Download Unit 15: Electrical Circuits

INQUIRY PHYSICS
A Modified Learning Cycle Curriculum
by Granger Meador
Unit 15:
Electrical Circuits
Student Papers
©2010 by Granger Meador
inquiryphysics.org
15 Electrical Circuits
Nam e
Lab A: BASIC CIRCUITRY
A continuous flow of electric charge creates an electric "current". The study of moving charges is called electrodynamics. You
already know some important information about electricity in motion. You know that electric motors are used in electric
appliances such as mixers, vacuum cleaners, pumps, drills, sanders, and saws. Each of those appliances exerts a force over a
distance.
Any object that exerts a force over distance is capable of doing
You can now deduce that electricity must be a form of
EXPLORATION
.
.
answer questions with complete sentences
To begin our study of current electricity, we must start with the basics. At your lab station you will find some electric leads (wires
with clips on each end for easy attachment), a dry cell, light bulbs, and light bulb holders.
Step 1: Arrange one bulb (without a holder), one dry cell, and wire in as many ways as you can to make the bulb emit light.
Sketch each of your arrangements in the space below, including failures as well as successes. Label the sketches of the
successes. Include a drawing of how to light a bulb using only ONE wire.
1.
Describe the similarities among your successful trials. Be specific about where the wires must touch both the bulb and
the dry cell.
Step 2: Use a bulb in a bulb holder (instead of a bare bulb), the dry cell, and wire. Arrange these in as many ways as you can
to make the bulb light.
2.
W hat two parts of the bulb does the holder make contact with?
Step 3: Using one dry cell, light as many bulbs in holders as you can. Sketch each of your successful arrangements in the space
below.
Unit 15: Electrical Circuits, Lab A: Basic Circuitry
©2009 by G. Meador – www.inquiryphysics.org
3.
Compare your results to those of other lab groups. You should note that the brightness of a given number of bulbs is
affected by the way the wires are connected. Specify below what sort of setup yields the most bright bulbs.
The dry cell is the source of electric energy and the light bulb is the user. W hen an electric energy source and an electrical energy
user are connected so that electrical energy is used, that hookup is called an electrical circuit. Every electrical circuit must have
at least one energy source and one energy user. It must also have a way to connect the energy source and the energy user. The
connectors, the energy source, and the energy user are the circuit elements.
You know that until the circuit elements were connected there was no evidence that energy was being used. The interaction among
the elements of an electrical circuit causes an electric current. The electric current moves through the circuit elements.
Step 4: Diagrams for electric circuits use symbols like the ones shown
at right to represent the circuit elements.
Connect the bulbs in holders, the dry cell, and wire as shown
in each circuit diagram shown below. Circuits like these are
examples of series circuits.
4.
How does the brightness of the bulbs in the two circuits differ?
Step 5: In the circuit with two bulbs, unscrew one of the bulbs.
5.
W hat happens to the other bulb?
Step 6: Set up the circuit diagramed at right. A circuit like this is called a
parallel circuit.
6.
Do both bulbs light?
Step 7: Unscrew one of the bulbs in the parallel circuit.
7.
W hat happens to the other bulb?
8.
In your own words, describe the differences between series and parallel circuits. Discuss both their physical differences
as well as their behavior when a bulb fails.
Unit 15: Electrical Circuits, Lab A: Basic Circuitry
©2009 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
Lab B: CURRENT
You have constructed both series and parallel circuits, and noted some of the differences between them. We
will now concentrate on series circuits to develop the concepts of current, voltage, and resistance. We will
also eventually discover a relationship between the current, voltage, and resistance of a circuit.
The first concept we must master is current. The Exploration stated that circuit elements, when properly
connected, have a current that moves through them. The current can be thought of as the amount of charge
flowing through the circuit each second.
Current is measured in units called amperes (A) with a device called an ammeter. The ammeter is put into
a circuit so that electricity flows through it. Hooking up the ammeter properly is very important. Improper
hookup can destroy an ammeter.
Ammeter Hookup
Connect the positive (+) terminal of the ammeter to the part of the circuit leading to the
positive (+) terminal of the battery.
Connect the negative (-) terminal of the ammeter to the part of the circuit leading to the
negative (-) terminal of the battery.
Never hook an ammeter into a circuit that does not have a resistor (such as a light bulb)
in it.
Analog Meters
An analog ammeter may have two or more red positive terminals. You must read the terminal’s label to
determine which scale on the meter is to be used. Always hook the circuit up with largest range terminal
first. If the measured current is less than the maximum value for the next lower terminal, you should switch
to it for greater precision.
If the ammeter needle ever "pegs out" by shooting up beyond the scale limits, disconnect it immediately and
ask the instructor for assistance.
Digital Multimeters
Digital multimeters have multiple plugs and settings to measure current, voltage, and resistance and may
operate with both direct current (DC) and alternating current (AC) circuits. Your instructor will guide you
in setting it up for use as a DC ammeter.
MEASURING CURRENT IN SERIES CIRCUITS
Ammeters are represented in circuit diagrams by a capital "A" with a circle around it. Connect dry cells,
light bulbs, and an ammeter as shown in the diagrams on the back. Record each ammeter reading under the
appropriate diagram.
Unit 15: Electrical Circuits, Lab B: Current
©2010 by G. Meador – www.inquiryphysics.org
Circuit #1
Current =
Circuit #3
Current =
A
Circuit #2
Current =
A
A
Circuit #4
Current =
A
1.
Which circuit had the brightest bulb(s)?
Which had the dimmest bulb(s)?
2.
State the relationship between the measured current and the observed brightness of the bulbs.
ANSWER THIS AND ALL REMAINING QUESTIONS WITH COMPLETE SENTENCES
3.
Which pair(s) of circuits would allow you to see how the number of sources affects current?
4.
State how the number of energy sources affects the current in a circuit.
5.
Which pair(s) of circuits would allow you to see how the number of users affects current?
6.
State how the number of energy users affects the current in a circuit.
