Parallel Resistive Circuits Part 1 Electronics Lesson Plan Performance Objective At the end of the lesson, students will demonstrate the ability to apply problem solving and analytical techniques to calculate parallel circuit electrical values by completing the Sample Problems With Two Resistors Worksheet. Specific Objectives Identify a parallel resistive circuit Use current loops to determine electrical polarity Apply Kirchhoff s Voltage Law to parallel circuits Apply Kirchhoff s Current Law to parallel circuits Use Kirchhoff s Law to derive circuit analysis tools Analyze circuits and calculate a variety of electrical values using the information given for a parallel circuit Recite the formulas in the parallel circuit tool kit from memory Describe a step-by-step problem solving process used for solving two resistor parallel circuit problems Solve a two resister parallel circuit for total resistance and total current Terms Parallel Circuit- a circuit with more than one path for current flow Parallel Resistive Circuit- a parallel circuit containing only resistors Ohm s Law- a formula that shows the mathematical relationship between current, voltage, and resistance Kirchhoff s Voltage Law- the sum of all voltages in a closed loop equals zero Kirchhoff s Current Law- the sum of the currents into a node is equal to the sum of the currents leaving the node Node- a branching point where current splits or combines Series Circuit- a circuit with only one path for current flow Voltage Drop- a voltage difference measured across a device Total Resistance- the equivalent resistance of the circuit; the resistance the battery sees Reciprocal- inverse; the one divided by x function Time It should take approximately two 50-minute periods to teach the lesson and two 50-minute periods to work problems through guided practice then independent practice. 1
Preparation TEKS Correlations This lesson, as published, correlates to the following TEKS. Any changes/alterations to the activities may result in the elimination of any or all of the TEKS listed. Electronics 130.368 (c) o (5) The student implements the concepts and skills that form the technical knowledge of electronics using project-based assessments. The student is expected to: (C) demonstrate knowledge of the fundamentals of electronics theory; (D) perform electrical-electronic troubleshooting assignments; and (E)develop knowledge of voltage regulation devices. 130.368 (c) o (6) The student applies the concepts and skills to simulated and actual work situations. The student is expected to: (A) measure and calculate resistance, current, voltage, and power in series, parallel, and complex circuits; and (D) demonstrate knowledge of common devices in optoelectronics. 130.368 (c) o (8) The student learns the function and application of the tools, equipment, and materials used in electronics through project-based assignments. The student is expected to: (A) safely use tools and laboratory equipment to construct and repair circuits; and (B) use precision measuring instruments to analyze circuits and prototypes. 130.368 (c) o (9) The student designs products using appropriate design processes and techniques. The student is expected to: (A) interpret industry standard circuit schematics; and (D) produce schematics to industry standards. Interdisciplinary Correlations Algebra I 111.32 (b) o (3) Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to: (A) use symbols to represent unknowns and variables; and (B) look for patterns and represent generalizations algebraically. 2
Geometry 111.41 (c) o (1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (A) apply mathematics to problems arising in everyday life, society, and the workplace; and (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Occupational Correlation (O*Net www.onetonline.org/) Job Title: Electricians O*Net Number: 47-2111.00 Reported Job Titles: Chief Electrician; Control Electrician; Electrician; Industrial Electrician; Inside Wireman; Journeyman Electrician; Journeyman Wireman; Maintenance Electrician; Mechanical Trades Specialist, Electrician; Qualified Craft Worker, Electrician (QCW, Electrician) Tasks Plan layout and installation of electrical wiring, equipment, or