3-Electronics-Math-1-Series-Parallel-Circuits-Worksheet
docx
keyboard_arrow_up
School
Modesto Junior College *
*We aren’t endorsed by this school
Course
221
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
9
Uploaded by akhilpatel
Electronics Math 1 Series Parallel Circuits Worksheet
Prerequisite Assumptions
Before beginning the lesson, students should understand;
Circuit modeling of resistive DC circuits,
Series and Parallel connected voltage sources,
Application of Ohm’ Law,
Application of the Power Rule,
How to manipulate and solve a linear equation.
Specific Objectives
By the end of this lesson, you should understand;
Components and structure of an ideal circuit model
Circuit Equivalency (Simplification / Reduction)
How to mathematically determine equivalent resistance of series and parallel connected
resistors
Circuit analysis using Ohm’s Law and the Power Rule
By the end of this lesson, you should be able to;
Apply Ohm’s Law and the Power Rule to analyze circuits
Develop an equivalent model for a simple DC circuit
Calculate the equivalent resistance for series and parallel connected resistors
AET 19-20
Page
1
of
9
Lesso
n
Objectives
Material
3.1
Creating a linear equation
Linear Equations
3.2
DC Circuits: Series Resistors
A birthday card
3.3
DC Parallel Resistors
A valentine card
3.4
Combined DC Parallel and Series Resistors
Circuit Analysis
3.5
Combined DC Parallel and Series Resistors
A new and improved card
Electronics Math 1 Series Parallel Circuits Worksheet
Problem Situation 3. 1 – Linear Equations
1)
What are your observations?
What do you wonder?
2)
How much CO
2
gas emissions can these panels offset?
3)
Write the linear equation used to determine the CO
2
gas emissions these panels offset.
4)
What do you need to know to determine how many homes the solar panel modules can
power?
5)
Determine how many homes all 582 solar panel modules can power.
6)
Write the linear equation used to determine the number of homes above.
AET 19-20
Page
2
of
9
Electronics Math 1 Series Parallel Circuits Worksheet
Problem Situation 3.2 – Series Resistors
Remember that a schematic is a recipe for a circuit, and we use these schematics for design
and analysis.
A good model is key to a mathematical prediction of the circuit behavior.
A good
picture speaks more than a thousand words.
It is good practice to sketch the circuit you are
analyzing before you start predicting outcomes or making calculations.
Cupcake Paper Circuit Card with LED Light
www.youtube.com/watch?v=7hb-9eUpfbQ
1)
What do you need to know to design and sketch a circuit for this birthday card?
2)
Sketch your design.
Remember to always indicate component polarities and current
direction.
3)
Using your own design, calculate the current through the load?
4)
How much power is consumed by the load?
5)
Can the LED consume this much power without damage?
If not, what would you
change in your design so that the power delivered to the load is under the rating for the
LED?
AET 19-20
Page
3
of
9
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Electronics Math 1 Series Parallel Circuits Worksheet
Resistors can be in a series configuration like the circuit below.
Series resistors are connected daisy chain in a single line.
Series resistors have the
same
current running through
each one of them on the same conductive wire.
Series resistors produce equivalent resistance that can be
represented with a
single
resistor.
R
TOTAL
or R
T
represents the
equivalent
or
total
resistance of all the
resistors in a circuit.
For resistors in series; R
T
= R
1
+ R
2
+ R
3
….+ R
n
The circuit above would have an equivalent resistance of; R
T
= 100Ω + 200Ω + 300Ω = 600Ω
The equivalent circuit model is shown below.
Now the circuit is easier to analyze to find current.
The current is
I
=
V
R
T
=
36
V
600
Ω
=
0.06
A
=
60
mA
.
6)
Use the following circuits to practice analyzing series resistance.
Determine the
requested information and sketch the minimized equivalent circuit
R
T
=
I
T
=
V
R1
=
V
R2
=
P
R1
=
P
R2
=
P
T
=
R
T
=
I
T
=
V
R1
=
V
R2
=
V
R3
=
V
R4
=
P
T
=
Sketch the equivalent circuit:
Sketch the equivalent circuit:
AET 19-20
Page
4
of
9
560 Ω
1.1 kΩ
6 V
Electronics Math 1 Series Parallel Circuits Worksheet
7)
Is the total resistance larger than the largest single resistor or smaller than the smallest
resistor?
