Silver: accurate to ± 10% Gold: accurate to ± 5% xkcd.com So a resistor labeled BROWN-BLACK-BROWN-GOLD means 1 0 x 10 = 100 Ù to within ± 5%, or ± 5 Ù. So it is between 95 Ù and 105 Ù. While a resistor labeled RED-GREEN-YELLOW-SILVER means 2 5 x 10,000 = 250,000 Ù within ± 10%, or ± 25,000 Ù, or 225,000 Ù to 275,000 Ù. What would be the color code for a high-quality 66 Ù resistor? What would be the color code for a high-quality 37,000 Ù resistor? Let's find out how close the theoretical value of some resistors are to their measured values in an actual circuit. At your lab station you will find three resistors, leads, a power supply or dry cell, and meters. Set up a circuit like the one diagramed at right to test your resistors. DO NOT EXCEED 1.5 VOLTS Resistor Voltage (V) Current (A) Actual Resistance (Ù) found with Ohm s Law Labeled Resistance (Ù) Percentage Error Unit 15: Electrical Circuits, Enrichment on Resistors

13 15 Electrical Circuits Nam e Lab D: SERIES CIRCUITS We will now use your new voltmeter and ammeter skills to discover how current, voltage, and resistance operate in any series circuit. You will be using a series circuit with a power supply set at 3 V (or the equivalent battery) and three resistors. Ammeter and voltmeter readings will be taken for each of the resistors and the power supply/batteries. DO NOT EXCEED 3 V. Step 1: Set up the circuit with the ammeter positioned to measure the current entering resistor one (R 1). (See diagram A.) Enter the reading in the "R 1" row of the table. Diagram A Step 2: Move the ammeter to measure the current entering R 2 (diagram B) and enter the reading in the "R " row of the table. 2 Step 3: Move the ammeter to measure the current entering R 3 (diagram C) and enter the reading in the "R " row of the table. 3 Diagram B Step 4: Move the ammeter so that it measures the total current entering the power supply (diagram D) and enter that reading in the "Measured Total" row. Resistor Voltage (V) Current (A) M easured Resistance (Ù) R 1 Diagram C R 2 R 3 Measured Total Diagram D Diagram E Step 5: Remove the ammeter from the circuit entirely. Now set the voltmeter across R 1 to measure how much voltage it is using or "dropping". (See diagram E.) You are measuring the voltage drop across R 1. Enter the voltage drop in the "R " row of the table. 1 Step 6: Move the voltmeter to measure the voltage drop across R 2 (diagram F). Enter the reading in the "R " row. 2 Step 7: Move the voltmeter to measure the voltage drop across R 3 (diagram G). Enter the reading in the "R " row. 3 Step 8: Move the voltmeter so that it measures the total voltage provided by the power supply (diagram H). Enter the reading in the "M easured Total" row. Diagram F Diagram G Diagram H Unit 15: Electrical Circuits, Lab D: Series Circuits

14 Use Ohm's Law to calculate the resistance for R 1, R 2, and R 3. Then use the "Total" voltage and current values to calculate the total resistance of the circuit. Record all of your results in the "Resistance" column of the table. answer all questions in complete sentences 1. How do the four current readings compare with each other? 2. What does this tell you about the current flowing through each part of the circuit? 3. How do the individual voltages compare with the total voltage? 4. How would you compute the total voltage of a series circuit if you only knew the values of the individual voltages? (Look at your data for a mathematical relationship.) 5. Voltage and energy are proportional. Look at the voltage data for the various individual resistors. Is energy distributed evenly? If not, what seems to make a particular resistor use more energy? 6. How would you compute the total resistance of a circuit like the one you just worked with for any number of resistors if you knew the values of the individual resistors? (Look at your data - see the pattern?) PROPERTIES OF SERIES CIRCUITS 7. You can now formulate the relationships between the total and individual values for current, voltage, and resistance in any series circuit. Use your answers to questions 1-6 to guide you. The current: The resistance: The voltage: Unit 15: Electrical Circuits, Lab D: Series Circuits