fixtures, based on job specifications and local codes. Connect wires to circuit breakers, transformers, or other components. Test electrical systems or continuity of circuits in electrical wiring, equipment, or fixtures, using testing devices, such as ohmmeters, voltmeters, or oscilloscopes, to ensure compatibility and safety of system. Use a variety of tools or equipment, such as power construction equipment, measuring devices, power tools, and testing equipment, such as oscilloscopes, ammeters, or test lamps. Inspect electrical systems, equipment, or components to identify hazards, defects, or the need for adjustment or repair, and to ensure compliance with codes. Prepare sketches or follow blueprints to determine the location of wiring or equipment and to ensure conformance to building and safety codes. Diagnose malfunctioning systems, apparatus, or components, using test equipment and hand tools to locate the cause of a breakdown and correct the problem. Work from ladders, scaffolds, or roofs to install, maintain, or repair electrical wiring, equipment, or fixtures. Advise management on whether continued operation of equipment could be hazardous. Maintain current electrician's license or identification card to meet governmental regulations. Soft Skills Dependability Attention to Detail Integrity Analytical Thinking Initiative Leadership Self-Control 3
Adaptability/Flexibility Persistence Stress Tolerance Accommodations for Learning Differences It is important that lessons accommodate the needs of every learner. These lessons may be modified to accommodate your students with learning differences by referring to the files found on the Special Populations page of this website. Preparation Cover Series Resistive Circuits lesson as a prerequisite Parallel Resistive Circuits Part 1 and Part 2 lessons are designed to be presented together in their entirety Review Parallel Resistive Circuits Part 1 slide presentation and lesson documents prior to each class Review and become familiar with the terminology and the example problems Have handouts and worksheets ready prior to the start of the lesson References Roberts, Gerrish, and Dugger. (1999). Electricity & electronics. Tinley Park, Illinois: Goodheart-Willcox Company. Mitchel E. Schultz. (2007). Grob s basic electronics fundamentals of DC and AC circuits. Columbus, Ohio: McGraw Hill. Instructional Aids Tool Kit for Solving Two Resistor Parallel Circuit Problems Handout, a summary of the tool kit and the troubleshooting method Sample Problems with Two Resistors Worksheet (and key) Introduction The purpose of this lesson is to help students develop a systematic, step-by-step method to analyze parallel resistive circuits and solve problems. Say o In the last lesson we covered series resistive circuits. Those kind of circuits are found in just about every type of electronic device including computers and cell phones. o However, those kinds of electrical circuits are only one type of circuit found in electronics. o Today, we are going to talk about the type of electrical circuit often found in houses and businesses. Show o A light switch 4
Ask o Do you think this switch controls different lights in a series circuit? o Why not? Say o Because if you turned off one light, all the lights would go out. Ask o When I turn one light on or off, does it affect the other lights in the room? o What kind of circuit do you think we use for the lights in this room? Say o We use a parallel circuit! (then start presentation) 5
MI OUTLINE Outline I. Introduction to Parallel Resistive Circuits (slides 1-5) A. Parallel resistive circuits expand the number of formulas used as tools to solve problems. B. Parallel resistive circuits represent a more practical example of real world application of electricity than series circuits. C. The applied math in this lesson reinforces many of the concepts learned in other math courses. D. Students should know common electrical symbols and terms. II. Voltage in a Parallel Resistive Circuit (slides 6-13) A. Current paths are shown in red, but current only flows inside the wires. B. Current loops are shown to identify different current paths. C. Using Kirchhoff s Voltage Law, polarities are