Erie Community College
Title III Grant
Proportion of Voltage to Resistance in a Series Circuit
Interdisciplinary Course Materials
Telecommunications
Course: MT006 and MT013
Course Outline Topic: Linear Equations: Ratio & Proportion, Formulas, Word problems, Applications
Project Title: Proportion of Voltage to Resistance in a Series Circuit
Project description: Given a series circuit with multiple resistances, students will compute the voltage across a single resistor.
Author: Colleen Doll - Mathematics
Curriculum Expert: Robert Stranz – Telecommunications
Semester Created: Fall 2009
A. Essential Question (What does this project attempt to answer?) Given a series circuit with multiple resistances: What is the ratio of resistance to total resistance for a single resistor? Given the total voltage in the circuit, what is the voltage across the resistor? You will be using two algebraic methods to find the voltage across a single resistor.
B. Introduction
A series electrical circuit has resistors which are arranged in a chain.
A series circuit is shown in the diagram above. V represents the total voltage and I represents the current. The three sets of jagged lines represent resistors with resistances represented by the variables R1, R2 and R3. Resistance is measured in ohms, represented by the symbol Ω.
The total resistance, RTotal, of a series circuit is found by adding up the resistance values of the individual resistors.
A single voltage, Vs, can be measured across each resistor. There exists a very important relationship between voltage and resistance:
In a series electrical circuit with multiple resistances, the ratio of voltage across any single resistor to the total voltage is equal to the ratio of the resistance of the resistor to the total resistance.
This relationship can also be expressed using the formula
In this project you will be calculating:
· total resistance, RTotal
· the ratio of the resistance of a single resistor to total resistance,
· the voltage, Vs, across that single resistor
We will be using two algebraic methods to find the voltage across a single resistor.
C. Basic Directions
· Read and understand B. Introduction
· The data you will be given is:
o The resistance across each resistor, R1, R2, …Rn
o The total Voltage, V.
· What you will be required to calculate is:
1. The total resistance; RTotal = R1 + R2+…Rn
2. The ratio of the resistance of a single resistor to the total resistance;
3. The amount of voltage, Vs, across the resistor.
o In problem 1, you will be asked to set up a proportion, Method I
o In problem 2, you will be asked to use a formula, Method II
o In problem 3, you may use either method, or just reason it out.
o Methods I and II are outlined in the example below
· Write ratios as fractions in lowest terms.
· Label units appropriately.
· Write neatly and show all your work for problems 1 and 2.
Example Problem:
The above diagram represents three resistors connected to a 12 volt battery. R1 = 6Ω, R2 = 10Ω, and R3 = 4Ω. Find the voltage across R2.
1. Calculate Total Resistance: RTotal = 6 + 10 + 4 = 20Ω
2. Find the ratio of the resistance R2 to RTotal: =
a) Method I: Proportion
o Set up the proportion:
o Solve the proportion for Vs: Vs = 6 volts
b) Method II: Formula
o Plug values into the formula:
o Calculate: Vs = 6 volts
D. Things to Learn Before Starting the Project
· Solve Ratio and Proportion problems
· Use a Formula
E. The Project Assignment
Problem #1
V= 9volts
R1 = 12Ω
R2 = 6Ω
The diagram above represents an electrical circuit in which two resistors with resistances of 12Ω and 6Ω are connected in series to a 9 volt battery.
a. What is the total resistance?
b. What is the ratio of R1 to the total resistance? Write the ratio, , as a fraction in lowest terms.
c. Set up the proportion to find the voltage across R1.
Problem #2
V= 18volts
R1=10 Ω
R2=10 Ω
The diagram above represents an electrical circuit in which two resistors with equal resistances of 10Ω are connected to an 18 volt battery.
a. What is the total resistance?
b. What is the ratio of R1 to the total resistance? Write the ratio, , as a fraction in lowest terms.
c. Use the formula to find the voltage across R1.
Problem #3
V= 60 volts
R1=10 Ω
R2=20 Ω
The diagram above represents an electrical circuit in which two resistors are connected to a 60 volt battery.
a. What is the total resistance?
b. Can you now see without writing it down, that R1 is 1/3 of the total resistance? Therefore, what is the ratio of the voltage across R1 to the battery voltage?
c. What is the value of the voltage across R1?
d. What is the ratio of the voltage across R2 to the battery voltage?
e. What is the value of the voltage across R2?
F. Student Resources (websites, books, technology, etc.)
Textbook, Notes
G. Faculty Resources (teacher notes, websites, books, technology, etc.)
Basic information on electrical circuits can be found on Wikipedia:
http://en.wikipedia.org/wiki/Series_and_parallel_circuits
H. Grading Rubric
Problem 1 (30%)
a. 10%
b. 10%
c. 10%
Problem 2 (30%)
a. 10%
b. 10%
c. 10%
Problem 3 (40%)
a. 10%
b. 10%
c. 10%
d. 10%
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