Download Unit 5: Electricity

Name:
Using an Electric Meter
Date:
13.2
Most people who work with electric circuits use a digital multimeter to measure electrical quantities. These
measurements help them analyze circuits. Most multimeters measure voltage, current, and resistance. A typical
multimeter is shown below:
Page 2 of 3
This table summarizes how to use and interpret any digital meter in a battery circuit. Note: A component is
any part of a circuit, such as a battery, a bulb, or a wire.
13.2
Measuring Voltage
Measuring Current
Measuring Resistance
Circuit is ON
Circuit is ON
Circuit is OFF
Turn meter dial to voltage,
Turn meter dial to current,
Turn meter dial to resistance,
labeled Ω
Connect leads to meter following
meter instructions
Connect leads to meter following
meter instructions
Connect leads to meter following
meter instructions
Place leads at each end of
component (leads are ACROSS
the component)
Break circuit and place leads on
each side of the break (meter is IN
the circuit)
Place leads at each end of
component (leads are ACROSS
the component)
Measurement in VOLTS (V)
Measurement in AMPS (A)
Measurement in OHMS (Ω)
Battery measurement shows
relative energy provided
Measurement shows the value of
current at the point where meter is
placed
Measurement shows the resistance
of the component
Component measurement shows
relative energy used by that
component
Current is the flow of charge
through the wire
When the resistance is too high,
the display shows OL (overload)
or ∝ (infinity)
Page 3 of 3
13.2
Build a circuit containing 2 batteries and 2 bulbs in which there is only one path for the current to follow. The
batteries should placed so the positive end of one is connected to the negative end of the other. This is called a
series circuit, and it should form one large loop.
1.
Draw a circuit diagram or sketch that shows all the posts in the circuit (posts are where wires and holders
connect together).
2.
Measure and record the voltage across each battery.
3.
Measure and record the voltage across each bulb.
4.
Measure and record the total voltage across both batteries.
5.
Measure and record the total voltage across both bulbs.
6.
How does the total voltage across the bulbs compare to the total voltage across the batteries?
7.
Break the circuit at one post. Measure and record the current. Repeat until you have measured the current at
every post.
8.
How does the current compare at different points in the circuit?
9.
Disconnect one of the bulbs from its holder. Measure and record the bulb’s resistance. Repeat with the other
bulb.
10. Create a set of step-by-step instructions explaining how to use the meter to measure a bulb’s resistance, the
current through it, and the voltage across it. Find someone unfamiliar with the meter. See if they can follow
your instructions.
Name:
Date:
Ohm's Law
13.3
A German physicist, Georg S. Ohm, developed this mathematical relationship, which is present in most circuits.
This relationship is known as Ohm's law. This relationship states that if the voltage (energy) in a circuit increases,
so does the current (flow of charges). If the resistance increases, the current flow decreases.
Voltage (volts)
Current (amps) = ---------------------------------------------Resistance (ohms, Ω )
To work through this skill sheet, you will need the symbols used to depict circuits in
diagrams. The symbols that are most commonly used for circuit diagrams are
provided to the right.
If a circuit contains more than one battery, the total voltage is the sum of the
individual voltages. A circuit containing two 6 V batteries has a total voltage of 12 V.
[Note: The batteries must be connected positive to negative for the voltages to add.]
If a toaster produces 12 ohms of resistance in a 120-volt circuit, what is the amount of
current in the circuit?
Given
The resistance (R) is 12 ohms.
The voltage (V) is 120 volts.
Looking for
The amount of current (I) in the circuit.
Relationships
V
I = --R
Solution
volts- = 10 amps
I = V
--- = 120
--------------------R
12 ohms
The current in the toaster circuit is 10 amps.
If a problem asks you to calculate the voltage or resistance, you must rearrange the equation I=V/R to solve for V
or R. All three forms of the equation are listed below.
V
II == VV
--V = IR
R=
R
R
I
In this section, you will find some problems based on diagrams and others without diagrams. In all cases, show
your work.
1.
How much current is in a circuit that includes a 9-volt battery and a bulb with a resistance of 3 ohms?
2.
How much current is in a circuit that includes a 9-volt battery and a bulb with a resistance of 12 ohms?
3.
A circuit contains a 1.5 volt battery and a bulb with a resistance of 3 ohms. Calculate the current.
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4.
A circuit contains two 1.5 volt batteries and a bulb with a resistance of 3 ohms. Calculate the current.
5.
What is the voltage of a circuit with 15 amps of current and toaster with 8 ohms of resistance?
6.
A light bulb has a resistance of 4 ohms and a current of 2 A. What is the voltage across the bulb?
7.
How much voltage would be necessary to generate 10 amps of current in a circuit that has 5 ohms of
resistance?
8.
