Download Electricity Homework Packet NA

Unit 9. Electrostatic Forces and Circuits
Name:______________________________
Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have
internal structure.
Essential Knowledge 1.B.1: Electric charge is
conserved. The net charge of a system is equal
to the sum of the charges of all the objects in
the system.
a. An electrical current is a movement of
charge through a conductor.
b. A circuit is a closed loop of electrical
current.
Learning Objective (1.B.1.1):
The student is able to make claims about natural phenomena
based on conservation of electric charge.
Learning Objective (1.B.1.2):
The student is able to make predictions, using the conservation
of electric charge, about the sign and relative quantity of net
charge of objects or systems after various charging processes,
including conservation of charge in simple circuits.
Essential Knowledge 1.B.2: There are only two kinds of electric
Learning Objective (1.B.2.1):
charge. Neutral objects or systems contain equal quantities of
The student is able to construct an
positive and negative charge, with the exception of some
explanation of the two-charge model of
fundamental particles that have no electric charge.
electric charge based on evidence produced
a. Like-charged objects and systems repel, and unlike charged
through scientific practices.
objects and systems attract.
Essential Knowledge 1.B.3: The smallest observed unit of charge
Learning Objective (1.B.3.1):
that can be isolated is the electron charge, also known as the
The student is able to challenge the claim
elementary charge.
that an electric charge smaller than the
a. The magnitude of the elementary charge is equal to 1.6 x1019
elementary charge has been isolated.
coulombs.
b. Electrons have a negative elementary charge; protons have a
positive elementary charge of equal magnitude, although the mass of
a proton is much larger than the mass of an electron.
Big Idea 3: The interactions of an object with other objects can be described by forces.
Essential Knowledge 3.C.2: Electric force results from the
interaction of one object that has an electric charge with another
object that has an electric charge.
a. Electric forces dominate the properties of the objects in our
everyday experiences. However, the large number of particle
interactions that occur make it more convenient to treat everyday
forces in terms of nonfundamental forces called contact forces, such
as normal force, friction, and tension.
b. Electric forces may be attractive or repulsive, depending upon the
charges on the objects involved.
Learning Objective (3.C.2.1):
The student is able to use Coulomb’s law
qualitatively and quantitatively to make
predictions about the interaction between
two electric point charges.
Learning Objective (3.C.2.2):
The student is able to connect the concepts
of gravitational force and electric force to
compare similarities and differences
between the forces.
Big Idea 5: Changes that occur as a result of interactions are constrained by conservation laws.
Essential Knowledge 5.B.9: Kirchhoff’s loop
rule describes conservation of energy in
electrical circuits.
a. Energy changes in simple electrical circuits
are conveniently represented in terms of energy
change per charge moving through a battery and
a resistor.
b. Since electric potential difference times
charge is energy, and energy is conserved, the
sum of the potential differences about any
closed loop must add to zero.
c. The electric potential difference across a
Learning Objective (5.B.9.1):
The student is able to construct or interpret a graph of the
energy changes within an electrical circuit with only a single
battery and resistors in series and/or in, at most, one parallel
branch as an application of the conservation of energy
(Kirchhoff’s loop rule).
Learning Objective (5.B.9.2):
The student is able to apply conservation of energy concepts to
the design of an experiment that will demonstrate the validity of
Kirchhoff’s loop rule (V 0) in a circuit with only a battery
and resistors either in series or in, at most, one pair of parallel
branches.
Proficient
Unit 9. Electrostatic Forces and Circuits
resistor is given by the product of the current
and the resistance.
d. The rate at which energy is transferred from a
resistor is equal to the product of the electric
potential difference across the resistor and the
current through the resistor
Essential Knowledge 5.C.3:
Kirchhoff’s junction rule
describes the conservation of
electric charge in electrical
circuits. Since charge is
conserved, current must be
conserved at each junction in
the circuit. Examples should
include circuits that combine
resistors in series and
parallel
Name:______________________________
Learning Objective (5.B.9.3):
The student is able to apply conservation of energy (Kirchhoff’s
loop rule) in calculations involving the total electric potential
difference for complete circuit loops with only a single battery
and resistors in series and/or in, at most, one parallel branch.
