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Copyright © Texas Education Agency, 2012. All rights reserved. 1

Lesson Plan Course Title: Concepts of Engineering and Technology

Session Title: DC Circuits

Performance Objective: After completing this assignment, students will develop and apply problem solving skills by performing multiple step calculations using DC circuits and Ohm’s Law and demonstrate their understanding by completing the quiz. Specific Objectives: The student will be able to:

Recognize and label the different parts of an electrical circuit Identify and use the symbols in an electrical schematic Demonstrate mathematical and problem solving skills involving circuit analysis Apply mathematical formulas in a variety of different ways using algebra and logic

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. Concepts of Engineering and Technology:

130.362 (c)(1)(B)(C)(D) ...identify the inputs, processes, and outputs associated with technological systems; ...describe the difference between open and closed systems; ...describe how technological systems interact to achieve common goals;

130.362 (c)(6)(A)(B)(C)(D) ...identify and describe the fundamental processes needed for a project, including design and prototype development; ...identify the chemical, mechanical, and physical properties of engineering materials; ...use problem-solving techniques to develop technological solutions; ...use consistent units for all measurements and computations;

130.362 (c)(8)(A)(B)(C)(D)(E) ...describe applications of process control and automation systems; ...describe career opportunities in process control and automation systems; ...apply design concepts to problems in process control and automation systems; ...identify fields related to process control and automation systems; and ...identify emerging issues in process control and automation systems.

Interdisciplinary Correlations:


Algebra I:

111.32 (b)(1)(A)(B)(C)(D)(E) ...describe independent and dependent quantities in functional relationships; ...gather and record data and use data sets to determine functional relationships between quantities; ...describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations; ...represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and ...interpret and make decisions, predictions, and critical judgments from functional relationships.

111.32 (b)(3)(A)(B) ...use symbols to represent unknowns and variables; and ...look for patterns and represent generalizations algebraically.

111.32 (b)(4)(A)(B) ...find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations; ...use the commutative, associative, and distributive properties to simplify algebraic expressions;

Teacher Preparation: Review this lesson plan and the DC Circuits PowerPoint presentation. DC Circuits lesson should precede Basic Electricity and Electronics Module 1 lesson. References: Gerrish, H. & Dugger, W. Jr., & Roberts, R. Electricity and Electronics. Goodheart-Willcox. Instructional Aids:

1. Electricity and Electronics textbook 2. DC Circuits PowerPoint presentation

Materials Needed:

1. A battery 2. DC Circuits quiz for each student

Equipment Needed:

1. Computer 2. Projector

Learner Preparation: A good attitude and ready to learn.


Introduction

Introduction (LSI Quadrant I): SAY: Today we are going to learn about electrical circuits. ASK: Does anyone know the difference between AC voltage and DC voltage? (AC varies, DC is constant) SHOW: A battery. SAY: This voltage produces a constant, steady voltage. ASK: Does anyone know how this battery works? (converts chemical energy into electrical energy) SAY: Even though AC voltage is the commonly used power source in our homes, we are going to use DC voltage to show how an electrical circuit works. ASK: Does anyone know why we want to use DC voltage to describe circuit operation? SAY: Because a steady, constant voltage is much easier to deal with mathematically. So, even though some of this material may seem difficult to you, this is actually the easiest way to learn about how circuits work.

Outline

Outline (LSI Quadrant II): Instructors can use the PowerPoint presentation, slides, handouts, and note pages in conjunction with the following outline.

MI Outline Notes to Instructor

I. Common circuit elements (slide 2)

A. Battery cells connect in series to make a battery. Note: POLARITY

B. One common circuit element missing from this picture is a switch (EE pg 59)

C. The LED is an electronic device and is not covered here, but it is ON D. Note how the voltmeter and the ammeter are connected

Begin DC Circuits PowerPoint presentation. Refer to Electricity and Electronics textbook page 59. This presentation starts off pretty basic, but by the end gets pretty hard, requiring some advanced problem solving skills.

.

II. Circuit devices and symbols (slides 3-8)

A. Definitions make good board work B. Students need to write, draw, make their

own circuits

Continue PowerPoint presentation. Voltage and current are covered in more detail in Basic Electricity and Electronics Module 1 lesson.


III. A simple electric circuit (slides 9-13) A. Introduce the switch as a control element B. A complete circuit needs a path from one side of the battery to the other C. Interrupt the circuit anywhere, current stops flowing D. This switch is a single pole, single throw (SPST)

Continue PowerPoint presentation. Kirchoff’s Law shows that in a series circuit, the ratio of the voltage drops equals the ratio of the resistances.

