By Kevin C. Emery
Teaching High School Physics
Physics 301
Fall Semester 1998
Illinois State University
Carl J. Wenning, Instructor
I. Unit Overview
A. Summary
This unit is dedicated to the study of basic electric circuits. Using a conceptual, experimental, and a somewhat historical approach, students will gain a broad understanding of electricity, electric circuits, and some information about some of the scientists responsible for the development of electrical circuits. Examples of some procedures that will be incorporated into this unit include expository lessons, cooperative learning exercises, and inquiry lessons. Expository lessons involve a dialogue between the instructor and the class as a whole. They are designed to efficiently present information to the students in a clear and organized manner. Cooperative learning exercises involve activities that the students perform in small groups. Some advantages of cooperative learning include individual as well as group accountability, positive interdependence, and improved social skills. Inquiry lessons can also involve groups of students working together. The students, using the inquiry strategy, are forced to think about the concepts and apply the scientific process while doing so. The intended audience, or students, for this unit plan include high school juniors and seniors in the first year standard or accelerated physics classes. Prerequisites include an understanding of algebra and some basic knowledge of currents. The textbook used with this unit is Physics - Principles and Problems by Murphy, Hollon, Zitzewitz, and Smoot.
B. Goals
Some broad goals for this unit plan include a general but clear understanding of basic electric circuits. Students should be able to recognize how electric circuits are used in everyday life. They should, upon completion of the unit, be able to conduct a scientific experiment in which the student would collect and analyze data to reach a conclusion. They should also acquire application skills that allow them to research the topic at a deeper level. These goals, although very broad, meet national and state standards as they incorporate the use of technology in the form of computers to develop and apply scientific skills.
C. Rationale
1) Personal
On a personal level, after the unit is completed, the student should be able to understand the basic concepts that govern electric circuits. This knowledge can become very useful on a utilitarian level. With the technology of household appliances increasing, basic knowledge of electric circuits can give a better understanding of common electrical appliances. In addition, the knowledge learned in this unit provide an excellent basis for further study of the topic of electric circuits.
2) Social
On a societal level, the knowledge and understanding regarding electric circuits is a benefit economically. Having an understanding of electric circuits gives the consumer knowledge which, applied correctly, can help him/her make informed decisions regarding electrical equipment and appliances. Society also benefits by the ability to minimize the cost required to operate such equipment and appliances.\par
3) Professional
The scientific profession can benefit from the knowledge and understanding of electric circuits because now, more than ever, electrical equipment is being used in all branches of scientific research. New and better ways of inquiry and research stemming from an increased knowledge and understanding of electric circuits may lead to new discoveries in science.\par
II. Content/Procedures Outline
A. Definitions
1) Electric Current
2) Battery
3) Photovoltaic cells
4) Coulomb
5) Ampere
6) Voltage
7) Watt
8) Resistance
9) Capacitance
10) Inductance
11) Ammeter v. Voltmeter
B. Graphical Representations
} 1) Ohm\rquote s Law
a) Current v. Resistance
b) Voltage v. Resistance
2) Electric Current
a) Direct Current
b) Alternating Current
3) Circuit Schematic
4) Series Connection v. Parallel connection
5) Electric Potential
6) Effective Circuits
a) Resistance
b) Capacitance
c) Inductance
7) Kirchoff\rquote s Law
III. Major Objectives
A. Major Content Knowledge Objectives
1) Upon completion of the unit, students should be able to correctly identify components of an electric circuit and articulate the relationships between each component.
2) Upon completion of the unit, the student should be able to recognize the direction of the flow of current in an electric circuit and make qualitative and quantitative predictions about the activity in that circuit at a given position.
B. Major Process Skill Objectives
1) Upon completion of the unit, students should be able to correctly define all variables associated with Ohm\rquote s Law (Voltage ({\i V}), Current ({\i I}), and Resistance ({\i R})).
2) Upon completion of the unit , the student should also be able to manipulate Ohm\rquote s Law, as it applies to different situations, to solve simple problems, quantitatively, at 80% accuracy.
3) Upon completion of the unit, students should be able to apply Kirchoff\rquote s Law to answer specific questions about unknowns in a given circuit to an 80% accuracy.
4) Upon completion of the unit, students should be able to interpret data from a graph showing Ohm\rquote s Law relationships, and answer qualitative and quantitative questions about the data from the graph at an 80% accuracy.
C. Major Scientific Disposition Objectives
1) While completing the unit, students should portray a proper scientific attitude toward the activities. Proper attitude includes, but is not limited to curiosity, enthusiasm, appropriate ethics, and cooperation.
2) While completing the unit, student should follow an objective, critical, and logical path when solving a problem a problem or completing an activity.
3) Upon completion of the unit, students should show a confident attitude when approached with a problem or question involving electric circuits.
