unit 7: current electricity · 2013-03-21 · assignment #5: ohm’s law calculations 1. what...
TRANSCRIPT
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Regents Physics:
March – April 2012
Unit 7: Current Electricity
Focus Question for the Unit: How can electron flow be described and manipulated in a circuit?
YOU SHOULD BE ABLE TO ANSWER THIS IN DETAIL BY THE END OF THE UNIT
Name____________________________________________________________
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UNIT 7: Current Electricity
TABLE OF CONTENTS
Calendar………………………………………………………………….………3 Vocabulary/Study Guide ……………………………………………………….4 Topic #1: Circuit Basics ………………………………………………………..6 Topic #2: Ohm’s Law …………...………………………..…………….........11 Topic #3: Resistance & Resistivity ………………………………………….20 Topic #4: Types of Circuits – Series vs. Parallel ………………….………25 Topic #5: Electrical Power …………………………………………………...43
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March - April 2012 Sunday Monday Tuesday Wednesday Thursday Friday Saturday
25 26 27 28 29 30 31
C D E F A 1 2 3 4 5 6 7
B C D E Spring Recess!
8 9 10 11 12 13 14
SPRING RECESS!
15 16 17 18 19 20 21
F A B C D
22 23 24 25 26 27
E F A B C
Other Grading Information:
Labs
Lab #20: Ohm’s Law Lab #21: Resistance in a Wire
Lab #22: Series Circuits Lab #23: Parallel Circuits
Quiz & Test
Your quiz will be on .
Your test will be on .
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Unit 7 Study Guide: Current Electricity Vocabulary
Current
Amperes
Voltage
Volts
Resistance
Ohm
Circuit
Resistivity
Series
Parallel
Equivalent Resistance
Electrical Power
Electrical Energy
Reference Tables:
List of Physical Constants (p. 1)
Electricity, Circuit Symbols, Resistivities at 20oC (p. 4)
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Objectives: You Should KNOW: 1.) SI units (International System of units).
2.) Slopes have physical significance (i.e. – V vs. I).
3.) A circuit is a closed path with a potential difference, in which current can exist.
4.) The total current entering any junction of wires must equal the total current leaving.
5.) Around any closed loop in a circuit, the sum of potential drops must equal the sum of potential
increases.
6.) For resistors in series, the equivalent resistance is the sum of their values.
7.) For resistors in parallel, the equivalent resistance is less than the value of any individual resistor.
8.) Resistance is directly related to temperature, length, resistivity, and voltage, but indirectly related to
cross-sectional area and current.
9.) Ohm’s Law (V=IR)
10.) Energy can be converted between many forms including mechanical, electromagnetic, nuclear,
and thermal.
11.) Power is a rate.
You Should BE ABLE TO: 12.) Develop skills and protocols in selecting and using proper formulas that require calculating
resistance, voltage, current, energy, power, cross-sectional area, resistivity, and charge.
13.) Assemble simple series and parallel circuits.
14.) Compare and contrast series and parallel circuits, including the behavior of light bulbs.
15.) Measure current and voltage in a circuit using an ammeter, voltmeter, and multi-meter.
16.) Use measurements to determine the resistance of a circuit element.
17.) Draw and interpret graphs involving current, resistance, voltage, length, and power.
18.) Measure and compare the resistance of conductors of various lengths and cross-sectional areas.
19.) Draw and interpret circuit diagrams which include voltmeters and ammeters.
You Should UNDERSTAND: 20.) Electricity is a form of energy that can be transformed by moving electric charges doing work in
various devices.
21.) Electric fields provide the force that moves charged particles.
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Topic #1: Circuit Basics
Additional Resources:
Text Reference: p. 531 – 534 & p. 548 – 550
The Physics Classroom – http://www.physicsclassroom.com/Class/circuits/u9l2a.cfm
St. Mary’s Physics Online – http://www.stmary.ws/highschool/physics/home/notes/electricity/circuits/CurrentBasics.htm
APlusPhysics Tutorial – http://aplusphysics.com/courses/regents/electricity/regents_electric_current.html
APlusPhysics Video Tutorial – http://aplusphysics.com/courses/regents/videos/Current/Current.html
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Assignment #1: Circuit Building 1.) Which of the following circuits will light the light bulb? Explain your choice:
________________________________________________________________
________________________________________________________________
________________________________________________________________
________________________________________________________________
2.) Try hooking up the light bulb, wires, and battery in each of the scenarios above.
Which one/s light? _________________________
3.) Was your prediction correct? ________
4.) Based on your results, what feature(s) must a successful circuit have? Explain.
1 2 3 4 5 6 7 8 9 10
(two wires)
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Assignment #2: Basic Circuits Internet Activity
Open you web browser and type in the following address: www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=29
Username: rh student 4 Password: 4
Click on the Intro to E & M activity.
Click on the Moving Charge button. Go through the activity and answer the following questions.
1) What happens inside a wire when an electromotive force is applied?
2) What is current?
3) How is a car driving down a flat open road like an electron moving through a wire with low
resistance?
4) What happens when electrons get “joggled” around trying to move through a substance with
moderate resistance?
5) What is needed to make an electron move away from its nucleus?
6) What kind of energy is stored in a battery?
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Click on the button for Circuits. 7) What four things make up a common circuit? 8) Before closing the switch of the circuit, move your mouse onto the battery, wire and light bulb.