How many ohms of resistance must be present in a circuit that has 120 volts and a current of 10 amps?
9.
An alarm clock draws 0.5 A of current when connected to a 120 volt circuit. Calculate its resistance.
13.3
10. A portable CD player uses two 1.5 V batteries. If the current in the CD player is 2 A, what is its resistance?
11. You have a large flashlight that takes 4 D-cell batteries. If the current in the flashlight is 2 amps, what is the
resistance of the light bulb? (Hint: A D-cell battery has 1.5 volts.)
12. Use the diagram below to answer the following problems.
a.
What is the total voltage in each circuit?
b.
How much current would be measured in each circuit if the light bulb has a resistance of 6 ohms?
c.
How much current would be measured in each circuit if the light bulb has a resistance of 12 ohms?
d.
Is the bulb brighter in circuit A or circuit B? Why?
13. What happens to the current in a circuit if a 1.5-volt battery is removed and is replaced by a 9-volt battery?
14. In your own words, state the relationship between resistance and current in a circuit.
15. In your own words, state the relationship between voltage and current in a circuit.
16. What could you do to a closed circuit consisting of 2 batteries, 2 light bulbs, and a switch to increase the
current? Explain your answer.
17. What could you do to a closed circuit consisting of 2 batteries, 2 light bulbs, and a switch to decrease the
current? Explain your answer.
18. You have four 1.5 V batteries, a 1 Ω bulb, a 2 Ω bulb, and a 3 Ω bulb. Draw a circuit you could build to
create each of the following currents. There may be more than one possible answer for each.
a.
1 ampere
b.
2 amperes
c.
3 amperes
d.
6 amperes
Name:
Date:
Series Circuits
14.1
In a series circuit, current follows only one path from the positive end of the battery toward the negative end. The
total resistance of a series circuit is equal to the sum of the individual resistances. The amount of energy used by
a series circuit must equal the energy supplied by the battery. In this way, electrical circuits follow the law of
conservation of energy. Understanding these facts will help you solve problems that deal with series circuits.
To answer the questions in the practice section, you will have to use Ohm's law. Remember that:
Voltage (volts)
Current (amps) = --------------------------------------Resistance (ohms)
Some questions ask you to calculate a voltage drop. We often say that each resistor (or light bulb) creates a
separate voltage drop. As current flows along a series circuit, each resistor uses up some energy. As a result, the
voltage gets lower after each resistor. If you know the current in the circuit and the resistance of a particular
resistor, you can calculate the voltage drop using Ohm’s law.
Voltage drop across resistor (volts) = Current through resistor (amps) × Resistance of one resistor (ohms)
1.
2.
Use the series circuit pictured to the right to answer
questions (a)-(e).
a.
What is the total voltage across the bulbs?
b.
What is the total resistance of the circuit?
c.
What is the current in the circuit?
d.
What is the voltage drop across each light bulb?
(Remember that voltage drop is calculated by
multiplying current in the circuit by the resistance of a
particular resistor: V = IR.)
e.
Draw the path of the current on the diagram.
Use the series circuit pictured to the right to answer
questions (a)-(e).
a.
What is the total voltage across the bulbs?
b.
What is the total resistance of the circuit?
c.
What is the current in the circuit?
d.
What is the voltage drop across each light bulb?
e.
Draw the path of the current on the diagram.
3.
What happens to the current in a series circuit as more light bulbs are added? Why?
4.
What happens to the brightness of each bulb in a series circuit as additional bulbs are added? Why?
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5.
6.
7.
8.
9.
Use the series circuit pictured to the right to answer
questions (a), (b), and (c).
a.
What is the total resistance of the circuit?
b.
What is the current in the circuit?
c.
What is the voltage drop across each resistor?
Use the series circuit pictured to the right to answer
questions (a)-(e).
a.
What is the total voltage of the circuit?
b.
What is the total resistance of the circuit?
c.
What is the current in the circuit?
d.
What is the voltage drop across each light bulb?
e.
Draw the path of the current on the diagram.
Use the series circuit pictured right to answer questions
(a), (b), and (c). Consider each resistor equal to all others.
a.
What is the resistance of each resistor?
b.
What is the voltage drop across each resistor?
c.
On the diagram, show the amount of voltage in the
circuit before and after each resistor.
Use the series circuit pictured right to answer questions (a) (d).
a.
What is the total resistance of the circuit?
b.
What is the current in the circuit?
c.
What is the voltage drop across each resistor?
d.
What is the sum of the voltage drops across the three
resistors? What do you notice about this sum?
Use the diagram to the right to answer
questions (a), (b), and (c).
a.
How much current would be measured
in each circuit if each light bulb has a
resistance of 6 ohms?
b.