Unit 15: Electrical Circuits, Lab B: Current
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
Alternate Lab A/B: AMMETERS AND VOLTMETERS
You have completed electrostatics, the study of electrical charges at rest. Mankind's earliest knowledge of electrostatics dates
back many centuries. W e are now entering the study of electrical charges that are in motion - electrodynam ics. Electric circuits,
with currents to run lamps and motors, did not develop until batteries were invented around the year 1800. The growth of the use
of electricity was then so rapid that it produced not just a part of physics but a new electrical civilization in less than a century.
An electric energy source and an electric energy user can be connected in a way that furnishes evidence that electrical energy is
being used. That hookup is called an electrical circuit. Every electrical circuit must have at least one energy source and one
energy user. It must also have a way to connect the energy source and the energy user. The connectors, the energy source, and
the energy user are the circuit elements.
In this lab, you will be hooking up various simple circuits and measuring quantities known as voltage and current. One can
compare the flow of electrons through a circuit to the flow of water through a stream. Current in an electrical circuit is much like
current in a stream - it is a measurement of flow. Electrons flow in circuits, of course, not water. As for voltage, synonyms for
voltage include "potential difference" and "electromotive force". Voltage is literally the potential energy difference per unit charge
in a circuit. In the analogy to a stream, voltage would be like a waterfall that provides the impetus for the current.
In constructing electrical circuits, one follows (or creates) diagrams to signify
the various elements and how they are connected. At right are some common
symbols used for circuit elements.
Please note that in physics parlance, a "battery" is a connection of several wet
or dry cells, not a single dry cell as is used colloquially. Your car "battery"
is a true battery because it consists of several connected wet cells.
An ammeter is a device that measures how much current is moving through
a circuit. Current is measured in amperes. That is why the current measurer
is called an ammeter. A voltmeter is a device that measures how much
voltage is generated or used by a circuit element. Voltage is measured in
volts. Ammeters and voltmeters are designed to be hooked into a circuit in very specific ways. Improper connection of these
meters to a circuit can destroy them. Be very careful when hooking meters into circuits!
Ammeter Procedure
W hen you measure the current in a circuit, you connect the ammeter directly into the circuit, with one wire connecting
the positive (+) terminal of the ammeter to the part of the circuit leading to the positive (+) terminal of the dry cell.
The second wire connects the negative (-) terminal of the ammeter to the part of the circuit leading to the negative
(-) terminal of the dry cell.
Another rule is that you should never hook an ammeter into a circuit that does not have some sort of resistor (such
as a light bulb) in it. Otherwise, you will be setting up a short circuit and may overload the ammeter.
Voltmeter Procedure
W hen you measure a dry cell's voltage, one wire is connected from the positive (+) terminal of the dry cell to the
positive (+) terminal of the voltmeter. The second wire connects the negative (-) terminals of the dry cell and the
voltmeter. The voltmeter is then hooked across the dry cell. W henever a voltmeter is used to measure (in volts) the
voltage of any electrical circuit element, the voltmeter is always hooked across that element, such that the side of the
element corresponding to the positive side of the circuit is attached to the positive terminal of the meter, and the
negative side of the element is attached to the negative terminal of the meter.
Unlike ammeters, voltmeters can be hooked into circuits that have no resistors in them. If there are resistors, however,
voltmeters should be hooked across the circuit, not directly into it.
Before you begin the main experiment, let’s try lighting a bulb using only one wire and one battery.
Unscrew a light bulb from its socket and figure out how to connect the parts.
Sketch in the space below how you make the connections.
Then deduce how the light bulb is wired, and complete the wires in the diagram at right to show how they
must connect to the base of the bulb.
Unit 15: Electrical Circuits, Alternate Lab A/B: Ammeters and Voltmeters
©2010 by G. Meador – www.inquiryphysics.org
Now hook up the four circuits shown below. (Each lab partner should independently build one of the circuits.) Record the current
and voltage for each circuit in the table as well as the relative brightness of the bulbs.
Circuit #1
Circuit #2
Circuit
Current (amperes)
Circuit #3
Voltage (volts)
Circuit #4
Bulb Brightness
(qualitative)
1
2
3
4
1.
W hich circuit(s) had the brightest bulb(s)? answer all questions in complete sentences
2.
W hat simple explanation (in terms of energy sources and energy users) can you give for your answer to question 1?
3.
W hich circuit(s) had the dimmest bulb(s)?
4.
W hat simple explanation (in terms of energy sources and energy users) can you give for your answer to question 3?
5.
In the scientific method, one should only change one variable to observe how it affects another variable. (You cannot
change two variables simultaneously to see how only one of them affects a third variable.) W hich pairs of circuits should
you compare to see if the number of bulbs affects the voltage readings? W hat effect, if any, do you see?
6.
W hich pairs of circuits should you compare to see if the number of bulbs affects the current readings? W hat effect, if
any, do you see?
7.
W hich pairs of circuits should you compare to see how voltage affects current? W hat effect, if any, do you see?
Unit 15: Electrical Circuits, Alternate Lab A/B: Ammeters and Voltmeters
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
Lab C: OHM'S LAW
You will recall from our electrostatics unit that voltage is energy change per unit charge. The instructor will demonstrate how
to use a voltmeter, a device which measures the change in electrical energy per unit charge occurring across a circuit element.
The instructions are summarized below:
Voltmeter Procedure
To measure the voltage across a circuit element, one wire is connected from the positive (+) terminal of
the voltmeter to the positive (+) side of the circuit element. Another wire connects the negative (-)
terminal of the voltmeter to the negative (-) side of the circuit element. Voltmeters are always hooked
across an element, not in series with it. The voltmeter can be thought of as a small parallel circuit added
onto the existing circuit. Never hook a voltmeter in series.
You will experiment to discover the relationship between voltage (V), current (I), and resistance (R). W e will begin by examining
how voltage affects current when resistance is held constant. Connect circuits 1, 2, and 3. Set the power supply as indicated or
hook up dry cells to create the required voltages. Measure and record in Table I the voltage and the current for each. (M easure
the voltage - do not assume it is what you set on the supply or what you see on a dry cell’s label.)