What is happening in each when the switch is open?
- Battery:
- Wire: - Light Bulb:
9) Now close the switch of the circuit. Move your mouse onto the battery, wire and light bulb. What
is happening in each when the switch is closed?
- Battery:
- Wire: - Light Bulb:
10) In our labs we use resistors that cannot change. But in the next activity, set the battery to a
certain voltage and use the slider to change the resistance. What happens to the current as resistance decreases? Explain.
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Assignment #3: What is Current?
We have looked at Charges being transferred through friction, polarization, conduction, grounding, and induction. Now we are going to look at not only how much but how fast charge moves. 1. What is the unit for Charge? ________________
2. What is a rate? _____________________________________________________________ 3. If I want to know the rate at which charges are moving, what mathematical operation should I use?
______________________ 4. If Current is defined as the rate at which charges flow, what is the equation for current? 5. Check your reference table for an equation involving current and charge. Was your prediction
correct? If not, fix the equations above! ***The units for Current are Amperes (Amps), abbreviated with a capital letter, A. The SI unit for
Current is Coulombs per seconds or C/s 6. Current is often compared to the amount of water flowing in a faucet or stream. If you have two
streams flowing how do you know which one is moving faster or slower? 7. Using the previous analogy, how can you tell if the current is faster or slower? 8. 20 Coulombs of charge pass a given point in a conductor in 4.0 seconds. What is the current in
the conductor? 9. In a circuit with a battery supplying 12 volts, the current is 10 amperes.
(a) How much charge flows through the circuit in 2.0 minutes?
(b) How many electrons were transferred during these 2.0 minutes?
Current = I =
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Topic #2: Ohm’s Law
Additional Resources:
Text Reference: p. 535 – 538
The Physics Classroom – http://www.physicsclassroom.com/Class/circuits/u9l3c.cfm
St. Mary’s Physics Online – http://www.stmary.ws/highschool/physics/home/notes/electricity/circuits/OhmsLawEquation.htm
APlusPhysics Tutorial – http://aplusphysics.com/courses/regents/electricity/regents_electric_current.html
APlusPhysics Video Tutorial – http://aplusphysics.com/courses/regents/videos/OhmsLaw/OhmsLaw.html
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Assignment #4: What is Ohm’s Law? Question: What are voltage, current and resistance? How do they work? An Analogy:
Putting It All Together… a.) The gumballs in this demonstration represent the flow of _______________ through the
pipe. b.) The height the pipe is raised above the desk represents potential difference, or
____________________. c.) The nails placed in the pipe represent _______________ and slow down the flow of the
gumballs. d.) The higher we raise the pipe, the _______________ the gumballs flow; the more nails we
place in the pipe, the _______________ the gumballs flow. In summary, the current (rate of gumball flow per second) through the pipe depends on the voltage (height the end of the pipe is raised) and the resistance (number of nails in the pipe).
Ohm’s Law is the mathematical formula used to explain this relationship.
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Ohm’s law states that voltage is equal to current times resistance. Find a version of this equation on p. 4 of your Reference Tables & write it below!
R = resistance and has the unit of ohms (Ω)
V = potential difference, or voltage, and has units of volts (V) I = current and has the unit of amperes (or amps, A)
Questions: Show all work! 1. We can rearrange this equation to solve for V or I.
a.) Solve for potential difference (V). b.) Solve for current (I) in Ohm’s Law.
2. What voltage is used by an electrical appliance that draws 0.4 amps of current and has a
resistance of 3 ohms? 3. A light bulb uses 240 volts of electricity and draws a current of 2 A. What is its resistance? 4. Calculate the current used by a television that runs on 240 volts and has a resistance of 600 ohms. 5. A 20 ohm resistor has 40 Coulombs of charge passing through it in 5 s. What is the potential
difference across this resistor?
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6. A wire carries a current of 2.0-amperes. How many electrons pass a given point in this wire in 1.0 second?
7. Complete the following table:
Current (amps)
Resistance (ohms)
Voltage (volts)
(a) 0.1 600
(b) 0.25 1,000
(c) 0.4 240
(d) 0.5 240
(e) 1,000 200
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NOTES: Current Electricity
Resistance:
o Abbreviation:
o Units:
o Symbol in a circuit:
Current:
o Abbreviation:
o Units:
o Symbol in a circuit:
Voltage:
o Abbreviation:
o Units:
o Symbol in a circuit:
Power:
o Abbreviation:
o Units:
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How to Build a Circuit
There are two necessary components that all circuits must have: 1 – 2 – Example of a Simple Circuit: Attaching Meters – Ammeters & Voltmeters
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Assignment #5: Ohm’s Law Calculations 1. What current flows through a circuit in which the resistance is 20 ohms and the potential
difference is 90 volts? 2. An ammeter and voltmeter in a circuit respectively read: 2.48 A and 88.4 V. What is the
resistance of the circuit? 3. A battery supplies a potential difference of 120 volts to a circuit in which the resistance is 15
ohms. What current flows in this circuit? 4. What potential difference is needed to produce a current of 345 milliamps in a circuit having a
resistance of 8.74 ohms? 5. When a wire is connected to a 9.0 V battery, the current is 0.020 A. What is the resistance of the
wire?