IV. Ohm’s Law (slides 14-19)

A. There are 3 forms of Ohm’s Law B. The Ohm’s Law circle is also shown as a triangle, either form works the same (EE pg 72) C. Use the circle to help solve the first 3 problems

Continue PowerPoint presentation. The Ohm’s Law circle is a memory aid to relate the 3 electrical values, but students should also be able to use algebra to solve for different unknowns. Refer to Electricity and Electronics textbook page 72.

V. Series Circuits (Slides 20-23) (EE Ch 6)

A. These additional formulas create a “tool chest” to solve different types of problems B. Ohm’s Law is the basis for most of these additional formula’s, but they will look new C. The formula’s are derived from simple electrical properties

Continue PowerPoint presentation and refer to Electricity and Electronics textbook chapter 6. This section starts to get harder, but this is where we can point to some academic rigor. The ability to work through multiple steps to solve a problem is a valuable skill.

VI. Parallel Circuits (slides 24-28) (EE Ch 7)

A. Each branch is a separate and independent circuit

B. What happens in one branch does not affect any other branch

C. Total resistance in a parallel circuit is lower than the smallest resistor value

D. Using the calculator’s 1/x button can make parallel circuit calculations easy

Continue PowerPoint presentation and refer to Electricity and Electronics textbook chapter 7. Many of these problems are designed to develop logical and problem solving ability in students. These circuits are arguably


the easiest way to develop these skills.

Verbal Linguistic

Logical Mathematical

Visual Spatial

Musical Rhythmic

Bodily Kinesthetic

Intra- personal

Inter- personal

Naturalist Existentialist

Application

Guided Practice (LSI Quadrant III): Show students how to work the problems using the presentation. Change some of the electrical values and guide the students through the steps to the solution. Independent Practice (LSI Quadrant III): Have students work problems from chapters 1-7 of Electricity and Electronics (EE) textbook. Have students take the DC Circuits quiz.

Summary

Review (LSI Quadrants I and IV): Question: What are some of the key concepts used in a series circuit? Answer: Resistance adds, current is the same everywhere, voltage drops are split up between components in a ratio depending on their resistance. Question: What are some of the key concepts used in a parallel circuit? Answer: Voltage is the same across each branch, current is different in each branch and depends on branch resistance, total current adds and is the sum of the individual branch currents, total resistance divides using the inverse formula, and total resistance is always lower than the smallest branch resistance.

Evaluation

Informal Assessment (LSI Quadrant III): Teacher observation of board work and problems from the Electricity and Electronics textbook. (Series Circuits: page 104, problems 1-7; Parallel Circuits: page 111, problems 1-5) Formal Assessment (LSI Quadrant III, IV): The DC Circuits quiz.


Extension

Extension/Enrichment (LSI Quadrant IV): Have students build different circuits in lab, and then take measurements to verify that calculated values can predict actual values.


DC Circuits Quiz 1. Where does a voltmeter go in a circuit? (How does a voltmeter connect to

measure voltage?)

a. In the circuit just after the power supply b. Across the device to be measured c. In the circuit just before the power supply d. In series with the load

2. Where does an ammeter go in a circuit? (How does an ammeter connect to

measure current?)

a. Across the power supply b. Across the load c. Same as for voltage d. In series with the load

3. Which of the following is a protection element?

a. Fuse b. Switch c. Wire d. Ground

4. Which of the following is a control element?


5. How are battery cells connected to make a battery?

a. Positive to positive b. Negative to negative c. In series with each other d. In parallel with each other

6. Which of the following is the schematic symbol of a battery?

a. b. c. d.

(alternate) Draw the schematic symbol of a battery and label the polarity.


7. What is usually done with the negative side of a battery? a. Connect to the positive side of the battery b. Connect to ground c. Connect to a resistor d. Connect to a fuse 8. Which of the following is not a physical device?


9. Why is ground voltage defined to be zero volts? a. To be a common reference for all voltage measurements b. Because there is never any voltage on ground c. To allow you to measure voltage and current the same way d. Because ground is isolated from the rest of the circuit 10. Why is ground usually connected to the most negative point in a circuit? a. To be a common reference for all voltage measurements b. Because ground is isolated from the rest of the circuit c. To make every voltage measured to ground a positive voltage d. To make ground a protection element 11. Why is ground also called common? a. Because it connects to both sides of the power supply b. Because it is shared with many components c. Because there is nothing special about ground d. Because it only connects to one device 12. Which of the following is the symbol for ground?

a. b. c. d.

(alternate) Draw the schematic symbol for a ground.