Circuit #1: Voltage Set at 1.5V
Circuit #2: Voltage Set at 3V
Circuit #3: Voltage Set at 4.5V
Table I - Voltage and Current Data
read the meters to the limit of their precision
Circuit
Voltage = V
(volts)
Current = I
(amperes)
Resistance = R
(ohms)
1
2
3
Use the computer to construct a graph of the data with current on the x-axis and voltage on the y-axis.
1.
The shape of your graph indicates the relationship between voltage and current. W hat is that relationship?
2.
Use the program’s regression line capability to fit a line to your graph. W rite out the complete linear equation relating
voltage (V) and current (I), inserting properly rounded slope and y-intercept numbers.
3.
The slope of the graph is related to what was held constant in the experiment. Identify the proper relationship and use
it to re-write your equation in purely symbolic form.
4.
W e will consider your graph’s slope to be a “measured” value. The supposed value of the resistors can provide a
theoretical value for what the slope should have been. Compute the percentage error between those values.
show your work
Unit 15: Electrical Circuits, Lab C: Ohm’s Law
©2010 by G. Meador – www.inquiryphysics.org
Next we will examine how resistance affects current when voltage is held constant. Connect circuits 4, 5, 6, and 7. BE SURE
TO PROVIDE A VOLTAGE OF 1.5 V. Record all data in Table II.
Circuit #4
Circuit #5
Circuit #6
Circuit #7
Table II - Resistance and Current Data
read the meters to the limit of their precision
Circuit
Voltage (V)
Current (A)
Resistance (Ù)
4
5
6
7
Use the computer to construct a graph of the data. Graph resistance on the x-axis and current on the y-axis
5.
The shape of your graph indicates the relationship between resistance and current. W hat is that relationship?
6.
You cannot perform a linear fit to a curve. Select your data points and then have the computer perform a curve fit.
W hat type of fit did you select?
7.
The computer will provide the necessary constant(s) for your curve. W rite out the complete equation relating resistance
(R) and current (I), inserting the appropriately rounded constant(s).
8.
The constant in your equation is related to what was held constant in the experiment. Identify the relationship and rewrite your equation in purely symbolic form.
Your answers to questions 3 and 8 should be mathematically equivalent. If they are not, ask the instructor for assistance.
9.
Use the value from your graph as the “measured” value and the average voltage as the “theoretical” value to calculate
a percentage error.
show your work
10.
You have discovered a relationship known as Ohm's Law. It states that the current in a circuit is
to the
and
Unit 15: Electrical Circuits, Lab C: Ohm’s Law
to the
.
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
Reading: ELECTRIC SHOCK
Your body is controlled by electrical nerve impulses, so electric currents can disrupt normal bodily
functions. It is the current that passes through your body, not the voltage across it, which determines
the severity of the shock. The current can damage your organs, with the heart, brain, and spinal cord
being particularly susceptible.
Ohm's Law gives the amount of current actually passing through the body as I=V/R. The resistance
used varies with the situation. Internally, your blood and fluids are good conductors with a resistance
of about 200 Ù. Externally, current must first pass through the skin (unless it is cut) and it typically
has a much higher resistance. A calm person's dry skin may have a resistance of 500,000 Ù, while
sweaty palms may have a resistance 10 to 50 times lower. (This is why a lie detector measures skin
resistance along with other physiological factors.) A person standing in saltwater has a skin
resistance of only 500 Ù.
Usually the electric current must pass through three series resistances: your skin (e.g. your nose),
body fluids, and your skin again (e.g. your toes). Thus if your greasy nose has a resistance of
50,000 Ù, your blood has 200 Ù, and your sweaty feet have 10,000 Ù and you cross a 120 V
household circuit, a current of (120 V) / (50,000 Ù + 200 Ù + 10,000 Ù) = 0.002 A will pass through
you.
What would that do? A current greater than 1 mA (0.001 A) causes discomfort. Above 16 mA, you
lose control of your muscles and they undergo contractions. Between 25 mA and 100 mA, you have
difficulty breathing and eventually respiration stops. Between 100 mA and 200 mA, your heart stops
pumping and undergoes uncoordinated contractions called ventricular fibrillation. Above 200 mA,
irreversible heart damage occurs. So with a greasy nose and sweaty feet, the 2 mA current would
cause discomfort.
Special thanks to Dr. Stewart Ryan of the University of Oklahoma
PROBLEMS show your work
1.
Repairing his car in the rain, Victor Vector puts his hands on the terminals of its 12.0 V
battery. If his total resistance is 10,000 Ù, what current and effects will he experience?
2.
Despondent over the latest test results, Victor sharpens his fingers and puts them in the slots
of a 120 V wall outlet while bathing in saltwater. If his total resistance is 1,300 Ù, what
current and effects will he experience?
Unit 15: Electrical Circuits: Readings on Electric Shock, Power, & Appliances
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
Reading: POW ER AND APPLIANCES
Current is the rate of charge flow, so one ampere is equal to one
point in the circuit each
. So 1 A = 1
so one volt is equal to one
So 1 V = 1
/1
of charge flowing past a
/1
. Voltage is the energy change per unit charge,
of energy change for each
of charge that flows.
. If you multiply current and voltage, the result is measured in AV, but using the above
definitions of amperes and volts, that can be simplified to 1
/1
, which is the same thing as 1
indicating that the product of current and voltage is
,
.
Below is a table of common appliances and their current and power requirements.
Appliance
Current (A)
Power (W )
Stereo system
0.3
36
60-W incandescent light bulb
0.5
60
Desktop computer
1.4
168
1.2
1.6
1.7
2.7
147
193
208
328
Drip coffee maker
3.5
420
Garage-door opener
4.5
540
Vacuum cleaner
5.4
648
Televisions:
Average
Average
Average
Average
CRT
LCD
rear projection
plasma
3
2-door refrigerator (18 ft )
6.5
780
Steam iron
7
840
Toaster (2-slot)
7
840
Dishwasher
8.6
1032
Microwave oven
10
1200
Clothes washer
10
1200
Clothes dryer *
27
6480
W ater heater *
37.5
9000
Electric stove (4-burner) and oven *
45.4
10900
Forced-air heater *
80.6
19344
* this appliance runs on a 240 V circuit instead of 120 V
Mostly taken from The Physics Teacher, Vol. 32, p. 511; TV data from CNET.com, 4/2007
Your home's electrical system is split into several parallel circuits. Each circuit is protected from shorts (where wires cross,
causing low resistance and high current) or overloads (where too many appliances are turned on, causing high current) by a
fuse or circuit breaker. The fuse melts or the circuit breaker switch turns off when the current exceeds a safe value.