the key to understanding how voltage occurs across each parallel path. D. Parallel path voltage values are the same. E. Each parallel path is one independent circuit. F. These concepts can be contrasted with the way voltage works in a series circuit. III. Current in a Parallel Resistive Circuit (slides 14-29) A. Each parallel circuit path is independent. B. A current value in one path does not affect the current in another path. C. Current flow in a wire is similar to water flow in a pipe. D. Use the water flow pipe drawing to relate to current flow values in and out of a node. E. In any parallel circuit there are at least three different current values. F. Current into and out of the battery has the exact same amount and is total current. NOTES TO TEACHER Show Parallel Resistive Circuits slide presentation. After presentation, have students work practice problems using both guided and independent practice. Students start with simple problems to learn the formulas and the step-by-step process, then work their way to more difficult problems designed to teach problem-solving skills. Note: equations highlighted in a green box are the tools for parallel circuit analysis. Equations highlighted in a gray box are steps in the problem-solving sequence where students need to enter data or perform a calculation. 6
MI OUTLINE IV. Resistance in a Parallel Resistive Circuit (slides 30-31) A. Use the two equations developed so far plus Ohm s Law to derive the formula to calculate total resistance in a parallel circuit. B. Students should see that each step in the process is part of a logical sequence. C. This type of derivation is common in a math class; here it is used as a practical application of math. D. Resistance acts differently in a parallel circuit compared to a series circuit, and students need to see that there is a mathematical explanation. E. Every additional parallel path reduces circuit resistance and adds current. F. Additional current requires additional power where circuits and components need to be sized appropriately to keep from burning up. V. Parallel Resistive Circuit Equations (slides 32-34) A. There are three equations that form a tool kit to analyze parallel resistive circuits. B. There is one equation for voltage, one equation for current, and one equation for resistance. C. These equations need to be contrasted with their series circuit equivalents. D. Each of the equations is roughly the opposite of their series circuit equivalent. NOTES TO TEACHER Emphasize that problem solving is a skill developed by practice. Give students Tool Kit for Solving Two Resistor Parallel Circuit Problems Handout before going over example Problem 1 in the slide presentation. The handout can be used for guided practice. Give students Sample Problems With Two Resistors Worksheet. Example Problems 1 and 2 are used as guided practice by the teacher, and Problems 3 through 10 are independent practice by the students. VI. Understanding Resistance in a Parallel Circuit (slides 35-38) A. Lights are used to show how current increases and resistance decreases in a parallel circuit. B. This is like turning on lights in different rooms in a house. C. Turning Multiple on lights in Intelligences one room does not Guide affect the lights in another room. D. Once students understand the concepts logically, show the math so they can see how it applies. 7
MI OUTLINE VII. Example Problem 1 (slides 39-45) A. This section continues to emphasize the problem-solving process that was developed in the Series Resistive Circuits lesson. B. Students should always start by writing down exactly what the problem is asking for. C. Students should then write down (or note) the information given in the problem. D. Use the parallel circuit equation tools to figure out how to solve for unknown values that are needed to solve the problem. E. Even though a problem looks difficult, there is always enough information given to solve it. NOTES TO TEACHER Emphasize that problem solving is a skill developed by practice. Work the first two problems in Sample Problems With Two Resistors Worksheet as guided practice, and then have students work Problems 3 through 10 on their own. There is no quiz associated with this lesson because this is mostly conceptual information used to provide a foundation for the problems found in the Parallel Resistive Circuits Part 2 lesson. There is a quiz in that lesson that covers the material in both Part 1 and Part 2. Students can turn in their completed Sample Problems With Two Resistors Worksheet for a grade. Multiple I 8