Is this what you would have expected?
8)
Predict whether the voltage source equal the sum of the voltage drops across each resistor.
Can you calculate this to see if it is true or false?
Problem Situation 3.3 – Parallel Resistors
1)
Using information from the cupcake card, what do you need to know to design and sketch a
circuit for this Valentine’s Day card?
2)
Sketch your design.
Remember to always indicate component polarities and current
direction.
AET 19-20
Page
5
of
9
Electronics Math 1 Series Parallel Circuits Worksheet
3)
How many loads are there?
Calculate the current through the loads.
4)
How much power does each of the loads consume? Do you expect it to be the same for
each load?
5)
How much total power is consumed by the circuit?
6)
Considering your own design, how much resistance does the voltage source see?
This configuration for resistors is parallel.
Resistors are connected in parallel when
each
end
terminal of the resistors are connected or shared.
Parallel resistors produce a resistance
smaller
than
the
smallest
resistor.
R
T
represents the sum total of all the parallel resistances in a circuit.
1
R
T
=
1
R
1
+
1
R
2
+
1
R
3
…
+
1
R
n
Example
:
Determine the total resistance of the following circuit, sketch the equivalent circuit,
and determine the total current that leaves the voltage source.
1
R
T
=
1
90
+
1
200
+
1
1000
Calculator: (90
-1
+200
-1
+ 1000
-1
)
-1
= 58.4Ω
Using Ohm’s Law:
I
T
=
V
R
=
36
V
58.4
Ω
=
0.616
A
=
616
mA
AET 19-20
Page
6
of
9
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Electronics Math 1 Series Parallel Circuits Worksheet
6)
Use the following circuits to practice analyzing parallel resistance.
Determine the
requested information and sketch the minimized circuits.
R
T
=
I
T
=
I
R1
=
I
R2
=
P
R1
=
P
R2
=
P
T
=
7)
Is the total resistance larger than the largest single resistor or
smaller than the smallest resistor?
Is this what you would have
expected?
8)
Does the total current equal the sum of the currents through each resistor?
AET 19-20
Page
7
of
9
R
T
=
I
T
=
I
R1
=
I
R2
=
I
R3
=
P
T
=
Electronics Math 1 Series Parallel Circuits Worksheet
Problem Situation 3.4 – Series and Parallel Resistors
1)
Circuits typically have both series and parallel resistors. For the circuit below identify the
following.
a)
a node
b)
a branch
c)
series resistors
d)
parallel resistors
2)
How would you start
an analysis of this circuit?
3)
Analyze the circuits to determine the following.
Sketch the minimized equivalent circuit.
4)
Determine the value for the missing component in the following circuits.
R
1
= _____________________
R
3
= ____________________
AET 19-20
Page
8
of
9
47Ω
90Ω
3.3 kΩ
R
T
= 370Ω
8 kΩ
2.2 kΩ
233 mA
12 V
120Ω
R
T
=
I
T
=
P
T
=
R
T
=
I
T
=
P
T
=
Electronics Math 1 Series Parallel Circuits Worksheet
Problem Situation 3.5 – A better Valentine’s Day Card.
1)
Revisiting your design for this circuit, below is the data sheet for the LEDs and the battery
available to you.
2)
How many batteries will be required?
What configuration of batteries would you use?
3)
Would you place the LEDs in series or parallel?
How would this affect your battery ‘design’?
4)
Sketch your design.
Remember to indicate component polarities and current direction.
5)
Validate that your circuit meets the specifications of the LEDs.
AET 19-20
Page
9
of
9
LED datasheet
Current - (25 - 30 mA)
Voltage: (4.2 - 5 V)
Power Maximum: 125 mW
Battery:
2032 Button Batteries 3 volts each.
Measured resistance with voltage applied:
180 Ω
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help