A typical kitchen might have an electric oven, microwave, dishwasher, refrigerator, drip coffee maker, and four 60 W light
bulbs. If all were operating, the current would be:
45.4 A + 10 A + 8.6 A + 6.5 A + 3.5 A + 2 A = 76 A.
That large a current would require very large wires, so the kitchen would likely run off two separate circuits. One 50 A, 240
V circuit would be for the oven. Another 35 A, 120 V circuit would serve the rest of the kitchen.
PROBLEM : How much power could be output from a 35 A, 120 V circuit?
show your work
Unit 15: Electrical Circuits: Readings on Electric Shock, Power, & Appliances
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
Enrichm ent: RESISTORS
You have found that greater resistance in a circuit results in lower current. Any
material has some innate resistance to current, even such excellent conductors as
copper wire. In wires, that resistance is a nuisance. In other situations,
resistance is useful.
Everyday appliances and electrical gadgets contain resistors to regulate the
current. Too much current could easily overload the circuits in your calculator,
for example. Specialized resistors have color-coded rings on their outer
coverings that indicate exactly how much resistance in ohms (Ù) the resistor
will theoretically give to a circuit. The 4-band resistor color-coding scheme,
that yields 2 significant figures of precision, is shown below; some resistors use
5 bands for 3 sig figs.
Band 1
First Digit:
Band 2
Second Digit:
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
W hite
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
W hite
Band 3
Put the first two digits together and
then multiply by:
Band 4
Indicates Resistor Accuracy
(below are a few examples)
Silver:
Gold:
Black:
Brown:
Red:
Orange:
Yellow:
Green:
Blue:
Black or no band: accurate to ± 20%
Silver: accurate to ± 10%
Gold: accurate to ± 5%
multiply by .01
multiply by .1
multiply by 1
multiply by 10
multiply by 100
multiply by 1,000
multiply by 10,000
multiply by 100,000
multiply by 1,000,000
xkcd.com
So a resistor labeled BROW N-BLACK-BROW N-GOLD means
1 0 x 10 = 100 Ù to within ± 5%, or ± 5 Ù. So it is between 95 Ù and 105 Ù.
W hile a resistor labeled RED-GREEN-YELLOW -SILVER means
2 5 x 10,000 = 250,000 Ù within ± 10%, or ± 25,000 Ù, or 225,000 Ù to
275,000 Ù.
W hat would be the color code for a high-quality 66 Ù resistor?
W hat would be the color code for a high-quality 37,000 Ù resistor?
Let's find out how close the theoretical value of some resistors are to their measured values
in an actual circuit. At your lab station you will find three resistors, leads, a power supply
or dry cell, and meters. Set up a circuit like the one diagramed at right to test your
resistors. DO NOT EXCEED 1.5 VOLTS
Resistor
Voltage (V)
Current (A)
Actual Resistance (Ù)
found with Ohm’s Law
Labeled
Resistance (Ù)
Percentage Error
1
2
3
Unit 15: Electrical Circuits, Enrichment on Resistors
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
Lab D: SERIES CIRCUITS
W e will now use your new voltmeter and ammeter skills to discover how current,
voltage, and resistance operate in any series circuit.
You will be using a series circuit with a power supply set at 3 V (or the equivalent
battery) and three resistors. Ammeter and voltmeter readings will be taken for each of
the resistors and the power supply/batteries. DO NOT EXCEED 3 V.
Diagram A
Step 1: Set up the circuit with the ammeter positioned to measure the current entering
resistor one (R 1). (See diagram A.) Enter the reading in the "R 1" row of the
table.
Step 2: Move the ammeter to measure the current entering R 2 (diagram B) and enter
the reading in the "R 2" row of the table.
Step 3: Move the ammeter to measure the current entering R 3 (diagram C) and enter
the reading in the "R 3" row of the table.
Diagram B
Step 4: Move the ammeter so that it measures the total current entering the power
supply (diagram D) and enter that reading in the "M easured Total" row.
Resistor
Voltage (V)
Current (A)
M easured
Resistance (Ù)
Diagram C
R1
R2
R3
M easured
Total
Diagram D
Step 5: Remove the ammeter from the circuit entirely. Now set the voltmeter across
R 1 to measure how much voltage it is using or "dropping". (See diagram E.)
You are measuring the voltage drop across R 1. Enter the voltage drop in the
"R 1" row of the table.
Diagram E
Step 6: Move the voltmeter to measure the voltage drop across R 2 (diagram F). Enter
the reading in the "R 2" row.
Step 7: Move the voltmeter to measure the voltage drop across R 3 (diagram G).
Enter the reading in the "R 3" row.
Step 8: Move the voltmeter so that it measures the total voltage provided by the
power supply (diagram H). Enter the reading in the "M easured Total" row.
Diagram F
Diagram G
Unit 15: Electrical Circuits, Lab D: Series Circuits
Diagram H
©2010 by G. Meador – www.inquiryphysics.org
Use Ohm's Law to calculate the resistance for R 1, R 2, and R 3. Then use the "Total" voltage and current values to calculate the
total resistance of the circuit. Record all of your results in the "Resistance" column of the table.
answer all questions in complete sentences
1.
How do the four current readings compare with each other?
2.
W hat does this tell you about the current flowing through each part of the circuit?
3.
How do the individual voltages compare with the total voltage?
4.
How would you compute the total voltage of a series circuit if you only knew the values of the individual voltages?
(Look at your data for a mathematical relationship.)
5.
Voltage and energy are proportional. Look at the voltage data for the various individual resistors. Is energy
distributed evenly? If not, what seems to make a particular resistor use more energy?