How much current would be measured
in each circuit if each light bulb has a
resistance of 12 ohms?
c.
What happens to the amount of current
in a series circuit as the number of
batteries increases?
14.1
Name:
Date:
Parallel Circuits
14.2
A parallel circuit has at least one point where the circuit divides, creating more than one path for current. Each
path is called a branch. The current through a branch is called branch current. If current flows into a branch in a
circuit, the same amount of current must flow out again, This rule is known as Kirchoff’s current law.
Because each branch in a parallel circuit has its own path to the battery, the voltage across each branch is equal to
the battery’s voltage. If you know the resistance and voltage of a branch you can calculate the current with Ohm’s
Law (I=V/R).
1.
2.
3.
4.
Use the parallel circuit pictured right to answer
questions (a) - (d).
a.
What is the voltage across each bulb?
b.
What is the current in each branch?
c.
What is the total current provided by the battery?
d.
Use the total current and the total voltage to
calculate the total resistance of the circuit.
Use the parallel circuit pictured right to answer
questions (a) - (d).
a.
What is the voltage across each bulb?
b.
What is the current in each branch?
c.
What is the total current provided by the battery?
d.
Use the total current and the total voltage to
calculate the total resistance of the circuit.
Use the parallel circuit pictured right to answer
questions (a) - (d).
a.
What is the voltage across each resistor?
b.
What is the current in each branch?
c.
What is the total current provided by the
batteries?
d.
Use the total current and the total voltage to calculate the total resistance of the circuit.
Use the parallel circuit pictured right to answer
questions (a) - (c).
a.
What is the voltage across each resistor?
b.
What is the current in each branch?
c.
What is the total current provided by the
battery?
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14.2
In part (d) of problems 1, 2, and 3, you calculated the total resistance of each circuit. This required you to first
find the current in each branch. Then you found the total current and used Ohm’s law to calculate the total
resistance. Another way to find the total resistance of two parallel resistors is to use the formula shown below.
R to ta l =
R1 × R 2
R1 + R 2
Calculate the total resistance of a circuit containing two 6 ohm resistors.
Given
The circuit contains two 6 Ω resistors in parallel.
Looking for
The total resistance of the circuit.
Relationships
R to ta l =
1.
2.
Solution
6Ω×6Ω
6Ω +6Ω
= 3Ω
R to ta l =
R to ta l
The total resistance is 3 ohms.
R1 × R 2
R1 + R 2
Calculate the total resistance of a circuit containing each of the following combinations of resistors.
a.
Two 8 Ω resistors in parallel
b.
Two 12 Ω resistors in parallel
c.
A 4 Ω resistor and an 8 Ω resistor in parallel
d.
A 12 Ω resistor and a 3 Ω resistor in parallel
To find the total resistance of three resistors A, B, and C in parallel, first use the formula to find the total of
resistors A and B. Then use the formula again to combine resistor C with the total of A and B. Use this
method to find the total resistance of a circuit containing each of the following combinations of resistors
a.
Three 8 Ω resistors in parallel
b.
Two 6 Ω resistors and a 2 Ω resistor in parallel
c.
A 1 Ω, a 2 Ω, and a 3 Ω resistor in parallel
Name:
Date:
Electrical Power
14.3
How do you calculate electrical power?
In this skill sheet you will review the relationship between electrical power and Ohm’s law. As you work through
the problems, you will practice calculating the power used by common appliances in your home.
During everyday life we hear the word watt mentioned in reference to things like light bulbs and electric bills.
The watt is the unit that describes the rate at which energy is used by an electrical device. Energy is never created
or destroyed, so “used” means it is converted from electrical energy into another form such as light or heat. And
since energy is measured in joules, power is measured in joules per second. One joule per second is equal to one
watt.
We can calculate the amount of electrical power by an appliance or other electrical component by multiplying the
voltage by the current.
Current x Voltage = Power, or P = IV
A kilowatt (kWh) is 1,000 watts or 1,000 joules of energy per second. On an electric bill you may have noticed
the term kilowatt-hour. A kilowatt-hour means that one kilowatt of power has been used for one hour. To
determine the kilowatt-hours of electricity used, multiply the number of kilowatts by the time in hours.
.
You use a 1500 watt hair heater for 3 hours. How many kilowatt-hours of electricity did you use?
Given
The power of the heater is 1500 watts.
The heater was used for 3 hours.
Looking for
The number of kilowatt-hours.
Relationships
kilowatt-hours = kilowatts x hours
1.
2.
Solution
1500 watts ×
1 kilowatt
= 1.5 kilowatts
1000 watts
1.5 kilowatts × 3 hours = 4.5 kilowatt-hours
You used 4.5 kilowatt-hours of electricity.
Your oven has a power rating of 5000 watts.
a.
How many kilowatts is this?
b.
