Download Solutions: Chapter 8 Exercises 1. Excess electrons rubbed from your

Solutions: Chapter 8 Exercises
1. Excess electrons rubbed from your hair leave it with a positive charge; excess electrons on the
comb give it a negative charge.
2. Electrons are easily dislodged from the outer regions of atoms, but protons are held tightly
within the nucleus.
3. The law would be written no differently.
4. The electrons don’t fly out of the penny because they are attracted to the five thousand billion
positively charged protons in the atomic nuclei of atoms in the penny.
5. The forces they exert on each other are still the same! Newton’s third law applies to electrical
forces as well as all forces.
6. The inverse-square law is at play here. At half the distance the electric force field is four times
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as strong; at ⁄4 the distance, 16 times stronger. At four times the distance, one-sixteenth as
strong.
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7. At twice the distance the field strength will be ⁄4, in accord with the inverse-square law.
8. For both electricity and heat, the conduction is via electrons, which in a metal are loosely
bound, easy flowing, and easy to get moving. (Many fewer electrons in metals take part in heat
conduction than in electric conduction, however.)
9. 10 joules per coulomb is 10 volts. When released, its 10 joules of potential energy will become
10 joules of kinetic energy as it passes its starting point.
10. Voltage = 0.5 J0.0001 C = 5000 V.
11. As the current in the filament of a light bulb increases, the bulb glows brighter.
12. Your tutor is wrong. An ampere measures current, and a volt measures electric potential (a
sort of electric “pressure”). They are entirely different concepts; voltage produces amperes in a
conductor.
13. Only circuit number 5 is complete and will light the bulb. (Circuits 1 and 2 are “shortcircuits” and will quickly drain the cell of its energy. In circuit 3 both ends of the lamp filament
are connected to the same terminal and are therefore at the same potential. Only one end of the
lamp filament is connected to the cell in circuit 4.)
14. Current flows through electrical devices, just as water flows through a plumbing circuit of
pipes. If a water pump produces water pressure, water flows through both the pump and the
circuit. Likewise with electric current in an electric circuit. For example, in a simple circuit
consisting of a battery and a lamp, the electric current that flows in the lamp is the same electric
current that flows through the wires that connect the lamp and the same electric current that
flows through the battery. Current flows through these devices. (As a side point, it is common to
speak of electric current flowing in a circuit, but strictly speaking, it is electric charge that flows
in an electric circuit; the flow of charge is current. So if you want to be precisely correct
grammatically, say that current is in a circuit and charge flows in a circuit.)
15. An electric device does not “use up” electricity, but rather energy. And strictly speaking, it
doesn’t “use up” energy, but transforms it from one form to another. It is common to say that
energy is used up when it is transformed to less concentrated forms—when it is degraded.
Electrical energy ultimately becomes heat energy. In this sense it is used up.
16. A lie detector circuit relies on the likelihood that the resistivity of your body changes when
you tell a lie. Nervousness promotes perspiration, which lowers the body’s electrical resistance,
and increases whatever current flows. If a person is able to lie with no emotional change and no
change in perspiration, then such a lie detector will not be effective. (Better lying indicators
focus on the eyes.)
17. Most of the energy, typically 95%, of the electrical energy in an incandescent lamp goes
directly to heat. Thermal energy is the graveyard of electrical energy.
18. The thick filament has less resistance and will draw (carry) more current than a thin wire
connected across the same potential difference. (Important point: It is common to say that a
certain resistor “draws” a certain current, but this may be misleading. A resistor doesn’t “attract”
or “draw” current, just as a pipe in a plumbing circuit doesn’t “draw” water; it instead “allows”
or “provides for” the passage of current when an electrical pressure is established across it.)
19. Current will be greater in the bulb connected to the 220-volt source. Twice the voltage would
produce twice the current if the resistance of the filament remained the same. (In practice, the
greater current produces a higher temperature and greater resistance in the lamp filament, so the
current is greater than that produced by 110 volts, but appreciably less than twice as much for
220 volts. A bulb rated for 110 volts has a very short life when operated at 220 volts.)
20. Damage generally occurs by excess heating when too much current is driven through an
appliance. For an appliance that converts electrical energy directly to thermal energy this
happens when excess voltage is applied. So don’t connect a 110-volt iron, toaster, or electric
stove to a 220-volt circuit. Interestingly enough, if the appliance is an electric motor, then
applying too little voltage can result in overheating and burn up the motor windings. (This is
because the motor will spin at a low speed and the reverse “generator effect” will be small and
allow too great a current to flow in the motor.) So don’t connect a 220-volt power saw or any
220-volt motor-driven appliance to 110 volts. To be safe use the recommended voltages with
appliances of any kind.
21. In the first case the current passes through your chest; in the second case current passes only
through your arm. You can cut off your arm and survive, but you cannot survive without your
heart.
22. Electric power in your home is likely supplied at 60 hertz and 110-120 volts via electrical
outlets. This is ac (and delivered to your home via transformers between the power source and
your home. We will see in Chapter 9 that transformers require ac power for operation). Electric
power in your car must be able to be supplied by the battery. Since the + and – terminals of the
battery do not alternate, the current they produce does not alternate either. It flows in one
direction and is dc.
23. Auto headlights are wired in parallel. Then when one burns out, the other remains lit. If
you’ve ever seen an automobile with one burned out headlight, you have evidence they’re wired
in parallel.