13. What does a fuse protect?

a. People b. Ground c. Lawyers d. The circuit

14. What do you do with a fuse once it blows? a. Replace it with a bigger fuse b. Replace it with the same size fuse c. Replace it with a smaller fuse d. Replace it with a wire 15. Which of the following is the symbol for a fuse?

a. b. c. d.

(alternate) Draw the schematic symbol for a fuse. 16, Which of the following is the most often used component in a circuit? a. Power supply b. Ground c. Resistor d. Fuse 17. How is resistance value of a resistor usually indicated? a. A color band b. The size of the resistor c. The number of leads d. A small number of the side 18. What determines the power rating of a resistor? a. A color band b. The size of the resistor c. The number of leads d. A small number of the side


19. What does a resistor do? a. Turns on or off a circuit b. Protects a circuit from too much current c. Provides a common return path for current d. Used to limit or restrict current 20. Why doesn’t a voltmeter change circuit voltage values? a. Because it is never connected directly to the circuit b. Because it has almost infinite internal resistance c. Because it has almost zero internal resistance d. Because it uses its own internal voltage 21. Why doesn’t an ammeter change circuit current values? a. Because it is never connected directly to the circuit b. Because it has almost infinite internal resistance c. Because it has almost zero internal resistance d. Because it uses its own internal current 22. What two things must an electric circuit have? a. A power supply and ground b. A power supply and a load resistance c. A switch and a fuse d. A fuse and a load resistor 23. What direction does current flow? a. Always out of the power supply b. Always into the power supply c. Positive to negative d. Negative to positive 24. What formula shows the relationship between voltage, current, and resistance? a. Ohm’s Law b. Watts Law c. Pascals Law d. Newtons Law (alternate) Draw the Ohm’s Law circle


25. VS = 25 V, R = 455 Ω. What is I?

26. VS = 9 V, I = 13.6 mA. What is R? 27. I = 48 mA, R = 1125 Ω. What is VS ?


28. What is RT?

29. What is IT?

30. What is V1?

VS = 16 V, R

1 = 250 Ω, R

2= 150 Ω, R

3= 400 Ω


31. What is R1?

32.

What is R2?

VS = 27 V, V

1 = 7 V, V

2 = 6 V, R

3 = 600 Ω

VS = 18 V, V

1 = 6 V, R

3 = 600 Ω, I

T = 6 mA


33. 34. Solve the previous problem for IT.

35. Solve for I3.


DC Circuits Quiz Key 1. Where does a voltmeter go in a circuit? (How does a voltmeter connect to

measure voltage?)

e. In the circuit just after the power supply f. Across the device to be measured g. In the circuit just before the power supply h. In series with the load

2. Where does an ammeter go in a circuit? (How does an ammeter connect to

measure current?)

e. Across the power supply f. Across the load g. Same as for voltage h. In series with the load

3. Which of the following is a protection element?

e. Fuse f. Switch g. Wire h. Ground

4. Which of the following is a control element?


5. How are battery cells connected to make a battery?

e. Positive to positive f. Negative to negative g. In series with each other h. In parallel with each other

6. Which of the following is the schematic symbol of a battery? (Answer is d.)

a. b. c. d.

(alternate) Draw the schematic symbol of a battery and label the polarity.


7. What is usually done with the negative side of a battery? a. Connect to the positive side of the battery b. Connect to ground c. Connect to a resistor d. Connect to a fuse 8. Which of the following is not a physical device?


9. Why is ground voltage defined to be zero volts? a. To be a common reference for all voltage measurements b. Because there is never any voltage on ground c. To allow you to measure voltage and current the same way d. Because ground is isolated from the rest of the circuit 10. Why is ground usually connected to the most negative point in a circuit? a. To be a common reference for all voltage measurements b. Because ground is isolated from the rest of the circuit c. To make every voltage measured to ground a positive voltage d. To make ground a protection element 11. Why is ground also called common? a. Because it connects to both sides of the power supply b. Because it is shared with many components c. Because there is nothing special about ground d. Because it only connects to one device 12. Which of the following is the symbol for ground? (Answer is a.)

a. b. c. d.

(alternate) Draw the schematic symbol for a ground.


13. What does a fuse protect?

a. People b. Ground c. Lawyers d. The circuit

14. What do you do with a fuse once it blows? a. Replace it with a bigger fuse b. Replace it with the same size fuse c. Replace it with a smaller fuse d. Replace it with a wire 15. Which of the following is the symbol for a fuse? (Answer is b.)

a. b. c. d.