Learning Objective (5.C.3.1):
The student is able to apply conservation of electric charge (Kirchhoff’s junction
rule) to the comparison of electric current in various segments of an electrical
circuit with a single battery and resistors in series and in, at most, one parallel
branch and predict how those values would change if configurations of the circuit
are changed.
Learning Objective (5.C.3.2):
The student is able to design an investigation of an electrical circuit with one or
more resistors in which evidence of conservation of electric charge can be
collected and analyzed.
Learning Objective (5.C.3.3):
The student is able to use a description or schematic diagram of an electrical circuit
to calculate unknown values of current in various segments or branches of the
circuit.
Electrostatics Reading Assignment:
Read Chapter 20 sections 1 – 3 (the rest of the chapter and chapter 21 is HIGHLY recommended reading if you will
continue in future physics class but not required for AP Physics 1)
As you read answer all Stop to Think questions (Check your answers on page 664) and work through all example
problems. Below is a list of what you need to take away from your reading.
1. Define:
a. conductor and insulator
b. charge conservation
c. electrostatic equilibrium
d. electrically neutral
e. electric force
f.
Coulomb’s Law
2. Know:
a. the direction of electric forces for objects with like charge, unlike charge
b. the magnitude of charge on an electron, proton
c. the unit for charge
d. why metals are conductors
e. the equation for Coulomb’s law in terms of magnitude and direction
3. Be able to:
a. explain what happens to the negative charges in a conductor when a positively charged object is held nearby.
b. explain what happens to the negative charges in an insulator when a positively charged object is held nearby.
c. how objects acquire a positive charge if the protons are fixed in the nucleus of the atoms.
Unit 9. Electrostatic Forces and Circuits
Name:______________________________
d. in terms of forces, why the glass bead accelerates up toward the plastic bead in example 20.5.
Circuits Reading Assignment:
Read Chapter 22 (all sections) and Chapter 23 sections 1 – 5. As you read answer all Stop to Think questions (Check
your answers on page 726, 763) and work through all example problems. Below is a list of what you need to take
away from your reading.
1. Define/Know
a. electric current
b. direction of current
c. junction
d. emf
e. resistance (& units)
f. resistivity
g. ohm’s law
h.
i.
j.
k.
l.
m.
n.
terminal voltage
the meaning of symbols used in a circuit diagram
series connection
parallel connection
ammeter
voltmeter
kilowatt hour
2. Explain:
a. What creates current in a wire
b. why current entering a light bulb = current leaving a light bulb
c. The factors that affect resistance
d. what type of energy is dissipated at a resistor and why that results in a potential drop at a resistor
e. Kirchhoff’s Junction law
f. Kirchhoff’s loop law
g. what happens to the magnitude of current when it flows through a resistor
h. what happens to the magnitude of the potential when it flows through a resistor
i. why the bulbs are equally bright in example 23.2, but in figure 23.8 bulbs B&C are dimmer than bulb A.
j. why the bulbs in figure 23.5 are all equally bright
k. why batteries drain faster in a parallel circuit than in a series circuit
l. how a ammeter and voltmeter should be connected in a circuit
m. the steps for analyzing a complex circuit
3. Be able to:
a. calculate current (in terms of charge and time)
b. calculate current (in terms of voltage and current)
c. calculate resistance (in terms of voltage and current)
d. calculate resistance (in terms of resistivity, length and area)
e. calculate power
f. calculate the equivalent (total) resistance of series resistors
g. calculate the equivalent (total) resistance of parallel resistors
h. draw a circuit with an ammeter and voltmeter connected properly
i. analyze a complete circuit and solve for current, voltage and resistance at any point
j. calculate the equivalent (total) capacitance of series capacitors
k. calculate the equivalent (total) capacitance of parallel capacitors
Electrostatics Problems
1. Two lightweight balls hang straight down when both are neutral. They are close enough together
to interact, but not close enough to touch. Draw pictures showing how the balls hang if:
a. Both are touched with a plastic rod that was
rubbed with wool.
b. Ball A is touched by a plastic rod that was
rubbed with wool and ball B is touched by a
glass rod that was rubbed with silk.
c. Both are charged by a plastic rod, but ball A is
charged more than ball B.
d. Ball A is charged by a plastic rod. Ball B is
neutral.