If the oven is used for 2 hours to bake cookies, how many kilowatt-hours (kWh) are used?
c.
If your town charges $0.15/kWh, what is the cost to use the oven to bake the cookies?
You use a 1200-watt hair dryer for 10 minutes each day.
a.
How many minutes do you use the hair dryer in a month? (Assume there are 30 days in the month.)
b.
How many hours do you use the hair dryer in a month?
c.
What is the power of the hair dryer in kilowatts?
d.
How many kilowatt-hours of electricity does the hair dryer use in a month?
e.
If your town charges $0.15/kWh, what is the cost to use the hair dryer for a month?
Page 2 of 2
3.
Calculate the power rating of a home appliance (in kilowatts) that uses 8 amps of current when
plugged into a 120-volt outlet.
4.
Calculate the power of a motor that draws a current of 2 A when connected to a 12 volt battery.
5.
Your alarm clock is connected to a 120 volt circuit and draws 0.5 A of current.
14.3
a.
Calculate the power of the alarm clock in watts.
b.
Convert the power to kilowatts.
c.
Calculate the number of kilowatt-hours of electricity used by the alarm clock if it is left on for one year.
d.
Calculate the cost of using the alarm clock for one year if your town charges $0.15/kWh.
6.
Using the formula for power, calculate the amount of current through a 75-watt light bulb that is connected
to a 120-volt circuit in your home.
7.
The following questions refer to the diagram.
a. What is the total voltage of the circuit?
b. What is the current in the circuit?
c. What is the power of the light bulb?
8.
9.
A toaster is plugged into a 120-volt household circuit. It draws 5 amps of
current.
a.
What is the resistance of the toaster?
b.
What is the power of the toaster in watts?
c.
What is the power in kilowatts?
A clothes dryer in a home has a power of 4,500 watts and runs on a special 220-volt household circuit.
a.
What is the current through the dryer?
b.
What is the resistance of the dryer?
c.
How many kilowatt-hours of electricity are used by the dryer if it is used for 4 hours in one week?
d.
How much does it cost to run the dryer for one year if it is used for 4 hours each week at a cost of
$0.15/kWh?
10. A circuit contains a 12-volt battery and two 3-ohm bulbs in series.
a.
Calculate the total resistance of the circuit.
b.
Calculate the current in the circuit.
c.
Calculate the power of each bulb.
d.
Calculate the power supplied by the battery.
11. A circuit contains a 12-volt battery and two 3-ohm bulbs in parallel.
a.
What is the voltage across each branch?
b.
Calculate the current in each branch.
c.
Calculate the power of each bulb.
d.
Calculate the total current in the circuit.
e.
Calculate the power supplied by the battery.
Name:
Date:
Coulomb’s Law
15.2
In this skill sheet, you will work with Coulomb’s law. There are many similarities and some differences between
the equation of universal gravitation and the equation for Coulomb’s law. They are both inverse square law
relationships, and they both have similar arrangements of variables.
When two charges q1 and q2 are separated by a distance r, there exists a force between them that is given by:
where F equals the force in newtons and K is a constant equal to 9 × 109 N-m2/C2. The units of q1 and q2 are the
coulombs (C). Distance is given in meters. Here are some important points about the relationships of the
variables in Coulomb’s law.
•
Force is inversely proportional to the square of the distance between the charges. Therefore, if the distance
increases by a factor of 2, the force decreases by a factor of 4.
•
Force is proportional to the strength of each charge.
•
When the two charges have the same sign (positive or negative), the force between them is repulsive because
like charges repel.
•
When the charges have opposite signs, the force between them is attractive because unlike charges attract.
1.
What happens to the force between two charges if the distance between them is tripled?
2.
What happens to the force between two charges if the distance between them is quadrupled?
3.
What happens to the force between two charges if the distance between them is cut in half?
4.
What happens to the force between two charges if the magnitude of one charge is doubled?
5.
What happens to the force between two charges is the magnitude of both charges is doubled?
6.
What happens to the force between two charges if the magnitude of both charges is doubled and the distance
between them is doubled?
7.
What happens to the force between two charges if the magnitude of both charges is doubled and the distance
between them is cut in half?
Page 2 of 2
15.2
The example below shows how to use Coulomb’s law to calculate the strength of the force between two charges.
A 0.001 coulomb charge and a 0.002 coulomb charge are 2 meters apart. Calculate the force between them.
Given
The charges have magnitudes of 0.003 C and
0.005 C.
The charges are 2 meters apart.
Looking for
The force between the charges.
Relationships
V q q
FI == --Rk- 1 2 2
r
Solution
V
2- 2
F = (9 × 109 IN =
im-R/C )
(0.001 C)(0.002 C)
(2 m) 2
F = 4500 N
The force is 4500 newtons.