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6. A potential difference of 12 Volts is applied across a circuit having a 4 ohm resistance. What is the current in the circuit? For each of the following circuits use the rules and equations for electric circuits to determine the voltage (V), current (I), and resistance (R). 7.
8.
9.
V = 50 volts
R1 = ?
V = 200 volts
R1 = 20 ohms
R1 = 35
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Assignment #6: Ohm’s Law Problems _____1. A graph of voltage (y-axis) versus current for a given resistor would produce a
1) straight line 2) hyperbola 3) parabola 4) slope of zero _____2. The rate of flow of electrons in a circuit is called
1) resistance 2) voltage 3) current 4) power _____3. A volt is a
1) joule/sec 2) coulomb/sec 3) joule/coulomb 4) coulomb/joule _____4. An ampere is a
1) joule/sec 2) coulomb/sec 3) joule/coulomb 4) coulomb/joule _____5. A 10 ohm resistor is connected to a power supply producing 5 amperes of current
in that resistor. The voltage drop across the resistor must be
1) 2 volts 2) 50 volts 3) 0.5 volts 4) 15 volts _____6. If the voltage provided to a resistor increases, the current through that resistor
1) increases 2) decreases 3) remains the same _____7. As the resistance of a circuit increases, the current through that circuit
1) increases 2) decreases 3) remains the same _____8. Ten coulombs of charge pass a given point within a circuit in 2 seconds. The
current in the circuit is
1) 20 amps 2) 12 amps 3) 5 amps 4) 0.2 amps _____9. The opposition to the flow of electrons in a circuit is defined as electrical
1) current 2) power 3) resistance 4) voltage drop _____10. How much work is done in moving 100 coulombs of charge through a potential
difference of 10 volts?
1) 1000 joules 2) 100 joule 3) 10 joules 4) 1 joule
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Topic #3: Resistance & Resistivity
Additional Resources:
Text Reference: p. 534 – 535
The Physics Classroom – http://www.physicsclassroom.com/Class/circuits/u9l3b.cfm
St. Mary’s Physics Online – http://www.stmary.ws/highschool/physics/home/notes/electricity/circuits/ResistanceWire.htm
APlusPhysics Video Tutorial – http://aplusphysics.com/courses/regents/videos/Resistance/Resistance.html
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Assignment #7: Conductors vs. Insulators
In order to understand resistance, we first have to look at the types of materials with which we’re trying to allow a current to flow.
Directions: Obtain a conductivity tester from your teacher. Test the conductivity of 15 objects found throughout your classroom. You may want to consult p. 508 in your textbook to help in answering the questions that follow. Data:
Object Conductivity
1.) Define electrical conductivity.
2.) Out of the materials you tested, which would you rank as being conductors? Why?
3.) What is a conductor?
4.) Out of the materials you tested, which would you rank as being non-conductors? Why?
5.) Materials that are poor conductors are often called “insulators.” What is an insulator?
6.) Why are conductors important?
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7.) Why are insulators important?
8.) Most cords and electrical appliances have some sort of plastic surrounding the metal components. What is the purpose of the metal components? What is the purpose of the plastic?
View your teacher’s computer simulations for the following questions:
9.) According to the atomic model, what do you observe as the difference between conductors and insulators? What about similarities?
10.) A simple circuit is created using both an insulator and a conductor. Which material allows the bulb to be lit? Explain why.
NOTE: What do you notice about the direction of the flow of electrons in the circuit?
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NOTES: Resistance & Resistivity
Factors Affecting Resistance: On the Reference Table: 1 – Length 2 – Cross-Sectional Area 3 – Resistivity 4 – Temperature Equation: 1.) Which of the following metals has the lowest resistivity ()?
a) aluminum b) silver c) copper d) tungsten 2.) As the cross-sectional area of a wire increases, its resistance
a) increases b) decreases c) remains the same 3.) As the length of a wire increases, the amount of current flowing through it
a) increases b) decreases c) remains the same
4.) As the resistivity () of a wire increases, its resistance
a) increases b) decreases c) remains the same 5.) Electrical resistance can be calculated by
a) V/ I b) L/A c) all of the above
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Assignment #8: Resistance and Resistivity 1.) A 0.686-meter-long wire has a cross-sectional area of 8.23 × 10–6 meter2 and a resistance of
0.125 ohm at 20° Celsius. This wire could be made of
a) aluminum b) nichrome c) copper d) tungsten
2.) A copper wire at 20°C has a length of 10 m and a cross-sectional area of 1.00 × 10–3 m2. The wire is stretched, becomes longer and thinner, and returns to 20°C.
a.) What effect does this stretching have on the wire’s resistance?
b.) What effect does this stretching have on the wire’s resistivity? 3.) A 6.0 m long copper wire has a cross-sectional area of 3.0 mm2. What is the resistance of the
wire? 4.) What is the resistance of aluminum wire that is 4.0 m long and has a radius of 0.25 mm? 5.) A 10.0-meter length of copper wire is at 20°C. The radius of the wire is 1.0 × 10–3 meter.
a.) Determine the cross-sectional area of the wire.
b.) Calculate the resistance of the wire.