6.
How would you compute the total resistance of a circuit like the one you just worked with for any number of
resistors if you knew the values of the individual resistors? (Look at your data - see the pattern?)
PROPERTIES OF SERIES CIRCUITS
7.
You can now formulate the relationships between the total and individual values for current, voltage, and resistance
in any series circuit. Use your answers to questions 1-6 to guide you.
The current:
The resistance:
The voltage:
Unit 15: Electrical Circuits, Lab D: Series Circuits
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
W orksheet A: SERIES CIRCUIT PROBLEMS
be careful to use proper significant figures on all answers
1.
W hat would be the required voltage of an energy source in a circuit with a current of 10.0 A and a resistance of 11.0 Ù?
2.
Three 1.50 V cells are connected to form the energy source of a series circuit. The total resistance in the circuit is
100 Ù. How much current moves through the circuit?
3.
W hat is the total resistance of the circuit shown in the diagram at right?
4.
How much current moves through the 5.00 Ù resistor in that circuit?
5.
How much voltage is dropped across the 5.00 Ù resistor? (Remember, you must
use Ohm's Law to get the correct voltage drop.)
6.
How much voltage is dropped across the 2.00 Ù resistor?
7.
How much voltage is dropped across the 3.00 Ù resistor?
8.
Show the total of the above three answers in the space below. It should match the battery voltage. If it doesn't, you
need to go back and rework problems 5, 6, and 7.
9.
The circuit shown below has three numbered resistors, three voltmeters, and an ammeter positioned as shown. Use
Ohm's Law and the properties of series circuits to complete the table. (Hint: One way to avoid rounding errors is to
place any unrounded numbers outside the table near the rounded ones you place in the boxes. M ake sure your box
entries have 3 significant figures.)
Diagram
Position
Voltage
(V)
Current
(A)
1
6.00
0.0100
2
4.00
Resistance
(Ù)
3
Total
Unit 15: Electrical Circuits, Worksheet A: Series Circuit Problems
15.0
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
Lab E: PARALLEL CIRCUITS
W e will now discover how current, voltage, and resistance operate in any parallel
circuit. Set the power supply at 1.5 V for this lab, or use a single dry cell. DO NOT
EXCEED 1.5 V.
Step 1: Set up a circuit with a power supply set at 1.5 V and two resistors as shown in
diagram A. The ammeter is positioned to measure the current entering
resistor one (R 1), while the voltmeter measures its voltage drop. Enter the
readings in the "R 1" row of the table for the "Two-Resistor Circuit".
Diagram A
Step 2: Move the ammeter and voltmeter to measure the current entering R 2 and its
voltage drop (diagram B). Enter the readings in the "R 2" row of the table.
Step 3: Move the ammeter and voltmeter to measure the total current entering the
power supply and the total voltage supplied by the power supply (diagram C).
Enter those readings in the "Total" row.
Circuit
Resistor
TwoResistor
Circuit
R1
Voltage
(V)
Current
(A)
Theoretical
Resistance
(Ù)
Diagram B
Actual
Resistance
(Ù)
Diagram C
R2
Total
ThreeResistor
Circuit
R1
R2
R3
Diagram D
Total
Step 4: Now set up the three-resistor circuit shown in Diagram D. The ammeter and
voltmeter are initially positioned to measure the current entering and the
voltage drop across R 1. Enter those readings in the "R 1" row of the table for
the "Three-Resistor Circuit".
Diagram E
Step 5: Move the ammeter and voltmeter to measure the current entering R 2 and its
voltage drop (diagram E). Enter the readings in the "R 2" row of the table.
Step 6: Move the ammeter and voltmeter to measure the current entering R 3 and its
voltage drop (diagram F). Enter the readings in the "R 3" row of the table.
Step 7: Move the ammeter and voltmeter to measure the total current entering the
power supply and the total voltage supplied by the power supply (diagram G).
Enter those readings in the "Total" row.
Diagram F
Diagram G
Unit 15: Electrical Circuits, Lab E: Parallel Circuits
©2010 by G. Meador – www.inquiryphysics.org
answer all questions in complete sentences
1.
In either circuit you constructed, how do the voltage drops across the individual resistors compare with the voltage for the
power supply? Contrast this to the behavior in a series circuit.
2.
Your data shows how current flows through parallel circuits. Contrast this to the behavior in a series circuit.
3.
How are resistance and current related in the different parts of a parallel circuit? (Does higher resistance result in higher or
lower current, or does it have no effect?)
Determine the theoretical resistance of each resistor in the circuits, and then calculate the actual resistances using Ohm's Law. Record
those values in the table. Using Ohm's Law, you can also calculate the actual total resistance of the circuits, using the readings for total
voltage and total resistance. Record those values in the table.
4.
Adding a resistor to a series circuit increases the total resistance. Parallel circuits behave differently: compare the two total
resistance values in the table. How did the total resistance change when a third resistor was added?
5.
How do the total resistances compare with the individual resistances in parallel circuits?
There is a formula for computing the total resistance of a parallel circuit for any number of resistors. W e will derive this formula
together later.
PROPERTIES OF PARALLEL CIRCUITS
6.
You can now formulate the relationships between the total and individual values for current, voltage, and resistance in any
parallel circuit. Use your answers to questions 1-5 to guide you.
The current:
The voltage:
The resistance:
Unit 15: Electrical Circuits, Lab E: Parallel Circuits
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
W orksheet B: PARALLEL CIRCUIT PROBLEMS
1.
W hat is the total or effective resistance of the circuit shown in the diagram at right?
2.
How much voltage is there across the 20.0 Ù resistor?
3.
How much current moves through the 20.0 Ù resistor?
4.
How much voltage is there across the 15.0 Ù resistor?
5.
How much current moves through the 15.0 Ù resistor?
6.
Calculate the sum of answers three and five and show it below. It should equal the total current found by dividing
the battery voltage by the total resistance calculated in problem 1. If it doesn't, you need to go back and rework 1-5.
7.