15 15 Electrical Circuits Nam e W orksheet A: SERIES CIRCUIT PROBLEMS be careful to use proper significant figures on all answers 1. What would be the required voltage of an energy source in a circuit with a current of 10.0 A and a resistance of 11.0 Ù? 2. Three 1.50 V cells are connected to form the energy source of a series circuit. The total resistance in the circuit is 100 Ù. How much current moves through the circuit? 3. What is the total resistance of the circuit shown in the diagram at right? 4. How much current moves through the 5.00 Ù resistor in that circuit? 5. How much voltage is dropped across the 5.00 Ù resistor? (Remember, you must use Ohm's Law to get the correct voltage drop.) 6. How much voltage is dropped across the 2.00 Ù resistor? 7. How much voltage is dropped across the 3.00 Ù resistor? 8. Show the total of the above three answers in the space below. It should match the battery voltage. If it doesn't, you need to go back and rework problems 5, 6, and The circuit shown below has three numbered resistors, three voltmeters, and an ammeter positioned as shown. Use Ohm's Law and the properties of series circuits to complete the table. (Hint: One way to avoid rounding errors is to place any unrounded numbers outside the table near the rounded ones you place in the boxes. Make sure your box entries have 3 significant figures.) Diagram Position Voltage (V) Current (A) Resistance (Ù) Total 15.0 Unit 15: Electrical Circuits, Worksheet A: Series Circuit Problems

16 15 Electrical Circuits Name Lab E: PARALLEL CIRCUITS We will now discover how current, voltage, and resistance operate in any parallel circuit. Set the power supply at 1.5 V for this lab, or use a single dry cell. DO NOT EXCEED 1.5 V. Step 1: Set up a circuit with a power supply set at 1.5 V and two resistors as shown in diagram A. The ammeter is positioned to measure the current entering resistor one (R 1), while the voltmeter measures its voltage drop. Enter the readings in the "R " row of the table for the "Two-Resistor Circuit". 1 Diagram A Step 2: Move the ammeter and voltmeter to measure the current entering R 2 and its voltage drop (diagram B). Enter the readings in the "R " row of the table. 2 Step 3: Move the ammeter and voltmeter to measure the total current entering the power supply and the total voltage supplied by the power supply (diagram C). Enter those readings in the "Total" row. Diagram B Circuit Resistor Voltage (V) Current (A) Theoretical Resistance (Ù) Actual Resistance (Ù) Two- Resistor Circuit Three- Resistor Circuit R 1 R 2 Total R 1 R 2 R 3 Total Diagram C Diagram D Step 4: Now set up the three-resistor circuit shown in Diagram D. The ammeter and voltmeter are initially positioned to measure the current entering and the voltage drop across R 1. Enter those readings in the "R 1" row of the table for the "Three-Resistor Circuit". Diagram E Step 5: Move the ammeter and voltmeter to measure the current entering R 2 and its voltage drop (diagram E). Enter the readings in the "R " row of the table. 2 Step 6: Move the ammeter and voltmeter to measure the current entering R 3 and its voltage drop (diagram F). Enter the readings in the "R " row of the table. Step 7: Move the ammeter and voltmeter to measure the total current entering the power supply and the total voltage supplied by the power supply (diagram G). Enter those readings in the "Total" row. 3 Diagram F Diagram G Unit 15: Electrical Circuits, Lab E: Parallel Circuits

17 answer all questions in complete sentences 1. In either circuit you constructed, how do the voltage drops across the individual resistors compare with the voltage for the power supply? Contrast this to the behavior in a series circuit. 2. Your data shows how current flows through parallel circuits. Contrast this to the behavior in a series circuit. 3. How are resistance and current related in the different parts of a parallel circuit? (Does higher resistance result in higher or lower current, or does it have no effect?) Determine the theoretical resistance of each resistor in the circuits, and then calculate the actual resistances using Ohm's Law. Record those values in the table. Using Ohm's Law, you can also calculate the actual total resistance of the circuits, using the readings for total voltage and total resistance. Record those values in the table. 4. Adding a resistor to a series circuit increases the total resistance. Parallel circuits behave differently: compare the two total resistance values in the table. How did the total resistance change when a third resistor was added? 5. How do the total resistances compare with the individual resistances in parallel circuits? There is a formula for computing the total resistance of a parallel circuit for any number of resistors. We will derive this formula together later. PROPERTIES OF PARALLEL CIRCUITS 6. You can now formulate the relationships between the total and individual values for current, voltage, and resistance in any parallel circuit. Use your answers to questions 1-5 to guide you. The current: The voltage: The resistance: Unit 15: Electrical Circuits, Lab E: Parallel Circuits