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Topic #4: Types of Circuits – Series vs. Parallel
Additional Resources:
Text Reference: p. 550 – 558
The Physics Classroom – http://www.physicsclassroom.com/Class/circuits/u9l4b.cfm
St. Mary’s Physics Online – http://www.stmary.ws/highschool/physics/home/notes/electricity/circuits/default.htm
APlusPhysics Tutorial – Series - http://aplusphysics.com/courses/regents/electricity/regents_series_circuits.html Parallel - http://aplusphysics.com/courses/regents/electricity/regents_parallel_circuits.html
APlusPhysics Video Tutorial – http://aplusphysics.com/courses/regents/videos/Circuits/Circuits.html
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Assignment #9A: Series and Parallel Circuits Internet Activity Open your web browser to www.explorelearning.com Sign in using the Username: rh student 4 and Password: 4 Search “Circuits” Run the gizmo Circuits Series Circuits 1. Build the series circuit with three light bulbs and one battery shown at
the right. To do this, drag the necessary parts from the COMPONENTS pane to the CIRCUIT BOARD.
2. Click on the battery in your circuit, and then vary the voltage across the circuit by dragging the
Selected battery voltage (volts) slider. What happens to the brightness of the lights when the voltage is increased?
3. What happens to the brightness when the voltage is decreased? 4. Click Show current. Set the Selected battery voltage to 1 volt and click Show current. The
current is represented by moving arrows. Is there more or less current leaving the battery than flowing through ONE bulb?
5. How does the flow of current change when the voltage is increased? 6. How does the flow of current change when the voltage is decreased?
7. Does the current ever reach an intersection in the wires? 8. Increase the voltage to 30 Volts and observe the brightness of the bulbs. Add three more bulbs to
your circuit in series. How does the brightness of the bulbs change as more are added?
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Parallel Circuits 1. Build a parallel circuit as shown with three light bulbs and one
battery. To do this, drag the necessary parts from the COMPONENTS pane to the CIRCUIT BOARD.
2. Click on the battery in your circuit, and then vary the voltage
across the circuit by dragging the Selected battery voltage (volts) slider. What happens to the brightness of the lights when the voltage is increased?
3. What happens to the brightness when the voltage is decreased? 4. Set the Selected battery voltage to 1 volt and click Show current. The current is represented by
moving arrows. Is there more or less current leaving the battery than flowing through ONE bulb? 5. What happens to the current when it reaches an intersection in the wires? 6. Does an equal amount of current flow through each bulb? 7. Add one more bulb to the circuit in parallel. What happens to the brightness of the bulbs as more
are added? 8. Keeping the voltage set to 1 volt, what happens to the current leaving the battery as more bulbs
are added? 9. Explain three differences between series and parallel circuits:
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Assignment #9B: Series and Parallel Snap Circuits Activity
Part 1: Series Circuits
1. Use your supplies to build a circuit with single bulb connected to the battery as shown in the diagram.
2. Observe the brightness of the one bulb.
3. Draw a circuit showing TWO bulbs connected in a series circuit. 4. Use your supplies to build this circuit. What happens to the brightness of the two bulbs when compared to one bulb alone? 5. Gently unscrew one of the bulbs. What happens to the other bulb? Why? 6. Add another battery pack to your circuit to increase the voltage. What happens to the brightness of the bulbs? 7. What do you think is happening to the current flowing in the circuit as voltage increases?
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Part 2: Parallel Circuits 1. Connect the same two bulbs in a parallel circuit as shown. 2. Explain how is this circuit different from a series circuit. 3. Add another bulb to the circuit in parallel. Draw a picture of this parallel circuit in the space
below. 4. What happens to the brightness of the two bulbs in a parallel circuit when compared to three
bulbs? 5. Gently unscrew one of the bulbs. What happens to the two other bulbs? Why? Conclusion:
Three light bulbs are connected in series and the filament in one of the bulbs burns out or breaks! How will this affect the other two bulbs? Explain your answer.
Three light bulbs are connected in parallel and the filament in one of the bulbs burns out or
breaks! How will this affect the other two bulbs? Explain your answer. Do you think the electrical circuits in your house are wired in series or in parallel? Explain.
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Series & Parallel Circuits Notes
Series Circuit Parallel Circuit
Circuit Drawing
Voltage Rule
Around any closed loop in a circuit, the sum of potential drops must equal the sum of potential increases
Current Rule
The total current entering any junction of wires must equal the total current leaving
Ex. The current going into Point P is 7 Amps The current leaving Point P is also 7 Amps
(the sum of 3 A + 4 A)
Resistance Combine the rules with V = IR
*Textbook Reference pages 550-558.