The circuit shown below has two numbered resistors, a voltmeter, and an ammeter positioned as shown. Use Ohm's
Law and the properties of parallel circuits to complete the table. (Hint: One way to avoid rounding errors is to place
any unrounded numbers outside the table near the rounded ones you place in the boxes. M ake sure your box
entries have 3 significant figures.)
Diagram
Position
Voltage
(V)
1
2
Current
(A)
Resistance
(Ù)
0.100
6.00
12.0
Total
8.
The circuit shown below has three numbered resistors and an ammeter positioned as shown. Use Ohm's Law and the
properties of parallel circuits to complete the table.
Diagram
Position
Current
(A)
Resistance
(Ù)
1
250
2
500
3
750
Total
Unit 15: Electrical Circuits, Worksheet B: Parallel Circuit Problems
Voltage
(V)
3.00
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
W orksheet C: SERIES & PARALLEL CIRCUITS; POW ER IN CIRCUITS
1.
A 6.00 Ù resistor, a 54.0 Ù resistor, and a 32.0 Ù resistor are connected in series. Calculate their total resistance.
2.
Calculate the total resistance of four 8.00 Ù resistors connected in parallel.
3.
A 15.0 Ù resistor, a 6.00 Ù resistor, and a 39.0 Ù resistor are connected in series across a potential difference of
120 V.
a)
Calculate the current flowing through the circuit.
b)
Calculate the voltage drop across the 15.0 Ù resistor.
4.
Three resistors are connected in parallel across 20.0 V. The resistors draw a total of 5.00 A. Two of the resistors
have values of 24.0 Ù and 12.0 Ù. W hat is the value of the third resistor? Show your work, even if you use a
table.
5.
Fill out the table for the circuit diagramed at right. Showing work is optional here.
Circuit Position
Current (A)
Resistance (Ù)
1
10.0
2
20.0
3
30.0
Total
6.
Voltage (V)
6.00
Fill out the table for the circuit diagramed at right. Showing work is optional here.
Circuit Position
Voltage (V)
Current (A)
Resistance (Ù)
1
10.0
2
20.0
3
30.0
Total
6.00
Unit 15: Electrical Circuits, Worksheet C: Series & Parallel Circuits; Power in Circuits
©2010 by G. Meador – www.inquiryphysics.org
7.
A coffee pot rated at 360 W , an iron rated at 960 W , and an oven rated at 1200 W are connected in parallel across
120 V. The 15.0 A fuse in the circuit immediately blows. Calculate the total current drawn.
8.
Phluffy’s shock collar (she meows too much) delivers a current of 0.0500 A and runs on a 9.00 V battery.
a)
W hat is the power of the collar circuit in watts?
b)
Over a three month period the collar is in operation for a total of 600 seconds. How many joules of
electrical energy was consumed during that period of time? Show an equation for calculating energy
when you know the power and the time.
Unit 15: Electrical Circuits, Worksheet C: Series & Parallel Circuits; Power in Circuits
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
W orksheet D: COMPOUND CIRCUIT PROBLEMS
1.
2.
Use the diagram at right to answer the following questions. You may
use a table to guide your work, but you must show all relevant
equations and calculations in the spaces below.
a)
W hat is the effective resistance of the parallel part of the
circuit? (3.00 Ù)
b)
W hat is the total resistance of the entire circuit?
c)
W hat is the reading on the ammeter?
d)
W hat is reading on the voltmeter?
Fill out the table for the circuit diagramed at right. Showing work is optional here.
Circuit Position
Voltage (V)
1
2
3
Current (A)
Resistance (Ù)
0.200
30.0
20.0
3.00
Total
3.
Two 12.0 Ù resistors and a 6.00 Ù resistor are each connected in parallel. A 15.0 Ù resistor is added to the parallel
group in series. All of them are connected to a single voltage source, and an ammeter is placed to measure total
current.
a)
Draw the circuit, including the resistors, source, and ammeter.
b)
Calculate the voltage of the source if the ammeter shows a reading of 2.00 A. Show your equation and all
work.
Unit 15: Electrical Circuits, Worksheet D: Compound Circuit Problems
©2010 by G. Meador – www.inquiryphysics.org
15 Electrical Circuits
Nam e
W orksheet E: COMBINATION CIRCUITS, POW ER IN CIRCUITS, CAPACITORS
1.
A 200 Ù and a 300 Ù resistor are connected in parallel. This parallel arrangement is connected in series with a
10.0 Ù resistor. The total potential difference per unit charge in this circuit is 15.0 V, which is supplied by an
arrangement of six 5.00 V dry cells.
a.
Draw a diagram of the circuit, including how the six 5.00 V cells could be arranged to provide 15.0 V.
Include in your diagram an ammeter that would measure total current (see part d below) and a voltmeter that
could measure the voltage across a parallel resistor (see part f below).
b.
W hat is the effective resistance of the parallel portion of the circuit?
c.
W hat is the effective resistance of the entire circuit?
d.
W hat is the total current in the entire circuit?
e.
W hat is the voltage drop across the 10.0 Ù resistor?
f.
W hat is the voltage drop across the parallel portion of the circuit?
g.
W hat is the current through the 200 Ù resistor?
h.
W hat is the current through the 300 Ù resistor?
The correct answer is 0.0462 A.
Unit 15: Electrical Circuits, Worksheet E: Combination Circuits, Power in Circuits, Capacitors
Page 1 of 4
©2010 by G. Meador – www.inquiryphysics.org
2.
Fill out the table for the circuit diagramed at right. use proper sig figs
Circuit Position
Resistance (Ù)
10.0
2
20.0
3
30.0
6.00
Fill out the table for the circuit diagramed at right. use proper sig figs
Circuit Position
Voltage (V)
Current (A)
Resistance (Ù)
1
10.0
2
20.0
3
30.0
Total
4.
Current (A)
1
Total
3.
Voltage (V)
6.00
Fill out the table for the circuit diagramed at right. use proper sig figs
Circuit Position
Voltage (V)
Current (A)
Resistance (Ù)
1
10.0
2
20.0
3
30.0
Total
6.00
5.
If the cells are identical, which circuit would draw the most current from the cell?