18 15 Electrical Circuits Name W orksheet B: PARALLEL CIRCUIT PROBLEMS 1. What is the total or effective resistance of the circuit shown in the diagram at right? 2. How much voltage is there across the 20.0 Ù resistor? 3. How much current moves through the 20.0 Ù resistor? 4. How much voltage is there across the 15.0 Ù resistor? 5. How much current moves through the 15.0 Ù resistor? 6. Calculate the sum of answers three and five and show it below. It should equal the total current found by dividing the battery voltage by the total resistance calculated in problem 1. If it doesn't, you need to go back and rework The circuit shown below has two numbered resistors, a voltmeter, and an ammeter positioned as shown. Use Ohm's Law and the properties of parallel circuits to complete the table. (Hint: One way to avoid rounding errors is to place any unrounded numbers outside the table near the rounded ones you place in the boxes. Make sure your box entries have 3 significant figures.) Diagram Position Voltage (V) Current (A) Resistance (Ù) Total 8. The circuit shown below has three numbered resistors and an ammeter positioned as shown. Use Ohm's Law and the properties of parallel circuits to complete the table. Diagram Position Voltage (V) Current (A) Resistance (Ù) Total 3.00 Unit 15: Electrical Circuits, Worksheet B: Parallel Circuit Problems

19 15 Electrical Circuits Name W orksheet C: SERIES & PARALLEL CIRCUITS; POW ER IN CIRCUITS 1. A 6.00 Ù resistor, a 54.0 Ù resistor, and a 32.0 Ù resistor are connected in series. Calculate their total resistance. 2. Calculate the total resistance of four 8.00 Ù resistors connected in parallel. 3. A 15.0 Ù resistor, a 6.00 Ù resistor, and a 39.0 Ù resistor are connected in series across a potential difference of 120 V. a) Calculate the current flowing through the circuit. b) Calculate the voltage drop across the 15.0 Ù resistor. 4. Three resistors are connected in parallel across 20.0 V. The resistors draw a total of 5.00 A. Two of the resistors have values of 24.0 Ù and 12.0 Ù. What is the value of the third resistor? Show your work, even if you use a table. 5. Fill out the table for the circuit diagramed at right. Showing work is optional here. Circuit Position Voltage (V) Current (A) Resistance (Ù) Total Fill out the table for the circuit diagramed at right. Showing work is optional here. Circuit Position Voltage (V) Current (A) Resistance (Ù) Total 6.00 Unit 15: Electrical Circuits, Worksheet C: Series & Parallel Circuits; Power in Circuits

20 7. A coffee pot rated at 360 W, an iron rated at 960 W, and an oven rated at 1200 W are connected in parallel across 120 V. The 15.0 A fuse in the circuit immediately blows. Calculate the total current drawn. 8. Phluffy s shock collar (she meows too much) delivers a current of A and runs on a 9.00 V battery. a) What is the power of the collar circuit in watts? b) Over a three month period the collar is in operation for a total of 600 seconds. How many joules of electrical energy was consumed during that period of time? Show an equation for calculating energy when you know the power and the time. Unit 15: Electrical Circuits, Worksheet C: Series & Parallel Circuits; Power in Circuits

21 15 Electrical Circuits Name W orksheet D: COMPOUND CIRCUIT PROBLEMS 1. Use the diagram at right to answer the following questions. You may use a table to guide your work, but you must show all relevant equations and calculations in the spaces below. a) What is the effective resistance of the parallel part of the circuit? (3.00 Ù) b) What is the total resistance of the entire circuit? c) What is the reading on the ammeter? d) What is reading on the voltmeter? 2. Fill out the table for the circuit diagramed at right. Showing work is optional here. Circuit Position Voltage (V) Current (A) Resistance (Ù) Total 3. Two 12.0 Ù resistors and a 6.00 Ù resistor are each connected in parallel. A 15.0 Ù resistor is added to the parallel group in series. All of them are connected to a single voltage source, and an ammeter is placed to measure total current. a) Draw the circuit, including the resistors, source, and ammeter. b) Calculate the voltage of the source if the ammeter shows a reading of 2.00 A. Show your equation and all work. Unit 15: Electrical Circuits, Worksheet D: Compound Circuit Problems