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Assignment #10: Series Circuits Problems Series Circuit Example: 2.0-ohm (R1), 3.0-ohm (R2), and 1.0-ohm (R3) resistors are connected in series to a voltage source of 12. volts (VB) with a current of 2.0 amperes (I), as seen in the diagram to the right. Find the voltage drop at each resistor. Equations: I = I1 = I2 = I3 V = V1 + V2 + V3 Req = R1 + R2 + R3 R = V / I (V = IR)
Circuit V I R 1 4.0 V 2 A 2.0 Ω 2 6.0 V 2 A 3.0 Ω 3 2.0 V 2 A 1.0 Ω
Total (T) 12. V 2 A 6.0 Ω ______ 1.) As resistors are added to a circuit in series, the total resistance of the circuit
a) increases b) decreases c) remains the same ______ 2.) As resistors are added to a circuit in series, the voltage across each resistor
a) increases b) decreases c) remains the same ______ 3.) As resistors are added to a circuit in series, the current in the circuit
a) increases b) decreases c) remains the same Base your answers to questions 4-8 on a circuit consisting of two 10 ohm light bulbs in series with a 40 volt power supply. ______ 4.) The total resistance in the circuit is a) 10 ohms b) 20 ohms c) 5 ohms d) 100 ohms
______ 5.) The total current in the circuit is a) 800 Amps b) 20 Amps c) 4 Amps d) 2 Amps ______ 6.) The voltage drop across each light bulb is
a) 40 Volts b) 20 Volts c) 10 Volts d) 5 Volts
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______ 7.) If a third bulb is added to a circuit, the brightness of the original two bulbs will
a) increase b) decrease c) remain the same ______ 8.) If one of the light bulbs should burn out, the other two bulbs will
a) dim b) become brighter c) go out Base your answers to questions 9 – 11 on the diagram below and the following information. A 4.0 ohm resistor (R1), a 6.0 ohm resistor (R2), and an unmarked resistor (R3) are connected to a 24-volt source as shown. The ammeter reads a current of 2.0 amps.
9.) Determine the voltage drop across the 4.0 ohm resistor. Show all work. 10.) Determine the value of R3. Show all work. 11.) If the 4.0 ohm resistor were removed from the circuit and the remaining circuit elements were
reattached in series, what would be the reading on the ammeter? Show all work.
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Assignment #11: OUTSMARTING THE REGENTS EXAM
Although the NYS Regents Physics Exam is a difficult test, many of the questions you will face require NO knowledge of physics whatsoever!! All you need to answer the questions correctly is a Reference Table, eyeballs and just a little bit of thinking.
Here is a typical problem taken from the January 2008 Regents Exam:
STEP 1: Read the problem twice. Pick out the key words: circuit, parallel, and equivalent resistance. STEP 2: Look at your Reference Tables. Again, using only
your eyeballs, look on the Electricity page in the Circuits section and find the equations for Parallel Circuits. It doesn’t even matter if you know what a parallel circuit is! Just find the equation you need and solve it. Ka-ching!
1/Req = 1/R1 + 1/R2 + 1/R3 1/Req = 1/10 + 1/15 + 1/20 1/Req = 0.1 + 0.067 + 0.05 1/Req = 0.2167
Req = 4.62 ohms
STEP 3: Think carefully. Predict what the other choices will be! The Regents WILL try to trick you
and offer choices that may seem right if you don’t think.
So if the correct answer is choice (a) 4.62 ohms, choice (b) will be 0.2167 ohms for the students who forget to cross multiply in the last step.
Choice (c) is going to be 45 ohms, for the students who did not check the Reference Tables
and simply added the resistors to find the equivalent resistance. (This would be correct for a series circuit!)
Choice (d) will probably be 9.00 volts, for students who don’t realize voltage has nothing to
do with the question.
A circuit consists of a 10.0-ohm resistor, a 15.0-ohm resistor, and a 20.0-ohm resistor connected in parallel across a 9.00-volt battery. What is the equivalent resistance of this circuit?
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Now you try one. Here’s another problem from a Regents Exam.
What is the correct answer? Show all work. (a) ________ What will choice (b) be? Explain. (b) ________
What will choice (c) be? Explain. (c) ________
What will choice (d) be? Explain. (d) ________
Here’s another: What is the correct answer? Show all work. (a) ________ What will choice (b) be? Explain. (b) ________
What will choice (c) be? Explain. (c) ________
What will choice (d) be? Explain. (d) ________
A circuit consists of 5.0-ohm resistor, a 10.0-ohm resistor, and a 15.0-ohm resistor connected in series across a 9.00 volt battery. What is the current
flowing through the 10.0-ohm resistor?
A circuit consists of three 10.0-ohm resistors connected in parallel across an 18.0 volt battery. What is the equivalent resistance of this circuit?
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Assignment #12A: Parallel Circuits Problems The circuit diagram to the right shows two resistors connected to a 24-volt source of potential difference. Equations: I = I1 + I2 V = V1 = V2
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111
RRReq
R = V / I (V = IR)
1.) Fill in all of the given quantities Circuit V I R
1 4.0 Ω 2 6.0 Ω
Total (T) 24 V
2.) Remember in a parallel circuit, voltage remains constant throughout each loop (V = V1 = V2) Circuit V I R
1 24 V 4.0 Ω 2 24 V 6.0 Ω
Total (T) 24 V
3.) Solve for current flowing through the 4.0 Ω and 6.0 Ω resistors. (I = V / R) Circuit V I R
1 24 V 6.0 A 4.0 Ω 2 24 V 4.0 A 6.0 Ω
Total (T) 24 V
4.) Solve for total current of the circuit (I = I1 + I2) Circuit V I R
1 24 V 6.0 A 4.0 Ω 2 24 V 4.0 A 6.0 Ω
Total (T) 24 V 10.0 A
5.) Solve for the total resistance (R = V / I) and check with the equivalent resistance
equation 21
111
RRReq
Circuit V I R 1 24 V 6.0 A 4.0 Ω 2 24 V 4.0 A 6.0 Ω
Total (T) 24 V 10.0 A 2.4 Ω
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Practice filling in the following VIR tables.