6.
If the resistors are identical, which circuit would have the lowest overall change in electrical potential
energy per unit charge?
Unit 15: Electrical Circuits, Worksheet E: Combination Circuits, Power in Circuits, Capacitors
Page 2 of 4
©2010 by G. Meador – www.inquiryphysics.org
7.
Use the diagram of the complex circuit to answer the following
questions. You may use a table to guide your work, but you must
show all relevant equations and calculations in the spaces below.
a)
W hat is the effective resistance of the parallel part of the
circuit?
b)
W hat is the total resistance of the entire circuit?
c)
W hat is the reading on the voltmeter? (You may use a table to guide your approach, but you must separately
show all equations and calculations.)
d)
W hat is the reading on the ammeter?
The correct answer is 1.76 A.
POWER IN CIRCUITS:
8.
Phluffy’s shock collar (she meows too much) delivers a current of 0.0600 A and runs on a 9.00 V battery.
a)
W hat is the power of the collar circuit in watts?
b)
Over a three month period the collar is in operation for a total of 600 seconds. How many joules of
electrical energy were consumed during that period of time? show the equation
c)
A typical 9.00 V battery might cost $2.40 and provide 19,250 J of energy. W hat is the cost of running the
shock collar as described in parts a and b?
Unit 15: Electrical Circuits, Worksheet E: Combination Circuits, Power in Circuits, Capacitors
Page 3 of 4
©2010 by G. Meador – www.inquiryphysics.org
CAPACITORS:
9.
10.
If the cells are identical, which circuit would store the most total charge?
The circuit diagram at right shows a 3.00 ìF capacitor hooked
up in parallel across a 5.00 Ù resistor that is in turn hooked up
in series with a 10.0 Ù resistor. The emf sources in the circuit
are two 12.0 V sources hooked in series with one another.
a)
Use the information provided to determine the voltage
across the capacitor after it is fully charged.
b)
Now find the charge on one of the plates of the fully-charged capacitor.
c)
How much current is detected by the ammeter once the capacitor is fully charged?
Unit 15: Electrical Circuits, Worksheet E: Combination Circuits, Power in Circuits, Capacitors
Page 4 of 4
©2010 by G. Meador – www.inquiryphysics.org
PHYSICS TEST REVIEW
Nam e
Electrostatics and Electrical Circuits
W rite a "P" in the blank by each statement that describes a parallel circuit. W rite a "S" in the blank by
each statement that describes a series circuit.
1.
W hen more light bulbs are added, they all still remain bright.
2.
Different voltages are dropped across each resistor.
3.
Different currents flow through each resistor.
4.
If one part of the circuit fails, the other parts still work.
5.
The total resistance is equal to the sum of the individual resistances.
W rite the letter corresponding to the best answ er in the blank by each question.
6. The total resistance of a parallel circuit is always...
A) greater than the sum of all the individual resistances.
B) greater than any of the individual resistances.
C) equal to the smallest of the individual resistances.
D) less than any of the individual resistances.
7. W hen another resistor is added to a parallel circuit, the total current...
A) goes up.
B) goes down.
C) is unaffected.
8. If a short occurs in one room of a house and it goes dark, but all the other rooms stay lit, it is because...
A) all of the fuses have blown.
B) the short has only blown one fuse and the rest of the house is still lit because it is in series.
C) the short has only blown one fuse and the rest of the house is still lit because it is in parallel.
D) the short has not blown any of the fuses.
9. Circuit "S" has three 10 Ù resistors in series with a 10 V battery. Circuit "P" has three 10 Ù resistors in parallel
with another 10 V battery. W hich statement is NOT true?
A) The total voltage of circuit "S" is greater than the total voltage of circuit "P".
B) The total current in circuit "S" is less than the total current in circuit "P".
C) The total resistance of circuit "S" is greater than the total resistance of circuit "P".
10. An
A)
B)
C)
D)
ammeter should have a very...
low resistance, since it is hooked in series.
low resistance, since it is hooked in parallel.
high resistance, since it is hooked in series.
high resistance, since it is hooked in parallel.
11.
A series circuit is composed of a 10.0 V battery and three resistors, which are 2.00 Ù, 6.00 Ù, and 12.0 Ù. How
much current flows through the 12.0 Ù resistor?
12.
A space heater has a current of 12.0 A flowing through it and an effective resistance of 9.00 Ù.
A)
Calculate the power of the heater.
B)
How many kilowatt-hours of heat energy could this heater produce if it operated for an hour?
C)
How many joules of energy is that?
D)
If PSO charges 6.00 cents per kW h, how much would it cost
to run the heater for 8.00 hours?
Test Review for Units 14-15: Electrostatics & Electrodynamics
©2010 by G. Meador – www.inquiryphysics.org
Physics Test Review over Electrostatics and Electrical Circuits
13.
Page 2
Fill in the table for each circuit, using 3 significant figures.
Series Position
Voltage (V)
Current (A)
Resistance (Ù)
1
5.00
2
10.0
3
15.0
Total
5.00
Parallel Position
Voltage (V)
Current (A)
Resistance (Ù)
1
5.00
2
10.0
3
15.0
Total
5.00
Com plex #1
Pos.
Voltage (V)
Current (A)
Resistance (Ù)
1
5.00
2
10.0
3
15.0
Total
5.00
Com plex #2
Pos.
Voltage (V)
Current (A)
Resistance (Ù)
1
9.00
2
30.0
3
30.0
Total
12.0
Test Review for Units 14-15: Electrostatics & Electrodynamics
©2010 by G. Meador – www.inquiryphysics.org
Physics Test Review over Electrostatics and Electrical Circuits
Page 3
14. W hen the distance between two charges is halved, the electrical force between them...
A) quadruples.
B) doubles.
C) halves.
D) reduces to one fourth.
15. If you comb your hair and the comb becomes negatively charged, ...
A) electrons were transferred from the comb onto your hair.
B) electrons were transferred from your hair onto the comb.
C) protons were transferred from the comb onto your hair.
D) protons were transferred from your hair onto the comb.