(alternate) Draw the schematic symbol for a fuse. 16, Which of the following is the most often used component in a circuit? a. Power supply b. Ground c. Resistor d. Fuse 17. How is resistance value of a resistor usually indicated? a. A color band b. The size of the resistor c. The number of leads d. A small number of the side 18. What determines the power rating of a resistor? a. A color band b. The size of the resistor c. The number of leads d. A small number of the side


19. What does a resistor do? a. Turns on or off a circuit b. Protects a circuit from too much current c. Provides a common return path for current d. Used to limit or restrict current 20. Why doesn’t a voltmeter change circuit voltage values? a. Because it is never connected directly to the circuit b. Because it has almost infinite internal resistance c. Because it has almost zero internal resistance d. Because it uses its own internal voltage 21. Why doesn’t an ammeter change circuit current values? a. Because it is never connected directly to the circuit b. Because it has almost infinite internal resistance c. Because it has almost zero internal resistance d. Because it uses its own internal current 22. What two things must an electric circuit have? a. A power supply and ground b. A power supply and a load resistance c. A switch and a fuse d. A fuse and a load resistor 23. What direction does current flow? a. Always out of the power supply b. Always into the power supply c. Positive to negative d. Negative to positive 24. What formula shows the relationship between voltage, current, and resistance? a. Ohm’s Law b. Watts Law c. Pascals Law d. Newtons Law (alternate) Draw the Ohm’s Law circle


25. VS = 25 V, R = 455 Ω. What is I?

.055 A or 55 mA 26. VS = 9 V, I = 13.6 mA. What is R? 660 Ω 27. I = 48 mA, R = 1125 Ω. What is VS ?

54 V


28. What is RT?

800 Ω 29. What is IT?

20 mA 30. What is V1?

5 V

VS = 16 V, R

1 = 250 Ω, R

2= 150 Ω, R

3= 400 Ω


31. What is R1?

300 Ω 32.

What is R2?

1400 Ω or 1.4 kΩ

VS = 27 V, V

1 = 7 V, V

2 = 6 V, R

3 = 600 Ω

VS = 18 V, V

1 = 6 V, R

3 = 600 Ω, I

T = 6 mA


33.

120 Ω 34. Solve the previous problem for IT.

.1 A or 100 mA


35. Solve for I3.

.025 A or 25 mA


Solution 1 - Problem 1 – Slide 21

1. What is total resistance? RT = R1 + R2 + R3 = 250Ω + 150Ω + 500Ω = 900Ω

2. What is total current? IT = = = .01333 A = 13.33 mA

3. What is V1? V1 = I1 x R1 = 13.33 mA x 250Ω = 3.33 V

4. Work the problem with VS = 16 V, R1 = 400Ω, R2 = 600Ω, R3 = 1000Ω

Follow steps 1 – 3 above with these new values. RT = 2000 Ω IT = .008 A= 8 mA V1 = 3.2 V


Solution 2 - Problem 2 – Slide 22

5. Write the formula you need: R1 = You have V1, but you don’t have I1.

Current in a series circuit is the same everywhere, though, so if you can solve for

any current you will have I1.

6. The formula for current is voltage divided by resistance, and you don’t seem to

have both of those values. However, you have R3 and can solve for V3 using the

formula

VT = V1 + V2 + V3 or V3 = VT – V1 – V2

V3 = 20 V – 6 V – 4 V = 10 V

7. I3 = = = .01667 A = IT = I1

8. R1 = = = 360 Ω

R1 = 360 Ω


Solution 3 – Problem 3 – Slide 23

9. Write the formula you need: R2 = You don’t seem to have either V2 or

I2.

In a series circuit, though, current is the same everywhere so I2 = I3 = IT = 6 mA

10. Now, you can solve for V3 using the formula V3 = I3 x R3, where IT = I3.

V3 = I3x R3= .006 A x 1500 Ω = 9 V

11. VT = V1 + V2 + V3 or V2 = VT – V1 – V3= 18 V – 3 V – 9 V = 6 V

= = 1000 Ω 12. R2 =

R2 = 1000 Ω


Solution 4 – Problem 4 – Slide 28 1. Write down the equation for I3. I3 =

You don’t seem to have either of the unknowns you need.

2. However, you can solve for V1 (which is the same as VS which is

the same as V3). V1 = I1 X R1 = .064 A X 250 Ω = 16 V

3. You can also solve for R3 because you have R1, R2, and RT.

Or

= - -

Which you can perform with the calculator:

= 840 R3 = 840 Ω. Now you can solve for I3.

4. I3 = = = .019 A = 19 mA

130 250 400

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