1.
Two particles, each with a charge of 1 C, are separated by a distance of 1 meter. What is the force between
the particles?
2.
What is the force between a 3 C charge and a 2 C charge separated by a distance of 5 meters?
3.
Calculate the force between a 0.006 C charge and a 0.001 C charge 4 meters apart.
4.
Calculate the force between a 0.05 C charge and a 0.03 C charge 2 meters apart.
5.
Two particles are each given a charge of 5 × 10-5 C. What is the force between the charged particles if the
distance between them is 2 meters?
6.
The force between a pair of charges is 100 newtons. The distance between the charges is 0.01 meter. If one
of the charges is 2 × 10-10 C, what is the strength of the other charge?
7.
Two equal charges separated by a distance of 1 meter experience a repulsive force of 1,000 newtons. What is
the strength in coulombs of each charge?
8.
The force between a pair of 0.001 C charges is 200 N. What is the distance between them?
9.
The force between two charges is 1000 N. One has a charge of 2 × 10-5 C, and the other has a charge of
5 × 10-6 C. What is the distance between them?
10. The force between two charges is 2 newtons. The distance between the charges is 2 × 10-4 m. If one of the
charges is 3 × 10-6 C, what is the strength of the other charge?
Unit 5
George Westinghouse
George Westinghouse was both an imaginative tinkerer and a bold entrepreneur. His inventions
had a profound effect on nineteenth-century transportation and industrial development in the
United States. His air brakes and signaling systems made railway systems safer at higher speeds,
so that railroads became a practical method of transporting goods across the country. He
promoted alternating current as the best means of providing electric power to businesses and
homes, and his method became the worldwide standard. Westinghouse obtained 361 patents over
the course of his life.
A boyhood among machines
George Westinghouse was born October 6, 1846, in
Central Bridge, New York. When he was 10, his
family moved to Schenectady, where his father opened
a shop that manufactured agricultural machinery.
George spent a great deal of time working and
tinkering there. After serving in both the Union Army
and Navy in the Civil War, Westinghouse attended
college for three months. He dropped out after
receiving his first patent in 1865, for a rotary steam
engine he had invented in his father’s shop.
An inventive train of thought
In 1866, Westinghouse was aboard a train that had to
come to a sudden halt to avoid colliding with a
wrecked train. To stop the train, brakemen manually
applied brakes to each individual car based on a signal
from the engineer. Westinghouse believed there could
be a safer way to stop these heavy trains. In April
1869, he patented an air brake that enabled the
engineer to stop all the cars in tandem. That July he
founded the Westinghouse Air Brake Company, and
soon his brakes were used by most of the world’s
railways.
The new braking system made it possible for trains to
travel safely at much higher speeds. Westinghouse
next turned his attention to improving railway
signaling and switching systems. Combining his own
inventions with others, he created the Union Switch
and Signal Company.
Long-distance electricity
Next, Westinghouse became interested in transmitting
electricity over long distances. He saw the potential
benefits of providing electric power to individual
homes and businesses, and in 1884 formed the
Westinghouse Electric Company. Westinghouse
learned that Nikola Tesla had developed alternating
current and he persuaded Tesla to join the company.
Initially, Westinghouse met with resistance from
Thomas Edison and others who argued that direct
current was a safer alternative. But direct current
could not be transmitted over distances longer than
three miles. Westinghouse demonstrated the potential
of alternating current by lighting the streets of
Pittsburgh, Pennsylvania, and, in 1893, the entire
Chicago World’s Fair. Afterward, alternating current
became the standard means of transmitting electricity.
From waterfalls to elevated railway
Also in 1893, Westinghouse began yet another new
project: the construction of three hydroelectric
generators to harness the power of Niagara Falls on
the New York-Canada border. By November 1895,
electricity generated there was being used to power
industries in Buffalo, some 20 miles away.
Another Westinghouse interest was alternating current
locomotives. He introduced this new technology first
in 1905 with the Manhattan Elevated Railway in New
York City, and later with the city’s subway system.
An always inquiring mind
The financial panic of 1907 caused Westinghouse to
lose control of his companies. He spent much of his
last years in public service. Westinghouse died in 1914
and left a legacy of 361 patents in his name—the final
one received four years after his death.
Name:
Date:
Reading reflection
Unit 5
1.
Where did George Westinghouse first develop his talent for inventing things?
2.
How did Westinghouse make it possible for trains to travel more safely at higher speeds?
3.
Why did Westinghouse promote alternating current over direct current for delivering electricity to
businesses and homes?
4.
How did Westinghouse turn public opinion in favor of alternating current?
5.
Together with a partner, explain the difference between direct and alternating current. Write your
explanation as a short paragraph and include a diagram.