16. W hich statement correctly describes how to charge something negatively by conduction?
A) Touch it with a positively charged object.
B) Touch it with a negatively charged object.
C) Momentarily ground it with a positively charged object nearby.
D) Momentarily ground it with a negatively charged object nearby.
17. If a
A)
B)
C)
D)
neutral conductor is touched by a rubber rod with a negative charge on it, what will happen?
Electrons will flow from the conductor onto the rubber rod.
Electrons will flow from the rubber rod onto the conductor.
Protons will flow from the conductor onto the rubber rod.
Protons will flow from the rubber rod onto the conductor.
18. Protons and electrons...
A) repel each other.
B)
attract each other.
C)
have no effect on each other.
19. Coulomb's law says that the force between any two charges depends...
A) inversely on the product of the charges.
B) directly on the square of the distance between the charges.
C) directly on the product of the charges.
D) inversely on the square root of the distance between the charges.
20. In a good insulator, electrons are usually...
A) free to move around.
B) free to move around after an impurity has been added.
C) semi-free to move around.
D) tightly bound in place.
21. A leaf electroscope is neutral. As a negative charge is brought close to the electroscope, the leaves spread apart
because the approaching negative charge...
A) attracts and pulls electrons away from them.
B) attracts and pulls protons away from them.
C) pushes electrons down onto them.
D) pushes protons down onto them.
22. The reason a pith ball will be attracted to a charged rubber rod is that...
A) the rod is positive and attracts electrons in the pith ball.
B) the rod is negative and repels electrons in the pith ball, attracting the nearer protons.
C) the rod is positive and repels electrons in the pith ball, attracting the nearer protons.
D) the rod is negative and attracts electrons in the pith ball.
23. A girl accidentally touches a partially plugged-in lamp plug one day. If the voltage from the wall outlet was
120 V and her skin's resistance was 120,000 Ù, how much current passed through her body?
A) 12,000,000 A
B) 1,000 A
C) 120 A
D) 0.0010 A
Test Review for Units 14-15: Electrostatics & Electrodynamics
©2010 by G. Meador – www.inquiryphysics.org
Physics Test Review over Electrostatics and Electrical Circuits
Page 4
24.
A positively charged metal ball was motionless on a flat table. Two charged rods
were brought up the ball as shown in the diagram. In what compass direction did
the ball move?
A) southwest
B) southeast
C) northwest
D) northeast
25.
Circuit "S" has three users in series with a cell. Circuit "P" has the same circuit elements as circuit "S", but
they are connected in parallel. W hich statement is true?
A) The total current in "P" is greater than the total current in "S".
B) The total voltage of "P" is greater than the total voltage of "S".
C) The total resistance of "P" is greater than the total resistance of "S".
26.
W hich statement correctly describes a short circuit?
A) Too many users are plugged into the circuit, lowering its total resistance, causing high currents.
B) Too many users are plugged into the circuit, raising the total resistance, causing low currents.
C) W ires in the circuit become crossed, making it a series circuit and thus causing high currents.
D) W ires in the circuit become crossed, making it "shorter" and thus causing high currents.
27.
W hen another user is activated in a parallel circuit...
A) the total resistance rises.
B) the total current falls.
C) the total resistance falls.
D) the total voltage increases.
28.
W hich statement correctly describes an ammeter?
A) It has high resistance because it hooks into a circuit in parallel.
B) It has high resistance because it hooks into a circuit in series.
C) It has low resistance because it hooks into a circuit in parallel.
D) It has low resistance because it hooks into a circuit in series.
For each of the procedures described below, place the letter of the diagram that best represents the resulting charge
arrangements on the electroscope.
29. A negatively charged rod is brought near, but not
touching an uncharged electroscope.
30. A negatively charged rod is used to charge the scope
by induction.
31. A positively charged rod is used to charge the scope
by conduction.
32. A negatively charged electroscope is grounded.
33.
A 5.00 Ù resistor, 10.0 Ù resistor, and a rheostat are connected in parallel and placed across a 12.0 V source. W hat
amount of resistance should be set for the rheostat in order to draw a total current of 4.20 A from the source?
Test Review for Units 14-15: Electrostatics & Electrodynamics
©2010 by G. Meador – www.inquiryphysics.org
Electrical Circuits Test Review
Nam e
ADDITIONAL CIRCUIT ANALYSIS PRACTICE:
1.
Use the diagram at right to answer the following questions.
a) W hat is the voltage across the capacitors after they are
fully charged?
B) W hat is the charge on the 6.00 ìF capacitor?
C) W hat is the total capacitance of the circuit?
2.
Use the diagram at right to answer the following questions.
a)
W hat is the effective resistance of the parallel part of the circuit?
B) W hat is the total resistance of the entire circuit?
C) W hat is the reading on the ammeter?
D) W hat is reading on the voltmeter?
Unit 15: Electrical Circuits, Test Review
©2010 by G. Meador – www.inquiryphysics.org
3.
Fill out the table for the circuit diagramed at right.
Circuit Position
Voltage (V)
Current (A)
1
Resistance (Ù)
20.0
2
0.300
3
40.0
40.0
Total
4.
Fill out the table for the circuit diagramed at right.
Circuit Position
Voltage (V)
1
Current (A)
Resistance (Ù)
0.200
30.0
2
3
20.0
3.00
Total
5.
Fill out the table for the circuit diagramed at right.
Circuit Position
Voltage (V)
1
2
Current (A)
Resistance (Ù)
15.0
2.00
3
30.0
Total
95.0
6.
Three resistors are connected in parallel across 20.0 V. The resistors draw a total of 5.00 A. Two of the resistors
have values of 24.0 Ù and 12.0 Ù. W hat is the value of the third resistor?
7.
A transistor radio operates by means of a 9.00 V battery that supplies it with 0.0500 A of current.
a) W hat is the power of the radio in watts?
b)
The battery cost is unfortunately $9.00 per kilowattChour. The same radio, by means of a converter, is plugged
into a household circuit by a homeowner who pays 5.00¢ per kilowattChour. Compute the cost of operating the
radio for 300 hours on battery power, and then compute the cost using house current.