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.
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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.
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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
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


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
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
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)
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Outline
MI
OUTLINE
I.
II.
III.
Introduction to Parallel Resistive Circuits (slides 15)
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.
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.
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.
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MI
OUTLINE
IV.
Resistance in a Parallel Resistive Circuit (slides 3031)
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.
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
on lights inIntelligences
one room does not
affect
Multiple
Guide
the lights in another room.
D. Once students understand the concepts
logically, show the math so they can see how it
applies.
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.
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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
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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?
Evaluation
Informal Assessment
The teacher will observe students working problems.
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.
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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 = I1 + I 2
VS = VR1 = VR2
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.
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Name_______________________________________Date_________________________Class____________
Sample Problems With Two Resistors
Worksheet
VS
R1
R2
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
___________________________
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Sample Problems With Two Resistors
Worksheet (KEY)
VS
R1
R2
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)_
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