Circuit V I R 1 2
Total (T)
Circuit V I R 1 2 3
Total (T)
10 Ω
4 Ω
2 Ω
4 A
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Assignment #12B: Parallel Circuits Problems For each of the following circuits use the rules and equations for circuits to determine the voltage (V), current ( I ) and resistance (R) for each resistor and the total circuit by making a VIR chart.
1.)
R1 = 20
R2 = 40
V = 200 volts
R1
R2
V = 60 volts
i = 2 a
i = 1.5 a
R1 = 30
R2 = 60
V = ?
i = 5 a
2.)
3.)
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Base your answers to questions 4 – 6 on the diagram below and the following information A 20.0 ohm resistor (R1), a 30.0 ohm resistor (R3), and an unmarked resistor (R2) are connected to a 24-volt source as shown. The ammeter reads a current of 3.0 amps.
4.) Determine the voltage drop across the 20.0 ohm resistor. Show all work. 5.) Determine the value of R2. Show all work. 6.) If the 20.0 ohm resistor were removed from the circuit and the remaining circuit elements were reattached in parallel, what would be the reading on the ammeter? Show all work.
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Answer the following questions:
______ 1.) As resistors are added to a circuit in parallel, the total resistance of the circuit a) increases b) decreases c) remains the same ______ 2.) As resistors are added to a circuit in parallel, the voltage across each resistor a) increases b) decreases c) remains the same ______ 3.) As resistors are added to a circuit in parallel, the current in the circuit a) increases b) decreases c) remains the same Base your answers to questions 4-9 on a circuit consisting of two 10 ohm light bulbs in parallel with a 40 volt power supply.
4.) Using the circuit symbols found in the Reference Tables for Physical Setting/Physics, draw a diagram of these components in a parallel circuit.
5.) In the diagram above, draw in a voltmeter and ammeter in the correct positions to measure the total amount of voltage and current, respectively, that are being delivered to the circuit.
______ 6.) The total current in the circuit is a) 8 Amps b) 20 Amps c) 4 Amps d) 2 Amps ______ 7.) The voltage drop across each light bulb is a) 40 Volts b) 20 Volts c) 10 Volts d) 5 Volts ______ 8.) If a third bulb is added to a circuit in parallel, the brightness of the original two
bulbs will a) increase b) decrease c) remain the same ______ 9.) If one of the light bulbs should burn out, the other two bulbs will a) dim b) become brighter c) go out d) remain the same
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Assignment #12C: Parallel Circuits Problems 1. A battery of 24 volts is connected to a circuit as shown at the right. Determine each of the following:
a) The equivalent resistance of the 4 ohm and 8 ohm resistors.
b) The equivalent resistance of the 4 ohm and 8 ohm resistors plus the 12 ohm resistor. c) The total resistance of the circuit d) The current in the 6 ohm resistor. e) The rate at which energy is dissipated (POWER) in the 12 ohm resistor.
6
4
8
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2. Three resistors are arranged in a circuit as shown. The battery has an unknown but constant voltage. Determine the potential difference across resistor R1. . 3. Determine the resistance of R1
R1 = 10
R3 = 40
V = 100 volts
i = 4 a
R1 = ?
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Series and Parallel Summary! Voltage Rule: Around any closed loop in a circuit, the sum of potential differences (V) must equal the sum of the voltage supplied by the battery.
SERIES: Vtotal = V1 + V2 + V3 PARALLEL: Vtotal = V1 = V2
Current Rule: The total current entering any junction of wires must equal the total current leaving
SERIES: Itotal = I1 = I2 = I3 PARALLEL: Itotal = I1 + I2 + I3
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Topic #5: Electrical Power
Additional Resources:
Text Reference: p. 543 – 544
The Physics Classroom – http://www.physicsclassroom.com/Class/circuits/u9l3d.cfm
St. Mary’s Physics Online – http://www.stmary.ws/highschool/physics/home/notes/electricity/circuits/power/ElectricPower.htm
HippoCampus – Parts 1, 3, & 6 ONLY
http://www.montereyinstitute.org/courses/AP%20Physics%20B%20II/course%20files/multimedia/lesson35/lessonp.html
APlusPhysics Video Tutorial – http://aplusphysics.com/courses/regents/videos/EEnergyPower/EEnergyPower.html
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NOTES: Electrical Power
Power: Power is the that work is done or the at
which electrical energy is converted into other forms (such as mechanical energy, light, heat, etc.)
, then W _______ ….. since
since …..
, then V _______ ….. P _______ since
….. then
ON YOUR REFERENCE TABLES: Work: The amount of work done on an electrical component is the amount of electrical energy used (Remember the W-E theorem?!)
, then W If
Example Problems: 1. How much electrical energy is used when 120 Volt appliance operates at 2.0 A for 1.0
second?