22 15 Electrical Circuits Name W orksheet E: COMBINATION CIRCUITS, POW ER IN CIRCUITS, CAPACITORS 1. A 200 Ù and a 300 Ù resistor are connected in parallel. This parallel arrangement is connected in series with a 10.0 Ù resistor. The total potential difference per unit charge in this circuit is 15.0 V, which is supplied by an arrangement of six 5.00 V dry cells. a. Draw a diagram of the circuit, including how the six 5.00 V cells could be arranged to provide 15.0 V. Include in your diagram an ammeter that would measure total current (see part d below) and a voltmeter that could measure the voltage across a parallel resistor (see part f below). b. What is the effective resistance of the parallel portion of the circuit? c. What is the effective resistance of the entire circuit? d. What is the total current in the entire circuit? e. What is the voltage drop across the 10.0 Ù resistor? f. What is the voltage drop across the parallel portion of the circuit? g. What is the current through the 200 Ù resistor? h. What is the current through the 300 Ù resistor? The correct answer is A. Unit 15: Electrical Circuits, Worksheet E: Combination Circuits, Power in Circuits, Capacitors Page 1 of 4

23 2. Fill out the table for the circuit diagramed at right. use proper sig figs Circuit Position Voltage (V) Current (A) Resistance (Ù) Total Fill out the table for the circuit diagramed at right. use proper sig figs Circuit Position Voltage (V) Current (A) Resistance (Ù) Total Fill out the table for the circuit diagramed at right. use proper sig figs Circuit Position Voltage (V) Current (A) Resistance (Ù) Total If the cells are identical, which circuit would draw the most current from the cell? 6. If the resistors are identical, which circuit would have the lowest overall change in electrical potential energy per unit charge? Unit 15: Electrical Circuits, Worksheet E: Combination Circuits, Power in Circuits, Capacitors Page 2 of 4

24 7. Use the diagram of the complex circuit to answer the following questions. You may use a table to guide your work, but you must show all relevant equations and calculations in the spaces below. a) What is the effective resistance of the parallel part of the circuit? b) What is the total resistance of the entire circuit? c) What is the reading on the voltmeter? (You may use a table to guide your approach, but you must separately show all equations and calculations.) d) What is the reading on the ammeter? The correct answer is 1.76 A. POWER IN CIRCUITS: 8. Phluffy s shock collar (she meows too much) delivers a current of A and runs on a 9.00 V battery. a) What is the power of the collar circuit in watts? b) Over a three month period the collar is in operation for a total of 600 seconds. How many joules of electrical energy were consumed during that period of time? show the equation c) A typical 9.00 V battery might cost $2.40 and provide 19,250 J of energy. What is the cost of running the shock collar as described in parts a and b? Unit 15: Electrical Circuits, Worksheet E: Combination Circuits, Power in Circuits, Capacitors Page 3 of 4

25 CAPACITORS: 9. If the cells are identical, which circuit would store the most total charge? 10. The circuit diagram at right shows a 3.00 ìf capacitor hooked up in parallel across a 5.00 Ù resistor that is in turn hooked up in series with a 10.0 Ù resistor. The emf sources in the circuit are two 12.0 V sources hooked in series with one another. a) Use the information provided to determine the voltage across the capacitor after it is fully charged. b) Now find the charge on one of the plates of the fully-charged capacitor. c) How much current is detected by the ammeter once the capacitor is fully charged? Unit 15: Electrical Circuits, Worksheet E: Combination Circuits, Power in Circuits, Capacitors Page 4 of 4