2. After combing your hair briskly, the comb will pick up small pieces of paper.
a. Is the comb charged? How do you know?
b. How can you be sure that it isn’t the paper that is charged? Propose an experiment to test this.
c. Is your hair charged after being combed? What evidence do you have for your answer?
d. What kind of charge is the comb likely to have? Why?
3. A negatively charged electroscope has separated leaves.
a. Suppose you bring a negatively charged rod close to the top of the electroscope, but not
touching. How will the leaves respond? Use diagrams and words to explain.
b. How will the leaves respond if you bring a positive charged rod close to the top of the
electroscope, but not touching? Use both charge diagrams and words to explain.
Electrostatics Problems
4. Metal sphere A is initially neutral. A positively charges rod is brought near, but not touching.
Is a now positive, negative or neutral? Explain
5. Metal spheres A and B are initially neutral and are touching. A positively charged rod is
brought near A, but not touching. Is A now positive, negative, or neutral? Explain.
6. Metal sphere A is initially neutral. It is connected by a metal wire to the ground. A
positively charged rod is brought near, but not touching. Is A now positive, negative, or
neutral? Explain.
7. A lightweight, positively charged ball and a neutral metal rod hang by threads. They are
close but not touching. A positively charged rod is held close to, but not touching, the
hanging rod on the end opposite the ball.
a. Draw a picture of the final positions of the hanging rod and the ball. Explain your
reasoning.
b. Suppose the positively charged rod is replaced with a negatively charged rod. Draw a picture of the final
positions of the hanging rod and the ball. Explain your reasoning.
8. For each pair of charges, draw a force vector on each charge to show the electric force acting on that charge.
The length of each vector should be proportional to the magnitude of the force. Each + and – symbol
represents the same quantity of charge.
--
--
++
--
++
++
--
++
++
++
Electrostatics Problems
9. What change in the number electrons would give an object the following charge?
a. + 1 C?
b. – 2 μC
c. +8 μC
d. – 3.2 μC
10. A marble is given a charge of +2.1μC, and a super-ball is given a charge of -7.0 μC. When they are separated by
52 mm, what is the electrical force between them?
11. In a Coulomb style experiment 2 pith balls of the same mass are given equal but opposite charges of 0.014 μC.
When separated by a distance of 10-cm, what is the electrical force between them?
12. A charge of 15.5 C is placed 12.8 cm from a second charge. If the force between the charges is 22.5 N, what
is the magnitude of the second charge?
13. A balloon is rubbed vigorously through someone’s hair, pulling electrons from the hair and depositing them
upon the balloon. If the balloon’s charge is -2.00-μC, what is the electrical force between the balloon and THE
person’s head when they are separated by a distance of 3.0-cm?
14. Find the distance (in cm) between 2 positively charged spheres (+56μC) if the electrical force between them is
186 N.
15. Two 25.0 g spheres are hanging from lightweight strings that are each 35.0 cm in length. Each has the
same charge. They repel each other and make an angle of 5.00 to the vertical.
a. Draw a free body diagram of each sphere below.
b. What is the magnitude of the charge on each sphere?
Electrostatics Problems
16. Two small objects, each with a charge of -4.0 nC, are held together by a 0.020 m length of insulating string as
shown in the diagram above. The objects are initially at rest on a horizontal, nonconducting frictionless surface.
The effect of gravity on each object due to the other is negligible.
(a) Calculate the tension in the string.
The masses of the objects are m1 = 0.030 kg and m2 = 0.060 kg. The string is now cut.
(c) Calculate the magnitude of the initial acceleration of each object.
(d) On the axes below, qualitatively sketch a graph of the acceleration a of the object of mass m2
versus the distance d between the objects after the string has been cut.
(e) Describe qualitatively what happens to the speeds of the objects as time increases, assuming that
the objects remain on the horizontal, nonconducting frictionless surface.
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
17. 7.45 x 1017 electrons take 0.810 seconds to flow past a point in the circuit. What is the current?