IV. Alternative Conceptions
Gabel, D.L. (1994). {\ Handbook of research on science teaching and learning}. New York, NY: MacMillan
Mr. Gabel, in his handbook, lists five versions of a distinct model that were used for this research to identify various preconceptions dealing with electricity and electric circuits among children. One of the most popular misconceptions was called the "single-wire" notion. This idea is the belief that current travels through one wire from a battery to a bulb. This bulb served as a type of electricity "sink" where the electricity fell, never to be seen again. Another popular misconception was discovered through the "clashing-currents" model. In this model, electricity leaves both terminals of the battery and travels toward the bulb, where it is "used up" - again, never to be seen again. Specific models called "unidirectional" models m identified more misconceptions. Three that were mentioned in this section were "unidirectional without conservation," "unidirectional with sharing," and "unidirectional with conservation.
The preconceptions mentioned here seem to be age-based. Younger children tend to believe in the single-wire model. Children in their middle years usually believe in the "clashing-current" model. This method is gradually replaced by the "unidirectional" models. The notion of conservation becomes somewhat evident in only about 10 percent of the children at age 12 but grows to about 60 percent acceptance by age 18.
V. Classroom Methods
Two example lesson plans:
A) Unit
Electric Circuits
Objectives
1) Define and explain Ohm's Law and the relationships between all variables involved.
2) Given a simple circuit and resistors in series, apply Ohm\rquote s law and solve for multiple variables at an 80% accuracy.
3) Given a simple circuit of resistors in parallel, apply Ohm\rquote s law and solve for multiple variables at an 80% accuracy.\par
Content:
1) Given that an applied voltage causes a current to flow in a conductor, the current is directly proportional to the voltage:
That is, the greater the voltage, the greater the current. This is analogous to more water flowing through a pipe when there is a greater gravitational potential.
2) Almost every conductor offers resistance to an electric current. This resistance causes a potential difference to exist between the ends of a conductor when current passes through it. The German scientist Georg Simon Ohm (1787-1854) found that the ratio of the potential difference between the ends of the conductor and the current through it is constant for many materials.
3) This ratio is known as the resistance of a conductor. It is constant for any given conductor kept at constant temperature. This relationship, known as Ohm's law, states that the current through a given conductor varies directly with the applied potential difference and inversely with the resistance.
The electric current, I, is in amperes. The potential difference, V, is in volts. The resistance of the conductor, R, is given in ohms.\par
Instructional Activities:
1) Review homework from the previous assignment. Work through problems about which the students specifically ask.
2) Lead an exploratory discussion about simple circuits covering the relationships between voltage, current, and resistance.\
3) Show Ohm\rquote s law demonstration (Demo. F). Explain all facets of the demonstration.
4) Give expository lesson covering the content in this lesson plan.
5) Work through example problem on an overhead projector.
6) Pass out homework assignment due the following class period.
B. Unit:
Electric Circuits
Objectives:
1) Explain, qualitatively and quantitatively, the concept of effective resistance in an electric circuit.
2) Given a simple circuit of multiple resistors in series, students should be able to calculate the effective resistance of the circuit at an 80% accuracy.
3) Given a simple circuit of multiple resistors in parallel, students should be able to calculate the effective resistance of the circuit at an 80% accuracy.
Content:
1) When resistors are connected in series, all current travels through each resistor, one after the other. The effective resistance is the resistance of a single resistor that could replace all the resistors in the circuit.
2) The effective resistance in a series circuit is the sum of the individual resistances.
3) In a parallel circuit, the current can flow through several paths. Consider rapids in a river. The water can divide into several channels. Some channels may have a large flow of water, some a small flow. However, the sum of the flows is equal to the flow of water in the river.
4) The total resistance of a parallel circuit decreases as each new resistor is added. The total current in a parallel circuit is the sum of the currents in its branches. The reciprocal of the effective resistance in a parallel circuit is the sum of each individual reciprocal resistances.
Instructional Activities:
1) Review homework from the previous assignment. Work through problems about which the students specifically ask.
2) Show Equivalent Series Resistance demonstration (Demo L.). Explain all facets of the demonstration.
3) Let students predict solutions for given situations using the Equivalent Series Resistance demonstration
4) Give expository lesson covering the content in this lesson plan.
5) Work through example problem on an overhead projector.
6) Pass out homework assignment due the following class period.
VI. Demonstrations
A. Field and Voltage
1) Concept
The voltage associated with a capacitor is proportional to the distance between the plates of the capacitor.
2) Description/Procedures
A parallel plate capacitor is built so the distance between the plates may be varied. Once the capacitor is charged, the field is essentially constant between the plates. One can then show that the voltage associated with a capacitor is proportional to the distance between the plates of the capacitor.
3) Referencesr
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.
B. Charge on a Capacitor
1) Concept
Energy, in the form of electric charge, can be stored in a circuit by a capacitor. The charge on a capacitor will remain stationary until it is allowed to discharge.