26 PHYSICS TEST REVIEW Nam e Electrostatics and Electrical Circuits Write a "P" in the blank by each statement that describes a parallel circuit. Write a "S" in the blank by each statement that describes a series circuit. 1. When more light bulbs are added, they all still remain bright. 2. Different voltages are dropped across each resistor. 3. Different currents flow through each resistor. 4. If one part of the circuit fails, the other parts still work. 5. The total resistance is equal to the sum of the individual resistances. Write the letter corresponding to the best answer in the blank by each question. 6. The total resistance of a parallel circuit is always... A) greater than the sum of all the individual resistances. B) greater than any of the individual resistances. C) equal to the smallest of the individual resistances. D) less than any of the individual resistances. 7. When another resistor is added to a parallel circuit, the total current... A) goes up. B) goes down. C) is unaffected. 8. If a short occurs in one room of a house and it goes dark, but all the other rooms stay lit, it is because... A) all of the fuses have blown. B) the short has only blown one fuse and the rest of the house is still lit because it is in series. C) the short has only blown one fuse and the rest of the house is still lit because it is in parallel. D) the short has not blown any of the fuses. 9. Circuit "S" has three 10 Ù resistors in series with a 10 V battery. Circuit "P" has three 10 Ù resistors in parallel with another 10 V battery. Which statement is NOT true? A) The total voltage of circuit "S" is greater than the total voltage of circuit "P". B) The total current in circuit "S" is less than the total current in circuit "P". C) The total resistance of circuit "S" is greater than the total resistance of circuit "P". 10. An ammeter should have a very... A) low resistance, since it is hooked in series. B) low resistance, since it is hooked in parallel. C) high resistance, since it is hooked in series. D) high resistance, since it is hooked in parallel. 11. A series circuit is composed of a 10.0 V battery and three resistors, which are 2.00 Ù, 6.00 Ù, and 12.0 Ù. How much current flows through the 12.0 Ù resistor? 12. A space heater has a current of 12.0 A flowing through it and an effective resistance of 9.00 Ù. A) Calculate the power of the heater. B) How many kilowatt-hours of heat energy could this heater produce if it operated for an hour? C) How many joules of energy is that? D) If PSO charges 6.00 cents per kwh, how much would it cost to run the heater for 8.00 hours? Test Review for Units 14-15: Electrostatics & Electrodynamics

27 Physics Test Review over Electrostatics and Electrical Circuits Page Fill in the table for each circuit, using 3 significant figures. Series Position Voltage (V) Current (A) Resistance (Ù) Total 5.00 Parallel Position Voltage (V) Current (A) Resistance (Ù) Total 5.00 Complex #1 Pos. Voltage (V) Current (A) Resistance (Ù) Total 5.00 Complex #2 Pos. Voltage (V) Current (A) Resistance (Ù) Total 12.0 Test Review for Units 14-15: Electrostatics & Electrodynamics

28 Physics Test Review over Electrostatics and Electrical Circuits Page When the distance between two charges is halved, the electrical force between them... A) quadruples. B) doubles. C) halves. D) reduces to one fourth. 15. If you comb your hair and the comb becomes negatively charged,... A) electrons were transferred from the comb onto your hair. B) electrons were transferred from your hair onto the comb. C) protons were transferred from the comb onto your hair. D) protons were transferred from your hair onto the comb. 16. Which statement correctly describes how to charge something negatively by conduction? A) Touch it with a positively charged object. B) Touch it with a negatively charged object. C) Momentarily ground it with a positively charged object nearby. D) Momentarily ground it with a negatively charged object nearby. 17. If a neutral conductor is touched by a rubber rod with a negative charge on it, what will happen? A) Electrons will flow from the conductor onto the rubber rod. B) Electrons will flow from the rubber rod onto the conductor. C) Protons will flow from the conductor onto the rubber rod. D) Protons will flow from the rubber rod onto the conductor. 18. Protons and electrons... A) repel each other. B) attract each other. C) have no effect on each other. 19. Coulomb's law says that the force between any two charges depends... A) inversely on the product of the charges. B) directly on the square of the distance between the charges. C) directly on the product of the charges. D) inversely on the square root of the distance between the charges. 20. In a good insulator, electrons are usually... A) free to move around. B) free to move around after an impurity has been added. C) semi-free to move around. D) tightly bound in place. 21. A leaf electroscope is neutral. As a negative charge is brought close to the electroscope, the leaves spread apart because the approaching negative charge... A) attracts and pulls electrons away from them. B) attracts and pulls protons away from them. C) pushes electrons down onto them. D) pushes protons down onto them. 22. The reason a pith ball will be attracted to a charged rubber rod is that... A) the rod is positive and attracts electrons in the pith ball. B) the rod is negative and repels electrons in the pith ball, attracting the nearer protons. C) the rod is positive and repels electrons in the pith ball, attracting the nearer protons. D) the rod is negative and attracts electrons in the pith ball. 23. A girl accidentally touches a partially plugged-in lamp plug one day. If the voltage from the wall outlet was 120 V and her skin's resistance was 120,000 Ù, how much current passed through her body? A) 12,000,000 A B) 1,000 A C) 120 A D) A Test Review for Units 14-15: Electrostatics & Electrodynamics

