Assignment
- Electricity
Reading Chapter Sections: 16: 1 – 6; 17: 1 – 2; 18:
1 – 10; 19: 1 – 11
Objectives/HW
|
|
The student will be able to: |
HW: |
|
1 |
Relate electrical phenomena to the motion and position
of the fundamental charge found on electrons and protons and recognize the
Coulomb as the SI unit of charge and e as the elementary quantum of
charge. |
1
– 8 |
|
2 |
State and apply Coulomb’s Law to solve
problems relating force, charge, and distance. |
9
– 14 |
|
3 |
Define electric potential and the Volt and
solve problems relating electric potential to charge and work or energy. |
15
– 19 |
|
4 |
Define electric current and the Ampere and
solve problems relating current to charge and time. |
20
|
|
5 |
Solve problems involving electric power. |
21
– 27 |
|
6 |
Define resistance the Ohm and solve problems
using Ohm’s Law to relate voltage, current, and resistance. |
28
– 40 |
|
7 |
Calculate the effective total resistance for multiple
resistors connected in series or parallel and analyze DC circuits consisting
of a combination of series and parallel branches of resistors and/or voltage
sources, determining voltage and current for each element. |
41
– 54 |
Homework Problems
1.
If you comb your hair on a dry day, your
hair may stand on end indicating that it has become electrically charged. Can the comb that you used remain
electrically neutral? Explain.
2.
As you walk across a rug electrons may be
removed from your shoes and deposited in the rug. Does the rug become positively or negatively
charged? What about your shoes?
3.
A positively charged rod is brought near
a neutral pith ball that is hanging from an insulating string. At first the pith ball is attracted to the
rod, but as soon as the two objects touch, the pith ball is repulsed from the
rod. (a)
Explain why the pith ball at first is attracted to the rod. (b) Explain why the
pith ball is repulsed from the rod after it is touched by the rod.
4.
Lightning usually occurs when negative
charge in a cloud is transported to Earth.
In the process the charge passes through the air, which is an insulator
and goes to the ground, which is a conductor.
If the Earth as a whole has a net charge of zero, explain what forces
make the charge leave the cloud, pass through the air, and go to the
ground.
5.
Compare and contrast Coulomb’s Law and
(a) In what ways are the two laws similar?
(b) In what ways are the two laws different?
6.
A certain pith ball is given a negative
electric charge. A metal rod that is
electrically neutral is brought near the charged pith ball but does not touch
it. It is observed that the pith ball is
attracted to the rod. Explain why this
happens.
7.
Suppose it is determined that a certain
pith ball has a charge of
– 4.00 ´
10-17 C. Of which are there
more in the pith ball, electrons or protons?
Determine how many more.
8.
How many coulombs of charge are on the
electrons in a nickel coin? Follow this
method to find the answer. (a) Find the
number of atoms in a nickel coin. A
nickel coin has a mass of 5.0 grams.
Each mole (6.02 ´
1023 atoms) has a mass of 58 grams.
(b) Find the number of electrons in the coin. Each nickel atom has 28 electrons. (c) Find how many coulombs of charge are on
the electrons. (d) Suppose this nickel
then obtains a net charge of + 2.0 nC. Explain this net charge as a surplus or
deficit of electrons and calculate how many.
(e) What percent of atoms would have gained or lost a single electron in
order for the nickel to get this net charge.
9.
Two negatively charged bodies with –5.0 ´ 10-5
C are 0.20 m from each other. What force
acts on each particle?
10. Two
identical positive charges exert a repulsive force of 6.4 nN
when separated by a distance of 0.38 nm.
Calculate the charge of each.
11. A
hydrogen atom consists of one proton, mass 1.67 ´
10-27 kg, orbited by one electron, mass 9.11 ´10-31
kg. The average distance between them is
5.3 ´ 10-11
m. The proton and electron have the same
amount of charge but opposite signs (±
e). (a) Determine the magnitude
of the electric force attracting one to the other. (b) Determine the magnitude of the
gravitational force attracting one to the other. (c) Which force is stronger and by what
factor? (And therefore is most
responsible for holding the electron in orbit about the proton)
(d) Determine the acceleration of the electron.
12. 
Three
charges are arranged in a line as shown in the diagram below. (a) Determine the net electric force on the
middle charge. (b) Determine the net
electric force on the left charge.