Multiple Intelligences Guide Existentialist Interpersonal Intrapersonal Kinesthetic/ Bodily Logical/ Mathematical Musical/Rhythmic Naturalist Verbal/Linguistic Visual/Spatial Application Guided Practice Tool Kit for Solving Two Resistor Parallel Circuit Problems Handout and Sample Problems With Two Resistors Worksheet (Problems 1 and 2) are guided practice. Independent Practice Sample Problems With Two Resistors Worksheet (Problems 3 through 10) are independent practice. Summary Review Recite the formulas in the parallel circuit tool kit from memory. Describe a step-by-step problem-solving process used for solving two resistor parallel circuit problems. How do you solve a two resister parallel circuit for total resistance and total current? Informal Assessment The teacher will observe students working problems. Evaluation Formal Assessment The teacher can give a quiz using the problems found in Sample Problems With Two Resistors Worksheet. The Parallel Resistive Circuits Quiz will be administered after completion of Parallel Resistive Circuits Part 2 lesson. Enrichment Extension The students will be able to create their own problems for a two resister parallel circuit. 9
Tool Kit for Solving Two Resistor Parallel Circuit Problems Handout Three formulas (plus Ohm s Law) make up the Tool Kit for solving two resistor parallel circuit problems. I T = I 1 + I 2 V S = V R1 = V R2 Summary of the step-by-step, problem-solving process: 1. Write down what the problem is asking for. 2. Write the formula(s) needed to solve for the value(s) that will solve the problem from Step 1. 3. If the values needed for the formula are given, plug them into the equation and solve. If the values needed are not given, use one of the above tools to find a formula to give what is needed. 4. Repeat Step 3 as necessary until you are finally able to calculate a value that leads to a solution. This process results in a sequence of problems that need to be solved in order. 5. Once you are able to solve for a value, plug that value into the previously developed formula. 6. Work your way back through the steps of the process developed in Steps 3 and 4 writing down each formula and solution. 7. Highlight or circle the answer to the problem from Step 1. 10
Name Date Class Sample Problems With Two Resistors Worksheet V S R 1 R 2 1. VS = 9 V, R1 = 450 Ω, R2 = 900 Ω, Solve for RT and IT 2. VS = 15 V, R1 = 2.7 kω, R2 = 900 Ω, Solve for RT and IT 3. VS = 24 V, R1 = 10.56 kω, R2 = 8.8 kω, Solve for RT and IT 4. VS = 14 V, R1 = 9.6 kω, R2 = 8.4 kω, Solve for RT and IT 5. VS = 26 V, R1 = 4.2 kω, R2 = 6.825 kω, Solve for RT and IT 6. VS = 18 V, R1 = 10.4 kω, R2 = 17.66 kω, Solve for RT and IT 7. VS = 6 V, R1 = 6 kω, R2 = 1.5 kω, Solve for RT and IT 8. VS = 10 V, R1 = 600 Ω, R2 = 600 Ω, Solve for RT and IT 9. VS = 13.3 V, R1 = 4.7 kω, R2 = 3.5 kω, Solve for RT and IT 10. VS = 21.2 V, R1 = 6.8 kω, R2 = 9.5 kω, Solve for RT and IT 11
Sample Problems With Two Resistors Worksheet (KEY) V S R 1 R 2 1. VS = 9 V, R1 = 450 Ω, R2 = 900 Ω, Solve for RT and IT (RT = 300 Ω, IT = 30 ma) 2. VS = 15 V, R1 = 2.7 kω, R2 = 900 Ω, Solve for RT and IT (RT = 675 Ω, IT = 22.2 ma) 3. VS = 24 V, R1 = 10.56 kω, R2 = 8.8 kω, Solve for RT and IT (RT = 4.8 kω, IT = 5 ma) 4. VS = 14 V, R1 = 9.6 kω, R2 = 8.4 kω, Solve for RT and IT (RT = 4480 Ω, IT = 3.125 ma)_ 5. VS = 26 V, R1 = 4.2 kω, R2 = 6.825 kω, Solve for RT and IT (RT = 2.6 kω, IT = 10 ma) 6. VS = 18 V, R1 = 10.4 kω, R2 = 17.66 kω, Solve for RT and IT (RT = 6.54 kω, IT = 2.75 ma) 7. VS = 6 V, R1 = 6 kω, R2 = 1.5 kω, Solve for RT and IT (RT = 1.2 kω, IT = 5 ma) 8. VS = 10 V, R1 = 600 Ω, R2 = 600 Ω, Solve for RT and IT (RT = 300 Ω, IT = 33.33 ma) 9. VS = 13.3 V, R1 = 4.7 kω, R2 = 3.5 kω, Solve for RT and IT (RT = 2 kω, IT = 6.63 ma) 10. VS = 21.2 V, R1 = 6.8 kω, R2 = 9.5 kω, Solve for RT and IT (RT = 3.96 kω, IT = 5.35 ma)_ 12