24. (a) volt
(b) ampere
(c) joule
25. The equivalent resistance of resistors in series is their sum, so connect a pair of resistors in
series for more resistance.
26. The equivalent resistance of resistors in parallel is less than the smaller resistance of the two.
So connect a pair of resistors in parallel for less resistance.
27. Agree with your friend, for a battery provides a source of constant voltage. The current
through it depends on the resistance of the external circuit.
28. Agree with your friend, for in series, more resistances add to the circuit resistance. But in
parallel, the multiple paths provide less resistance (just as more lines at a checkout counter
lessens resistance to flow).
29. Zero. Power companies do not sell electrons; they sell energy. Whatever number of electrons
flow into a home, the same number flows out.
30. How quickly a lamp glows after an electrical switch is closed does not depend on the drift
velocity of the conduction electrons, but depends on the speed at which the electric field
propagates through the circuit—about the speed of light.
31. Bulbs will glow brighter when connected in parallel, for the voltage of the battery is
impressed across each bulb. When two identical bulbs are connected in series, half the voltage of
the battery is impressed across each bulb. The battery will run down faster when the bulbs are in
parallel.
32. The leaves, like the rest of the electroscope, acquire charge from the charged object and repel
each other because they both have the same sign of charge. The weight of the conducting gold
foil is so small that even tiny forces are clearly evident.
33. Cosmic rays produce ions in air, which offer a conducting path for the discharge of charged
objects. Cosmic-ray particles streaming downward through the atmosphere are attenuated by
radioactive decay and by absorption, so the radiation and the ionization are stronger at high
altitude than at low altitude. Charged objects more quickly lose their charge at higher altitudes.
34. The penny will be slightly more massive with a negative charge, for it will have more
electrons than when neutral. If it were positively charged, it would be slightly lighter because of
missing electrons.
35. The paint particles in the mist are polarized and are therefore attracted to the charged chassis.
36. The forces on the electron and proton will be equal in magnitude, but opposite in direction.
Because of the greater mass of the proton, its acceleration will be less than that of the electron,
and be in the direction of the electric field. How much less? Since the mass of the proton is
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nearly 2000 times that of the electron, its acceleration will be about ⁄2000 that of the electron.
The greater acceleration of the electron will be in the direction opposite to the electric field. The
electron and proton accelerate in opposite directions.
37. The cooling system of an automobile is a better analogy to an electric circuit because like an
electric system it is a closed system, and it contains a pump, analogous to the battery or other
voltage source in a circuit. The water hose does not re-circulate the water as the auto cooling
system does.
38. Yes, the statement is correct. After the initial charge of the battery is spent, recharging occurs
as the motor is run, and this energy comes from the fuel.
39. (a) The resistance will be half, 5 ohms, when cut in half.
(b) The resistance will be half again when the cross-sectional area is doubled, so it will be 2.5
ohms.
40. There is less resistance in the higher wattage lamp. Since power = current × voltage, more
power for the same voltage means more current. And by Ohm’s law, more current for the same
voltage means less resistance. (Algebraic manipulation of the equations P = IV and I = V/R leads
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to P = V /R.)
41. If the parallel wires are closer than the wingspan of birds, a bird could short circuit the wires
by contact with its wings, be killed in the process, and possibly interrupt the delivery of power.
42. Most of the electric energy in a lamp filament is transformed to heat. For low currents in the
bulb, the heat that is produced may be enough to feel but not enough to make the filament glow
red or white hot.
43. Bulb C is the brightest because the voltage across it equals that of the battery. Bulbs A and B
share the voltage of the parallel branch of the circuit and have half the current of bulb C
(assuming resistances are independent of voltages). If bulb A is unscrewed, the top branch is no
longer part of the circuit and current ceases in both A and B. They no longer give light, while
bulb C glows as before. If bulb C is instead unscrewed, then it goes out and bulbs A and B glow
as before.
44. As more bulbs are connected in series, more resistance is added to the single circuit path and
the resulting current produced by the battery is diminished. This is evident in the dimmer light
from the bulbs. On the other hand, when more bulbs are connected to the battery in parallel, the
brightness of the bulbs is practically unchanged. This is because each bulb in effect is connected
directly to the battery with no other bulbs in its electrical path to add to its resistance. Each bulb
has its own current path.
45. The three circuits are equivalent. Each branch is individually connected to the battery.
46. Yes, there will be a decrease in brightness if too many lamps are connected in parallel
because of the increased current that flows through the battery. Internal voltage drop increases
with current in the battery, which means reduced voltage supplied at its terminals to the circuit it
powers. (If the parallel circuit is powered by a stronger source such as the power utility provides
via common wall sockets, no dimming of bulbs will be seen as more and more parallel paths are
added.)
47. Current divides in a branch with more passing in the branch of lower resistance. But current
in a branch never reduces to zero unless the resistance of the branch become infinite. In a noninfinite resistor, a voltage across it will produce current in accord with Ohm’s law.
48. The 100-watt bulb has the thicker filament and lower resistance (more current through the
filament) so in series where the current is the same in each bulb, less energy is dissipated in
going through the lower resistance. This corresponds to lower voltage across the resistance—a
lower voltage drop. So the greater voltage drop is across the 60-watt bulb in series. Interestingly,
in series the 60-watt bulb is brighter than the 100-watt bulb! When connected in parallel, the
voltage across each bulb is the same, and the current is greater in the lower resistance 100-watt
bulb, which glows brighter than the 60-watt bulb.
Solutions: Chapter 8 Problems