2. If energy is used at a rate of 20 J/s in an electric circuit, how much power is developed?
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Assignment #13: Electric Power Problems 1.) How much time is required for an operating 100 watt light bulb to dissipate 10 Joules of electrical
energy?
a) 1 sec b) 0.1 sec c) 10 sec d) 1000 sec
2.) While operating at 120 Volts, an electric toaster has a resistance of 15 ohms. The power used by the toaster is
a) 8 W b) 120 W c) 960 W d) 1800 W
3.) An electric clothes dryer consumes 6 x 106 J of energy while operating at 220 volts for 30 minutes. During operation, the dryer draws a current of
a) 10 Amps b) 15 Amps c) 20 Amps d) 25 Amps
4.) What is the approximate amount of electrical energy needed to operate a 1600 Watt toaster for 60 seconds?
a) 27 J b) 1500 J c) 1700 J d) 96,000 J
5.) Electric power is measured in
a) Volts b) Joules/sec c) Coulombs/sec d) Joules/ Coulomb
6.) Electric power can be calculated by
a) IV b) V2/R c) I2R d) all of the above
7.) Electric energy is measured in
a) Joules b) Watts c) Coulombs d) Ohms
8.) Electric energy can be calculated by
a) Pt b) VIt c) I2Rt d) all of the above
9.) A potential difference of 60 V is applied across a 15 ohm resistor. What is the power dissipated in the resistor?
a) 240 J b) 240 W c) 2.4 W d) 12 W
10.) A current of 0.4 amps is measured in a 150 ohm resistor. How much energy is expended by the resistor in 30 seconds?
a) 72 J b) 240 J c) 600 J d) 720 J
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Base your answers to the following questions on the diagram below. Show all work! 1.) What is the current reading in ammeter A1? 2.) Determine the power developed in resistor R2 alone.
3.) Determine the power developed in resistor R1 alone. 4.) How much electric energy is used by the 30 ohm resistor in 10 minutes? 5.) What would happen to the current in ammeter A2 if resistor R1 was removed? Explain. 6.) Given the following information for a radio:
P = 12 W Used for 30 min V = 120 V Cost of energy is 7 cents ( 0.07 $) per kilowatt-hour Calculate:
a) the current through the radio:
b) the amount of energy used (in kilowatt-hours)
c) the cost of your listening pleasure
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Assignment #14: Circuit Simulation – Review 1. Open up Internet Explorer and navigate to:
http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc
2. Click on “Run Now!”
3. Using four light bulbs and four batteries as well as a switch and as many wires as you need, build a circuit similar to used for Holiday lights, where one bulb burning out causes all bulbs to fail. Draw the schematic below (show resistors for light bulbs)
4. What type of circuit is this? _____________________ (series/parallel) 5. Add the Ammeter to the circuit. How much current is flowing through each of the light bulbs (L)? L1 : ________ L2 : ________ L3 : ________ L4 : ________ 6. What do you notice about the currents across each light bulb? ________________________ 7. Apply the Voltmeter across all four batteries. How much voltage is being applied to the entire circuit? __________________ 8. Apply the Voltmeter across each of the light bulbs. How much Voltage is dropped across each? L1 : ________ L2 : ________ L3 : ________ L4 : ________ 9. How does your answer for question #7 compare to the sum of your answers for question #8? 10. How much power is being dissipated by each of the light bulbs? Show all work: L1 : ________
L2 : ________
L3 : ________
L4 : ________
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11. Using four light bulbs and four batteries, and as many wires and resistors as required, design a circuit such that when one bulb goes out, the other three bulbs continue to function. Draw the schematic below (show resistors for light bulbs)
12. What type of circuit is this? _____________________ (series/parallel) 13. Add the Ammeter to the beginning of the circuit (next to the batteries). How much current is being delivered into the entire circuit? __________________ 14. Add the Ammeter to the circuit. How much current is flowing through each of the light bulbs (L)? L1 : ________ L2 : ________ L3 : ________ L4 : ________ 15. How does your answer for question #13 compare to the sum of your answers for question #14? 16. Apply the Voltmeter across all four batteries. How much voltage is being applied to the entire circuit? __________________ 17. Apply the Voltmeter across each of the light bulbs. How much Voltage is dropped across each? L1 : ________ L2 : ________ L3 : ________ L4 : ________ 18. What do you notice about the voltage drop across each light bulb? ________________________ 19. How does your answer to question #16 compare to you answer to question #17? _____________ 20. How much power is being dissipated by each of the light bulbs? Show all work:
L1 : ________
L2 : ________
L3 : ________
L4 : ________
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21. Using four light bulbs and four batteries, design a circuit such that each light bulb has a different
brightness. Draw the circuit schematic below. Indicate which bulb is the brightest, the dimmest, etc.
22. You have thirteen batteries in a single circuit and one light bulb. There are no resistors or anything to calm the flow of energy (amps). What will the circuit ultimately do? Build it and see. Explain below. 23. Now experiment with different resistors and/or light bulbs to see how many ohms it takes to calm the thirteen batteries it takes. Record what it took and explain how certain variables effect flow of energy.
24. Build a smaller circuit (2 or 3 batteries with one light bulb is big enough). Click on the “Advanced” Settings in the bottom right corner. Describe how the brightness of the bulb changes as the “Wire Resistivity” is changed from “Almost none” to “lots”. [Resistivity is our next topic!]
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Assignment #15: Graphing & Current Electricity 1.) The graph to the right shows the relationship between the
potential difference across a metallic conductor and the electric current through the conductor at constant temperature T1.
Which graph best represents the relationship between potential difference and current for the same conductor maintained at a higher constant temperature, T2?
2.) A long copper wire was connected to a voltage source. The voltage was varied and the
current through the wire measured, while temperature was held constant. The collected data are represented by the graph below.
Using the graph, the resistance of the copper wire is approximately
(1) 8.0 Ω (2) 25 Ω (3) 30 Ω (4) 2.5 Ω
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3.) A variable resistor was connected to a battery. As the resistance was adjusted, the current and power in the circuit were determined. The data are recorded in the table below.