6.
How did Westinghouse provide electrical power to the city of Buffalo, New York?
7.
Ordinary trains in Westinghouse’s time were coal-powered steam engines. How were Westinghouse’s
Manhattan elevated trains different?
8.
Research: Westinghouse had a total of 361 patents to his name. Use a library or the Internet to find out about
three inventions not mentioned in this brief biography, and describe each one.
Unit 5
Ben Franklin
Benjamin Franklin overcame a lack of formal education to become a prominent businessman,
community leader, inventor, scientist, and statesman. His study of “electric fire” changed our basic
understanding of how electricity works.
An eye toward inventiveness
Benjamin Franklin was born in Boston in 1706. With
only one year of schooling he became an avid reader
and writer. He was apprenticed at 12 to his brother
James, a printer. The siblings did not always see eye to
eye, and at 17, Ben ran away to Philadelphia.
In his new city, Franklin developed his own printing
and publishing business. Over the years, he became a
community leader, starting the first library, fire
department, hospital, and fire insurance company. He
loved gadgets and invented some of his own: the
Franklin stove, the glass armonica (a musical
instrument), bifocal eyeglasses, and swim fins.
‘Electric fire’
In 1746, Franklin saw some demonstrations of static
electricity that were meant for entertainment. He
became determined to figure out how this so-called
“electric fire” worked. Undeterred by his lack of
science education, Franklin began experimenting. He
generated static electricity using a glass rod and silk
cloth, and then recorded how the charge could attract
and repel lightweight objects. He read everything he
could about this “electric fire” and became convinced
that a lightning bolt was a large-scale example of the
same phenomenon.
Father and son experiment
In June 1752, Franklin and his 21-year-old son,
William, conducted an experiment to test his theory.
Although there is some debate over the details, most
historians agree that Franklin flew a kite on a stormy
day in order to collect static charges. Franklin
explained that he and his son constructed a kite of silk
cloth and two cedar strips. They attached a metal wire
to the top. Hemp string was used to fly the kite. A key
was tied near the string’s lower end. A silk ribbon was
affixed to the hemp, below the key.
Shocking results
It is probable that Franklin and his son were under
some sort of shelter, to keep the silk ribbon dry. They
got the kite flying, and once it was high in the sky they
held onto it by the dry silk ribbon, not the wet hemp
string. Nothing happened for a while. Then they
noticed that the loose threads of the hemp suddenly
stood straight up. The kite probably was not struck
directly by lightning, but instead collected charge
from the clouds. Franklin touched his knuckle to the
key and received a static electric shock. He had proved
that lightning was a discharge of static electricity.
Those are charged words
Through his experiments, Franklin determined that
“electric fire” was a single “fluid” rather than two
separate fluids, as European scientists had thought. He
proposed that this “fluid” existed in two states, which
he called “positive” and “negative.” Franklin was the
first to explain that if there is an excess buildup of
charge on one item, such as a glass rod, it must be
exactly balanced by a lack of charge on another item,
such as the silk cloth. Therefore, electric charge is
conserved. He also explained that when there is a
discharge of static electricity between two items, the
charges become balanced again. Many of Franklin’s
electrical terms remain in use today, including battery,
charge, discharge, electric shock, condenser,
conductor, plus and minus, and positive and negative.
Name:
Reading reflection
Date:
Unit 5
1.
Although Ben Franklin had only one year of schooling, he became a highly educated person. Describe how
Franklin learned about the world.
2.
What hypothesis did Franklin test with his kite experiment?
3.
Describe the results and conclusion of Franklin’s kite experiment.
4.
Franklin’s kite experiment was dangerous. Explain why.
5.
Silk has an affinity for electrons. When you rub a glass rod with silk, the glass is left with a positive charge.
Make a diagram that shows the direction that charges move in this example. Illustrate and label positive and
negative charges on the silk and glass rod in your diagram. Note: Show the same number of positive and
negative charges in your diagram.
6.
Research: Among Franklin’s many inventions is the lightning rod. Find out how this device works, and
create a model or diagram to show how it functions.
Name:
Date:
Order of Operations, Part 1
In arithmetic there are four operations: multiplication, division, addition, and subtraction. If you have an
expression that has only these symbols, then the rule to evaluate them is to do multiplication or division moving
from left to right. When this is completed, go back to the left and do the addition or subtraction moving left to
right.
Example 1:
Step 1
3+2×4–5
= 3+8–5
Multiply 2 and 4.
Step 2
3+8–5
= 11 - 5
Step 3
11 - 5
= 6
Do the addition and subtraction moving left to
right—add 3 and 8.
Then, subtract 5 from 11.
Step 1
1--× 48 – 6 × 2
3
=
Step 2
16 – 12
Example 2:
16 – 12
= 4
Evaluate the following expressions:
1.