2) Description/Procedures
A capacitor is charged with a battery and discharged through a ballistic galvanometer. The deflection is projected by means of a light beam reflected from a mirror attached to the galvanometer coil. The deflection may be obtained with various voltages and capacitors to argue that Q=CV.\
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.
C. Discharge of a Capacitor
1) Concept
When a capacitor is charged and allowed to discharge, the charge from the capacitor decays slowly according to the time constant which is the product of the meter resistance and the capacitance of the selected capacitor.
2) Description/Procedures
An electrolytic capacitor is charged with a battery. It is then discharged through the resistance of a multirange meter. The time constant is adjusted so that the voltage on the meter can be read during the charge decay.
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.
D. Energy Stored in a Capacitor
1) Concept
The energy stored in a capacitor can be used to do work on an object. There is a direct correlation between the energy stored in a capacitor and the energy used to do work.
2) Description/Procedures
A 500 {\f23 m}f electrolytic capacitor is charged to a known voltage. The capacitor is then discharged through a small motor which can raise a weight. The energy stored in the capacitor is compared to the work done in raising the weight.
3) References
Anderson, F.J. and G.D. Freier (1996). {A Demonstration Handbook for Physics. American Association of Physics Teachers.
E. Model of Resistance
1) Concept
When traveling through a conductor, there is a resistance to the flow of electricity. This resistance depends upon physical properties of the conductor.
2) Description/Procedures
A board is pounded randomly full of nails, spaced so that a ball bearing can roll between them. The balls are rolled through the maze of nails. Boards with different nail configurations may be used to show varying mean free paths.
Different numbers of balls may be used to show different numbers of charge carriers. The board may be inclined at different angles to illustrate the effects of applied E.M.F.
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.
F. Ohm's Law
1) Concept
The voltage across a circuit with resistance is proportional to the current traveling through the circuit and the equivalent resistance of the circuit (V=IR).
2) Description/Procedures
A rheostat, ammeter, and storage battery are connected in series. A voltmeter is connected across the rheostat. The length of wire used in the rheostat is proportional to the ratio of the voltage to the current.
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.\par
G. Temperature Dependence of Resistance
1) Concept
The resistance of a circuit is increased with a temperature increase and decreased with a temperature decrease.
2) Description/Procedures
A light bulb is placed in series with a coil and a storage battery. The coil is at the end of a rod which may be lowered into a dewer of liquid nitrogen. The light burns much more brightly when it is cooled because its resistance is decreased. The coil may then be placed in a Bunsen flame, and the light burns very dim because its resistance is increased. The coil should be made of bare wire wound on a porcelain core so that there will be no problems with burning insulation.
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.
H. Series and Parallel Lightbulbs
1) Concept
Current flowing through resistors in series behaves differently than current flowing through resistors in parallel.
2) Description/Procedures
A board is made which allows one to switch light bulbs in and out of the circuit. Similar or different size light bulbs may be switched in and out to give several combinations. The brightness of the bulbs indicates how the currents are flowing for different series and parallel combinations of resistance.
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.
I. Parallel Circuits
1) Concept
A parallel circuit is an electrical circuit in which electrons leaving a power supply have two or more paths they can follow to go back to the power supply. If several bulbs in a lamp were wired in parallel, and one failed, the others would continue to work. Your classroom lights are wired in parallel.
2) Description/Procedures
Connect one end of the switch to the battery\rquote s positive pole, and connect the other end of the switch to both bulb bases. Connect the battery\rquote s negative pole to both bulb bases. Close the switch, and both lightbulbs will light up. Gently unscrew one bulb. The other will remain lit and will shine a bit more brightly, because the voltage is not divided between two bulbs.
3) References
Kardos, Thomas (1996). 75 Easy Physics Demonstrations. Portland, Maine: J. Weston Walch\par
J. Kirchoff\rquote s Voltage Law
1) Concept
The sum of the voltage gains in a circuit equals the sum of the voltage drops across each individual component.
2) Description/Procedures
A 1.5 volt battery and 3 resistors are plugged into the board in series. The digital voltmeter readings show that the sum of the voltage gains in a circuit equals the sum of the voltage drops across each individual component. Resistors may be replaced by other batteries.
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.
K. Equivalent Series Resistance
1) Concept
The voltage and current from a battery is the same for multiple resistors as it is for one equivalent resistor.
2) Description/Procedures
A set of resistors is arranged in series. An equivalent resistor is then plugged into the circuit in their place. The meter may be used to show the voltage and the current from the battery are the same for the equivalent resistor as for the set of resistors it replaced.
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.
L. Equivalent Parallel Resistance
1) Concept
The voltage and current from a battery is the same for multiple resistors as it is for one equivalent resistors.