13. Four
charges are arranged in a square with sides equal to 10.0 cm. All four charges are equal to +2.5 nC. Determine the magnitude of electric force
acting on any one of these four charges due to the presence of the other three.
14. Two
pith balls, each with mass 0.50 grams, are attached to one another by a string
that is 20.0 cm long. The string is passed
over a very thin wire so that the two balls hang next to each other, just
touching. A rubber rod is used to
electrically charge the two pith balls, after which the two balls repel one
another. The pith balls reach an
equilibrium state of rest when their centers are 5.00 cm apart. Determine the electric charge on each pith
ball, assuming these values to be equal.
15. If
120 J of work are done to move one Coulomb of negative charge from a positive
plate to a negative plate, what voltage difference exists between the plates?
16. How
much work is done to transfer 0.15 C of charge through a potential difference
of 9.0 V?
17. An
electron is moved through a potential difference of 500 V. How much work is done on the electron?
18. A
12 V battery does 1200 J of work transferring charge. How much charge is transferred?
19. A
force of 0.053 N is required to move a charge of 37 mC a distance of
25 cm in an electric field. What is the
size of the potential difference between the two points?
20. How
many electrons flow past a point in a wire each second if the wire has a
current of 1.00 Amperes?
21. The
current through a toaster connected to a 120 V source is 8.0 A. What power is dissipated by the toaster?
22. A
current of 1.2 A flows through a light bulb when it is
connected across a 120 V source. What
power is dissipated by the bulb?
23. A
lamp draws 0.50 A from a 120 V generator.
(a) How much power does the generator deliver to the lamp? (b) How much electric energy does the lamp
convert to light and heat in a period of 5.0 minutes?
24. A
12 V automobile battery is connected to an electric starter motor. The current through the motor is 210 A. It takes 1.5 seconds to start the car’s
engine. (a) What is the power used by
the starter motor? (b) How much energy
is used to start the car? (c) How much
charge must pass through the starter motor (and through the battery) in order
to start the car?
25. A
4.0 kW clothes dryer is connected to a 220 V circuit. How much current does the dryer use?
26. A
flashlight bulb is connected across a 3.0 V power source. The current through the lamp is 1.5 A. (a) What is the power rating of the
lamp? (b) How much electric energy does
the lamp use in 11 minutes of operation?
27. A
60 W light bulb is connected to a voltage of 120 V and left on for 3.5
hours. The light bulb is 12%
efficient. (a) How much electric charge
passes through the bulb in this time period?
(b) How much light energy is given off by the bulb in this time
period? (c) How much heat energy is
given off by the bulb in this time period?
28. A
resistance of 60 W
has a current of 0.40 A through it when it is connected to the terminals of a
battery. What is the voltage of the
battery?
29. What
voltage must be applied to a 4.0 W
resistor if the current is to be 1.5 A?
30. What
voltage is placed across a motor of 15 W
operating resistance if the current through it is 8.0 A?
31. A
75 V battery is connected to a 15 W
resistor. (a) What is the current
through the resistor? (b) What is the
power output of the battery?
32. A
100 Watt light bulb operates on 120 Volts. Determine the resistance of the bulb.
33. A
12 V battery is connected to a certain device and it is observed that 24 mA current is drawn from the battery.
(a) Determine the resistance of the device.
(b) If the same device is connected to a 6.0 V battery how much current
will be drawn?
34. The
damage caused by electric shock depends on the current flowing through the body
– 1 mA can be felt; 5 mA is
painful. Above 15 mA,
a person loses muscle control, and 70 mA can be fatal. A person with dry skin has a resistance from
one arm to the other of about 100 kW. When skin is wet, the resistance drops to
about 5 kW. (a) What is the minimum voltage placed across
the arms that would produce a current that could be felt by a person with dry
skin?
(b) What current and what effect would the same voltage have if the person had
wet skin? (c) What would be the minimum
voltage that would produce a current that could be felt when the skin is wet?
35. A
certain lamp draws 66 mA when connected to a 6.0 V
battery and 75 mA when connected to a 9.0 V
battery.
(a) Show numerically whether or not this is an ohmic
device (i.e. show whether or not the resistance is constant).
(b) From 6.0 V to 9.0 V is a 50% increase in voltage. Determine the percent increase in power
output of the lamp.