25 – 5 × 3
2.
15 + 5 × 7
3.
5 + 0.5 × 7
4.
18 – 3 × 2 – 5
5.
18 × 3 – 2 × 5
6.
18 – 5 × 2 – 3
7.
3×2+5×2 +6
8.
7×2+3×2+6×2
9.
4×2+5×2+6
10. 7 + 3 × 2 – 1
11. 8 – 4 × 2 + 7
12. 25 – 6 + 7 – 2
1
Multiply --- and 48. Multiply 6 and 2.
3
Subtract 12 from 16.
Page 2 of 2
13. 1/2 × 20 + 4
14. 36 ÷ 3 × 2 – 5
15. 1/4 × 8 + 9 – 1
16. A large computer store has certain software on sale at 4 for $25.00 with a limit of 4 at the sale price.
Additional software is available at the regular price of $8.95 each.
a.
Write an expression you could use to find the cost of 6 software packages.
b.
How much would 6 software packages cost?
17. Valerie is signing up with a new internet provider. The service costs $5.99 a month, which includes
100 hours of access. If she is online for more than 100 hours she must pay an additional $0.95 per hour.
a.
Suppose Valerie is online for 120 hours the first month. Write an expression that represents what
Valerie must pay for the month.
b.
Now evaluate the cost.
18. Most bacteria reproduce by dividing into identical cells. This process is called binary fission. A certain type
of bacteria can double its numbers every 20 minutes. Suppose 150 of these cells are in one culture dish and
250 of the cells are in another culture dish.
a.
Write an expression that shows the total number of bacteria cells in both dishes after 20 minutes.
b.
Now, evaluate the expression to find out how many bacteria are in both dishes after 20 minutes.
19. Jamal and Alexandria are selling tickets for their school talent show. Floor seats cost $7.50 and balcony
seats cost $5.00. Alexandria sells 60 floor seats and 70 balcony seats. Jamal sells 50 floor seats and 90
balcony seats.
a.
Write an expression to show how much money Alexandria and Jamal have collected for tickets.
b.
Evaluate the expression to determine how much they collected.
Name:
Date:
Order of Operations, Part 2
In evaluating expressions sometimes grouping symbols such as parentheses, square parentheses, set notation, and
fraction bars are used. If these are present then the operations within them are done first. Expressions may also be
raised to a power. General steps for evaluating expressions with grouping symbols and values raised to a power
are as follows:
Step 1
Step 2
Step 3
Step 4
A
B
Evaluate expressions inside grouping symbols. If grouping symbols enclose grouping symbols start
at the innermost part of the expression and work out.
Evaluate all power expressions.
Do all multiplication or division from left to right. Note: Both “·” and “×” can be used to represent
“multiplied by.”
Do all additions or subtractions from left to right.
Step 1
2(8) + 5(4 + 3)
= 2(8) + 5(7)
Add within grouping symbol.
Step 2
2(8) + 5(7)
=
There are no power expressions to evaluate.
Step 3
2(8) + 5(7)
=
Step 4
16 + 35
= 41
Step 1
5 + 42
22 ⋅ 3
Step 2
5 + 42
22 ⋅ 3
16 + 35
This expression means: 2 × 8 + 5 × 7.
Multiply moving left to right.
Add 16 and 35.
This means (5 + 42) ÷ (22 × 3).
=
5 + 16
4⋅ 3
Evaluate the power number in the numerator and denominator.
=
21
12
Simplify the numerator and denominator.
=
7
4
Reduce the fraction.
Step 3
Step 4
Evaluate these expressions using the steps for working with grouping symbols and values raised to a power.
1.
(6 – 4) · 3 =
2.
(8 + 5) · 2 =
3.
10 + 5 × 6 =
Page 2 of 2
4.
10(5 + 6) =
5.
60 – 12 ÷ 4 =
6.
250 ÷ (5[(3 · 7) + 4]) =
7.
28 ÷ 4 · 2 – 32 =
8.
64 ÷ (2 · 4) + 2 =
9.
(6 + 5)(4 + 3) =
=
10.
11.
15 + 60
=
30 − 5
10(3) + 2(3)
32 − 3
=
12.
36 ÷9 ÷4 =
25⋅ 3+ 6 + 9
13.
82 − 2 2 =
(2 ⋅ 8) + 4
14. 390 ÷ [5(7 + 6)] =
15. 15 ÷ 3 · 5 – 42 =
16. Use grouping symbols so that the equation is true. If one grouping symbol needs to enclose another, use
brackets to enclose parentheses.
a.
10 · 5 + 4 = 90
b.
6 + 5 – 2 · 8 = 30
c.
3 + 4 · 5 – 1 = 28
d.