2) Description/Procedures
Resistors are arranged in parallel. They are then replaced by the equivalent resistance. The meter is used to show that the current and voltage from the battery are the same in each case.
3) References
Anderson, F.J. and G.D. Freier (1996). A Demonstration Handbook for Physics. American Association of Physics Teachers.\par
M. Motor Generator
1) Concept
The energy generated from a motor powered from electromagnetism can be used to do work.\par
2) Description/Procedures
A large flat coil is placed so it can rotate between the poles of a large Alnico magnet. The armature has both slip rings and a communicator. Both alternating current and direct current voltages can be obtained when the device is operated as a generator. The coil is driven by a falling weight. If the current is provided to the communicator, the device runs as a motor and winds up the weight.\par
3) Referencesr
Anderson, F.J. and G.D. Freier (1996). {\ul A Demonstration Handbook for Physics.} American Association of Physics Teachers.\par
VII. Laboratory Activities
A. Measurement of Resistance: Voltmeter-Ammeter Method
1) Concept
Different substances offer different amounts of resistance to an electric current. In general, metals are good conductors, although among the metals there is a wide range of conductivity. Physicists have found that four variables determine the resistance of a conductor to an electric current. These variables are: temperature, length, cross-sectional area, and the type of metal in which the conductor is made. This experiment shows the effects of length and cross-sectional area on the resistance of conductors of the same and different metals. By measuring the potential difference across the conductor specimen and the current in the conductor, the resistance of the specimen can be calculated from Ohm\rquote s Law. After completing this experiment, you should be able to determine the resistance of conductors by the voltmeter-ammeter method and the effect of length, diameter, and material on the resistance of a conductor.\par
2) Description/Procedures
a) Apparatus
1. Battery - 3 to 6 V
2. D-C ammeter, 0 to 0.1 A
3. Voltmeter, 0 to 7.5 V
4. Tubular rheostat
5. Annunciator wire, 18 ga, for connections
6. 3 nickel-silver resistance spools, 30 ga-200 cm, 28 ga-200 cm, 30 ga-160 cm (constantan or German-silver spools may be used)
7. 1 copper resistance spool, 30 ga-2000 cm brass connectors, double momentary contact switch, SPST
b) Procedure
1. Connect the apparatus as shown in Figure 1-b. The voltmeter V is connected {\i in parallel} with the resistance spool R{\fs16\dn4 x}, whose resistance is to be measured. The Ammeter A is connected {\i in series} with the resistance spool, the batter, and the rheostat R{\fs16\dn4 1}. The rheostat serves as a variable resistance to limit the circuit current.
2. With the rheostat resistance R{\fs16\dn4 1} in the circuit and the 200-cm spool of 30 ga nickel-silver wire connected across the terminals AB as R{\fs16\dn4 x}, gradually reduce the resistance R{\fs16\dn4 1} until the ammeter reads approximately 0.2 A. Open the switch and change the ammeter to its lower range. Read both the voltmeter and the ammeter, estimating to the nearest tenth of the smallest scare division. Then open the switch immediately. Record the data for V{\fs16\dn4 x} and I in the data table. Can you give two reasons for adjusting R{\fs16\dn4 1}, for the small current?
3. Substitute each of the remaining coils, in turn, for the coil just measured, adjust the circuit current to a suitable value, and read the voltmeter and ammeter to the precision each instrument allows. Record the data for each coil.
4. The voltmeter measures the potential difference across the resistance spool, and the ammeter measures the current in the resistance spool. By Ohm\rquote s law, determine the resistance R{\fs16\dn4 x} for each spool in terms of its trial values of V{\fs16\dn4 x} and I to the precision your measurements allow. Record R{\fs16\dn4 x} values in the data table. Complete the remaining columns in the data table. The diameters and cross-sectional areas of the wires are given by wire gauge numbers in Appendix B, Table 21 of the referenced manual.
Figure 1-a
Circuit - Mounting Board
Figure 1-b
Data and Calculations Table
Data Table
Calculations Table
c. Calculations
1) Compute the resistivity {\f23 r} of the metal composing the spool for each trial and record in the calculations table as your experimental values of {\f23 r}.
2) Compare your experimental values of {\f23 r} with the accepted values given in Appendix B, Table 20, and record your absolute error for each trial.
3) Compute your relative error for each trial and record
3) References
Trinklein, Frederick E. Modern Physics - Laboratory Experiments. Holt, Rinehart and Wilson 1990.
B. Resistance in Series and Parallel
1) Concept
When resistance coils are connected in series, the circuit current I{\fs16\dn4 T} is in each coil. Each succeeding coil adds its resistance to that of the others in series, and their combined resistance equals the sum of all the separate resistances.
When two or more resistance coils are joined in parallel, more paths are provided for the electric current and consequently the equivalent resistance equals the reciprocal of the equivalent resistance.