18. If the current in a circuit is 0.250 A, how many electrons are flowing past a set point in 0.155 second?
19. A wire carries a 4 A current. What is the current in a second wire that delivers twice as much charge in
half the time?
20. A hair dryer draws 1.12 A when plugged into a 120 V circuit. What is its resistance?
21. A light bulb has stamped upon it the following information, "60 W 120 V". How much current will flow
through the bulb?
22. A hot plate has an internal resistance of 22.0 . It operates on 120 V household AC electricity.
(a) How much current did it draw?
(b) How much power did it develop?
(c) If it operated for 15 minutes, how much heat did it develop (hint: work done by friction)?
(d) If a kWh costs 4.5 cents, how much did it cost to run the thing?
23. Is I2 greater than, less than or equal to I1? Explain.
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
24. All wires in this figure are made of the same material and have the same diameter.
Rank in order, from largest to smallest the currents I1 to I4
25. What is the size of the current in the fourth wire? Is the current into or out of
the junction? Explain.
26. What is the resistance of a copper wire, diameter of 1.50 mm and length 25.0 m? (cu = 1.72x10-8 Ωm)
27. You have a long wire with resistance R. You would like to have a wire of the same length but with a
resistance 2R. Should you (a) change to a wire of the same diameter but made of a material having twice
the reisistivity, or (b) change to a wire made of the same material but with half the diameter? Or will
either do? Explain.
28. Wire 1 and wire 2 are made of the same metal and are the same length. Wire 1 has twice the diameter and
half the voltage across its ends. What is the ratio of I1/I2?
29. A graph of current as a function of voltage is given for a
particular wire segment.
a. What is the resistance of the wire
b. Sketch and label on the same graph what I vs. V would
look like for a wire made of the same material but twice
as long as the wire in part a.
c. Sketch and label on the same graph what I vs. V would look like for a wire made of the same
material but with twice the cross-sectional area of the wire in part a.
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
30. Rank in order, from largest to smallest, the currents I1 to I 4 through these four resistors.
31. Two resistors of equal lengths are connected to a battery by ideal wires. The
resistors have the same radii but are made of different materials and have different
resistivity’s  with 1>2.
a. Is the current I1 in resistor 1 larger than, smaller than or the same as I2 in resistor
2? Explain.
b. Which of the two resistors dissipates the larger amount of power? Explain.
c. Is the voltage V1 across resistor 1 larger than, smaller than, or the same as V2 across resistor 2?
Explain.
32. Redraw the circuits below using standard circuit symbols with only right angle connections.
33. A flashlight bulb is connected between two 1.5 V batteries as shown. Does
the bulb light? Why or why not?
34. Current Iin flows into the three resistor connect togeher one after the other.
The graph shown the value of the voltage as a funciton of distance.
a. Is I out greater than, less than, or equal to Iin? Explain.
b. Rank in order, from largest to smallest, the three resistances R1, R2, and
R3 .
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
35. Examine this circuit.
a. Write the Kirchhoff’s Loop Rule equation for this circuit.
1
0
0
.0
5
0
.0
7
5
.0
b. What is the total current,
1
.2
0A
A
c. What is the voltage drop at each resistor?
V100
V50
V75
36. Draw a circuit for which the Kirchhoff loop rule equation is:
a. 6V - I1  2Ω - I1  4Ω = 0
b. 12 V - I1  4Ω = 12 V – I2  6Ω = 0
c. 9V – I1  8Ω – I2  3Ω = 9V – I1  8Ω- I3  3Ω = 0
25.0 
37. For the circuit to the right
a. Write the Kirchhoff’s Loop Rule equation.
12.0 V
b. Determine current through the circuit
15.0 
45.0 
35.0 
c. Determine the current that goes through each resistor
I25
I15
I45
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
I35
38. For the circuit on the right:
a. Write the Kirchhoff loop rule equation
b. Calculate the Voltage lost at the 4Ω and 2Ω resistor
in this circuit.
V4______
V2_______
c. On the graph of voltage vs. location in circuit, graph
the Voltage changes in the circuit.
39. For the circuit to the right:
a. Write the Kirchhoff loop rule equation.
b. Calculate the current in the circuit.
c. Calculate the voltage drop at each resistor
d. On the graph of voltage vs. location in circuit,
graph the Voltage changes in the circuit.