20 ÷ 2 · 5 + 8 = 10
e.
20 ÷ 2 · 5 + 8 = 58
f.
20 ÷ 2 · 5 + 8 = 130
17. Jared is signing up with a new cable company. The service costs $50.00 a month which includes 100 hours
of access. If he is online for more than 100 hours he must pay an additional $3.95 per hour. Suppose Jared is
online for 110 hours the first month.
a.
What is the expression that represents what Jared must pay for the first month?
b.
How much will the bill be for the first month?
Name:
Date:
Evaluating Algebraic Expressions
Algebraic expressions often contain more than one operation. Algebraic expressions can be evaluated when the
values of the variables are known.
Step 1
Step 2
Replace the variables with their values.
Find the value of the numerical expression using the rules for the order of operations.
Evaluate a2 – (b2 + 4c) when a = 8, b = 4, and c = 5.
Step 1
a2 – (b2 + 4c)
=
Step 2
82 – (42 + 4 · 5)
= 82 – (16 + 4 · 5)
Evaluate 42.
82 – (16 + 4 · 5)
= 82 – (16 + 20)
Multiply 4 and 5.
82 – (16 + 20)
= 82 – (36)
= 64 – (36)
Add 16 and 20.
82 – (36)
64 – (36)
1.
2.
82 – (42 + 4 · 5)
= 28
πr2 when π = 3.14 and r = 5 cm
4.
2(L + W) when L = 8 m and W = 12 m
6.
Evaluate 82.
Subtract 36 from 64.
m
---- when m = 0.30 grams and V = 0.040 cm3
V
v2 – v1
--------------- when v2 = 4 m/sec, v1 = 1 m/sec and t = 1 sec
t
3.
5.
Replace variables.
y2 – y1
---------------- when (x1, y1) = (4, 4) and (x2, y2) = (0, 0)
x2 – x1
The Pyramid of the Sun in Mexico is the third largest pyramid in the world. It
stands 60 meters high with a base of 200 meters2. The volume of any pyramid is
one-third the product of the area of the base (B) and its height (h).
a.
Write an expression that represents the volume (V) of a pyramid.
b.
Evaluate your expression using 200 m2 for B and 60 m for h to find the
volume of this pyramid.
Name:
Date:
Inverses
Every positive rational number can be paired with a negative rational number. These pairs are called opposites.
A number and its opposite are additive inverses of each other. When you add two opposites, the sum is always
zero.
Two numbers whose product is 1 are called multiplicative inverses or reciprocals.
Zero has no reciprocal because any number times zero equals zero.
Additive inverse examples:
+5 + (-5) = 0
–4 +(+4) = 0
Multiplicative inverse examples:
2/
3
× 3/2 = 1
8 × 1/8 = 1
2 3/5 × 5/13 = 1
1/
Give the additive inverse for the following:
1.
29
5.
–0.75
2.
–101
6.
24.7
3.
5/
9
7.
0
4.
– 4/3
8.
– 4.32
Give the multiplicative inverse for the following:
1.
5/
9
5.
-10
2.
2 2/3
6.
0
3.
-3/4
7.
–1 1/2
4.
0.06
8.
1/
0.5
4
×4=1
Name:
Date:
Inverse Operations
An inverse operation “undoes” the original operations. Addition and subtraction are the inverse operations of
each other. Division and multiplication are the inverse operations of each other.
Example 1:
Step 1
Step 2
Step 3
x + 4 = 10
(x + 4) – 4 = 10 – 4
x=6
Subtraction is the inverse operation of addition.
Subtract 4 from both sides of the equation.
Example 2:
Step 1
Step 2
Step 3
y – 7 = 12
(y – 7) + 7 = 12 + 7
y = 19
Addition is the inverse operation of subtraction.
Add 7 to both sides of the equation.
Example 3:
Step 1
Step 2
Step 3
3z = 4
3z
----- = 12
-----3
3
z=4
Division is the inverse operation of multiplication.
Divide both sides of the equation by 3.
Example 4:
Step 1
--t- = 25
5
Multiplication is the inverse operation of division.
Step 2
--t- × 5 = 25 × 5
5
Multiply both sides of the equation by 5.
Step 3
t=5
Find the value of the variable using inverse operations.
1.
a – 12 = 12
2.
3a – 12 = 12
3.
3a + 8 = 32
4.
b + 7 = 21
5.
2b + 7 = 21
6.
2b – 7 = 17
Page 2 of 2
7.
3c = 24
8.
3c – 5 = 28
9.
3c + 5 = 23
d
10. --- = 16
4
11.
d--- + 8 = 16
4
12.
d--- – 4 = 16
4
5
13. --- f = 45
9
5
14. --- f – 36 = 9
9
5
15. --- f + 36 = 117
9