36. (a)
Draw a schematic diagram to show a circuit that includes a 90 V battery,
an ammeter, and a resistance of 45 W
connected in series. Draw arrows showing
the direction of conventional current flow and label the positive and negative
terminals of the battery. (b) Determine
the reading of the ammeter.
37. (a)
Draw a series circuit diagram to include a 16 W
resistor, a battery, and an ammeter that reads 1.75 A. Draw arrow showing the direction of
conventional current flow and label the positive and negative terminals of the
battery. (b) Determine the voltage of
the battery.
38. A
220 W resistor is
rated 5.0 W. This is the maximum
allowable power for the resistor.
(a) Determine the maximum allowable current that can flow through this
resistor.
(b) Determine the maximum allowable voltage to which this resistor should be
connected.
39. A
certain wire in a household circuit has a resistance of 0.15 W and is
designed to carry up to 15 A of current.
(a) At its maximum current, what power is dissipated by the wire’s
resistance? (b) How much heat does the
wire give off in 10.0 minutes at its maximum capacity? (c) What is the electric potential difference
from one end of the wire to the other when operated at its maximum capacity? (This is how much the voltage “drops” from
its original value due to resistance of the wire.)
40. A
transistor radio operates by means of a 9.0 V battery that supplies it with a 50
mA current.
The cost of the battery is $0.90 and it will run the radio for 300
hours before going dead.
(a) What is the cost per kW-hr to operate the radio using the battery? (1 kW-hr is equal to 3.6 MJ) (b) The same radio, by means of a converter,
is plugged into a household circuit by a homeowner who pays $0.080 per kW-hr. What does it now cost to operate the radio
for 300 hours?
41. Why
does the equivalent resistance decrease as more resistors are added to a
parallel circuit?
42. Give
at least two reasons why household wiring is done in parallel instead of in
series.
43. (a)
Why should an ammeter have a very low resistance? (b) Why should a voltmeter have a very high
resistance?
44. Suppose
you have two “D” cells and wish to use them to power a light bulb. The two batteries can either be connected in
series or in parallel. (a) In order to
achieve maximum voltage, how should the cells be connected? Explain.
(b) In order to achieve maximum power, how should the cells be
connected? Explain. (c) In order to last longest before
going dead, how should the cells be connected?
Explain. (d) How many times
longer will the cells last when connected this way versus the other? Explain.
45. For
each part of this question, write the form of circuit that applies: series or parallel.
(a) The current is the same for each element in the circuit. (b) The voltage is the same for each element
in the circuit.
(c) The total resistance is equal to the sum of the individual
resistances. (d) Adding a resistor
decreases the total resistance.
46. A
20.0 W lamp and a
5.00 W lamp are
connected in series and placed across a potential difference of 50.0 V.
(a) Determine the equivalent resistance of the two lamps. (b) Determine the current delivered by the
power source.
(c) Determine the voltage across each lamp.
(d) Determine the power output of each lamp.
47. Three
identical lamps are connected in series to a 6.0 V battery. What is the voltage drop across each lamp?
48. The
load across a 12 V battery consists of a series combination of three resistors
of 15 W,
21 W, and 24 W. Determine the current in the circuit.
49. A
current of 0.10 A flows in a series circuit consisting of a battery and two
resistors: 15 W and 45 W. Determine the electric
potential of the battery.
50. An
electric potential of 5.0 V is required to run certain computer chips. A 6.0 V battery may be used to do this but it
must be connect to two resistors in series.
Supposing one has a resistance of 330 W
what should the other be? (The computer
chip will be driven by the voltage across only one of the two resistors.)
51. Three
identical lamps are connected in parallel to each other and then connected to a
6.0 V battery. What is the voltage drop
across each lamp?
52. A
40.0 V power source, a resistor of 16.0 W, and a
resistor of 20.0 W
are all connected in a parallel circuit.
(a) Determine the equivalent resistance of the two resistors. (b) Determine the current supplied by the
power source. (c) Determine the power
dissipated by each resistor.
53. 
Consider
the circuit shown below. (a) Determine
the current reading of the ammeter.
(b) Determine the voltage reading of the voltmeter. (c) Determine the power dissipated by the 500
W resistor.
54. 
Consider
the circuit shown below. (a) Determine
the current reading of the ammeter.
(b) Determine the voltage reading of the voltmeter. (c) Determine the power dissipated by the
45.0 W resistor.
Selected Answers