Using the information in the data table, construct a line graph on the grid provided, following the directions below.
a.) Plot the data points for power versus current.
b.) Draw the best-fit line.
c.) Using your graph, determine the power delivered to the circuit at a current of 3.5 amperes. d.) Calculate the slope of the graph. [Show all calculations, including the equation and substitution
with units.] e.) What is the physical significance of the slope of the graph?
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4.) An experiment was performed using various lengths of a conductor of uniform crosssectional area. The resistance of each length was measured and the data recorded in the table below.
Using the information in the data table, construct a graph on the grid provided following the directions below.
a.) Mark an appropriate scale on the axis labeled “Length (m).”
b.) Plot the data points for resistance versus length.
c.) Draw the best-fit line.
d.) Calculate the slope of the best-fit line. [Show all work, including the equation and substitution with units.]
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Assignment #16: Regents Current Electricity Problems 1.) Which is a vector quantity?
(1) electric charge (3) electric potential difference (2) electric field strength (4) electric resistance
2.) If 60. joules of work is required to move 5.0 coulombs of charge between two points in an electric
field, what is the potential difference between these points? (1) 5.0 V (2) 12 V (3) 60. V (4) 300 V
3.) The diagram below represents a simple circuit consisting of a variable resistor, a battery, an
ammeter, and a voltmeter.
What is the effect of increasing the resistance of the variable resistor from 1000 Ω to 10000 Ω? [Assume constant temperature.] (1) The ammeter reading decreases. (3) The voltmeter reading decreases. (2) The ammeter reading increases. (4) The voltmeter reading increases.
4.) In the diagram below, P is a point near a negatively charged sphere.
Which vector best represents the direction of the electric field at point P?
5.) Which quantity and unit are correctly paired?
(1) resistivity and m
(3) current and C•s
(2) potential difference and eV (4) electric field strength and C
N
6.) The current through a 10.-ohm resistor is 1.2 amperes. What is the potential difference across the
resistor? (1) 8.3 V (2) 12 V (3) 14 V (4) 120 V
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7.) A copper wire of length L and cross-sectional area A has resistance R. A second copper wire at the same temperature has a length of 2L and a cross-sectional area of ½ A. What is the resistance of the second copper wire? (1) R (2) 2R (3) ½ R (4) 4R
8.) A 6.0-ohm lamp requires 0.25 ampere of current to operate. In which circuit below would the lamp
operate correctly when switch S is closed?
9.) What is the total current in a circuit consisting of six operating 100-watt lamps connected in
parallel to a 120-volt source? (1) 5 A (2) 20 A (3) 600 A (4) 12 000 A
10.) An electric circuit contains a variable resistor connected to a source of constant potential
difference. Which graph best represents the relationship between current and resistance in this circuit?
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11.) In the circuit diagram below, two 4.0-ohm resistors are connected to a 16-volt battery as shown.
The rate at which electrical energy is expended in this circuit is (1) 8.0 W (2) 16 W (3) 32 W (4) 64 W
Base your answers to questions 12 through 14 on the diagram below, which represents an electric circuit consisting of four resistors and a 12-volt battery.
12.) What is the current measured by ammeter A?
(1) 0.50 A (2) 2.0 A (3) 72 A (4) 4.0 A
13.) What is the equivalent resistance of this circuit? (1) 72 Ω (2) 18 Ω (3) 3.0 Ω (4) 0.33 Ω
14.) How much power is dissipated in the 36-ohm resistor? (1) 110 W (2) 48 W (3) 3.0 W (4) 4.0 W
15.) Calculate the resistance of a 1.00-kilometer length of nichrome wire with a cross-sectional area
of 3.50 x 10–6 meter2 at 20°C. [Show all work, including the equation and substitution with units.] 16.) A generator produces a 115-volt potential difference and a maximum of 20.0 amperes of current.
Calculate the total electrical energy the generator produces operating at maximum capacity for 60. seconds. [Show all work, including the equation and substitution with units.]
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Base your answers to questions 17 and 18 on the information below. The magnitude of the electric field strength between two oppositely charged parallel metal plates is 2.0 x103 newtons per coulomb. Point P is located midway between the plates.
17.) On the diagram above, sketch at least five electric field lines to represent the field between the
two oppositely charged plates. [Draw an arrowhead on each field line to show the proper direction.]
18.) An electron is located at point P between the plates. Calculate the magnitude of the force
exerted on the electron by the electric field. [Show all work, including the equation and substitution with units.]
19.) An electric circuit contains a source of potential difference and 5-ohm resistors that combine to
give the circuit an equivalent resistance of 15 ohms. In the space provided below, draw a diagram of this circuit using circuit symbols given in the Reference Tables for Physical Setting/Physics. [Assume the availability of any number of 5-ohm resistors and wires of negligible resistance.]
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Base your answers to questions 20 through 22 on the information and diagram below. A 50.-ohm resistor, an unknown resistor R, a 120-volt source, and an ammeter are connected in a complete circuit. The ammeter reads 0.50 ampere.
20.) Calculate the equivalent resistance of the circuit. [Show all work, including the equation and
substitution with units.] 21.) Determine the resistance of resistor R. 22.) Calculate the power dissipated by the 50.-ohm resistor. [Show all work, including the equation
and substitution with units.]