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
40. What is the equivalent resistance of each group of resistors?
41. A 60 W light bulb and a 100 W light bulb are placed one after the other in a circuit.
The battery’s emf is large enough that both bulbs are glowing. Which one glows more
brightly? Explain.
42. Bulbs A, B and C are identical. Rank in order, from most to least, the brightness of the
three bulbs. Explain.
43. Initially bulbs A and B are glowing. Then the switch is closed. What happens to each
bulb? Does it get brighter, stay the same, get dimmer or go out? Explain.
44. What happens to the light intensity of a set of identical lamps in series when you add an additional lamp? How
come?
45. What happens to the light intensity of a set of identical lamps in parallel when you add an additional
lamp? How come?
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
46. Fill out the table for the circuit diagramed at the right
Circuit
Position
R1
R2
R3
Total
Resistance
(Ω)
10.0
20.0
30.0
Voltage (V)
Current (A)
6.00
47. Fill out the table for the circuit diagramed at the right
Circuit
Position
R1
R2
R3
Total
Resistance
(Ω)
10.0
20.0
30.0
Voltage (V)
Current (A)
6.00
48. Fill out the table for the circuit diagramed at the right
Circuit
Position
R1
R2
R3
Total
Resistance
(Ω)
10.0
20.0
30.0
Voltage (V)
6.00
Current (A)
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
49. Light bulbs of fixed resistance 3.0  and 6.0 , a 9.0 V battery, and a switch S are connected as shown in the
schematic diagram above. The switch S is closed.
(a)
Calculate the current in bulb A.
(b)
Calculate the current in bulb B and bulb C.
(c) Which light bulb is brightest? Justify your answer by calculating the power for each bulb.
(c)
Switch S is then opened. By checking the appropriate spaces below, indicate whether the brightness of
each light bulb increases, decreases, or remains the same. Explain your reasoning for each light bulb.
i. Bulb A: The brightness
increases
decreases
remains the same
Explanation:
ii. Bulb B: The brightness
Explanation:
increases
decreases
remains the same
iii. Bulb C: The brightness
Explanation:
increases
decreases
remains the same
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
50. Two lightbulbs, one rated 30 W at 120 V and another rated 40 W at 120 V, are arranged in two different circuits.
(a) The two bulbs are first connected in parallel to a 120 V source.
i. Determine the resistance of the bulb rated 30 W and the current in it when it is connected in this
circuit.
ii. Determine the resistance of the bulb rated 40 W and the current in it when it is connected in this
circuit.
(b) The bulbs are now connected in series with each other and a 120 V source.
i. Determine the resistance of the bulb rated 30 W and the current in it when it is connected in this
circuit.
ii. Determine the resistance of the bulb rated 40 W and the current in it when it is connected in this
circuit.
(c) In the spaces below, number the bulbs in each situation described, in order of their brightness.
(1= brightest, 4 = dimmest)
__ 30 W bulb in the parallel circuit
__ 40 W bulb in the parallel circuit
__ 30 W bulb in the series circuit
__ 40 W bulb in the series circuit
(d) Calculate the total power dissipated by the two bulbs in each of the following cases.
i. The parallel circuit
ii. The series circuit
Current Worksheet Problems
It doesn't matter how much you want. What really matters is how much you want it. The extent and complexity of the problem does
not matter was much as does the willingness to solve it. -- Ralph Marston
51. The circuit above contains a battery with negligible internal resistance, a closed switch S, and three resistors, each
with a resistance of R or 2R.
(a)
(i) Rank the currents in the three resistors from greatest to least, with number 1 being greatest. If two
resistors have the same current, give them the same ranking.
_______IA
_______IB
_______IC
(ii) Justify your answers.
(b)
(i) Rank the voltages across the three resistors from greatest to least, with number 1 being greatest. If
two resistors have the same voltage across them, give them the same ranking.
_______VA
_______VB
_______VC
(ii) Justify your answers.
For parts (c) through (e), use ε = 12 V and R = 200 Ω, .
(c) Calculate the equivalent resistance of the circuit.
(d) Calculate the current in resistor RC.