29 Physics Test Review over Electrostatics and Electrical Circuits Page A positively charged metal ball was motionless on a flat table. Two charged rods were brought up the ball as shown in the diagram. In what compass direction did the ball move? A) southwest B) southeast C) northwest D) northeast 25. Circuit "S" has three users in series with a cell. Circuit "P" has the same circuit elements as circuit "S", but they are connected in parallel. Which statement is true? A) The total current in "P" is greater than the total current in "S". B) The total voltage of "P" is greater than the total voltage of "S". C) The total resistance of "P" is greater than the total resistance of "S". 26. Which statement correctly describes a short circuit? A) Too many users are plugged into the circuit, lowering its total resistance, causing high currents. B) Too many users are plugged into the circuit, raising the total resistance, causing low currents. C) Wires in the circuit become crossed, making it a series circuit and thus causing high currents. D) Wires in the circuit become crossed, making it "shorter" and thus causing high currents. 27. When another user is activated in a parallel circuit... A) the total resistance rises. B) the total current falls. C) the total resistance falls. D) the total voltage increases. 28. Which statement correctly describes an ammeter? A) It has high resistance because it hooks into a circuit in parallel. B) It has high resistance because it hooks into a circuit in series. C) It has low resistance because it hooks into a circuit in parallel. D) It has low resistance because it hooks into a circuit in series. For each of the procedures described below, place the letter of the diagram that best represents the resulting charge arrangements on the electroscope. 29. A negatively charged rod is brought near, but not touching an uncharged electroscope. 30. A negatively charged rod is used to charge the scope by induction. 31. A positively charged rod is used to charge the scope by conduction. 32. A negatively charged electroscope is grounded. 33. A 5.00 Ù resistor, 10.0 Ù resistor, and a rheostat are connected in parallel and placed across a 12.0 V source. What amount of resistance should be set for the rheostat in order to draw a total current of 4.20 A from the source? Test Review for Units 14-15: Electrostatics & Electrodynamics

30 Electrical Circuits Test Review Nam e ADDITIONAL CIRCUIT ANALYSIS PRACTICE: 1. Use the diagram at right to answer the following questions. a) What is the voltage across the capacitors after they are fully charged? B) What is the charge on the 6.00 ìf capacitor? C) What is the total capacitance of the circuit? 2. Use the diagram at right to answer the following questions. a) What is the effective resistance of the parallel part of the circuit? B) What is the total resistance of the entire circuit? C) What is the reading on the ammeter? D) What is reading on the voltmeter? Unit 15: Electrical Circuits, Test Review

31 3. Fill out the table for the circuit diagramed at right. Circuit Position Voltage (V) Current (A) Resistance (Ù) Total 4. Fill out the table for the circuit diagramed at right. Circuit Position Voltage (V) Current (A) Resistance (Ù) Total 5. Fill out the table for the circuit diagramed at right. Circuit Position Voltage (V) Current (A) Resistance (Ù) Total Three resistors are connected in parallel across 20.0 V. The resistors draw a total of 5.00 A. Two of the resistors have values of 24.0 Ù and 12.0 Ù. What is the value of the third resistor? 7. A transistor radio operates by means of a 9.00 V battery that supplies it with A of current. a) What is the power of the radio in watts? b) The battery cost is unfortunately $9.00 per kilowatt hour. The same radio, by means of a converter, is plugged into a household circuit by a homeowner who pays 5.00 per kilowatt hour. Compute the cost of operating the radio for 300 hours on battery power, and then compute the cost using house current.