chapter 17 electric current and resistanceroselleachs.sharpschool.net/userfiles/servers/... · 24...
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Chapter 17
Electric Current and
Resistance
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Units of Chapter 17
Batteries and Direct Current
Current and Drift Velocity
Resistance and Ohm’s Law
Electric Power
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17.1 Batteries and Direct Current
Electric current is the
flow of electric
charge. A battery is a
source of electric
energy—it converts
chemical energy into
electric energy.
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17.1 Batteries and Direct Current
In a complete circuit, electrons flow from the
negative electrode to the positive one.
The positive electrode is called the anode; the
negative electrode is the cathode.
A battery provides a constant source of
voltage—it maintains a constant potential
difference between its terminals.
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Question 17.1 Connect the Battery
Which is the correct way to
light the lightbulb with the
battery?
d) all are correct
e) none are correct
a) c)b)
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Current can flow only if there is a continuous connection from
the negative terminal through the bulb to the positive terminal.
This is the case for only Fig. (3).
Question 17.1 Connect the Battery
Which is the correct way to
light the lightbulb with the
battery?
d) all are correct
e) none are correct
a) c)b)
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17.1 Batteries and Direct Current
The potential difference
between the battery
terminals when the battery
is not connected to
anything is called the
electromotive force, emf.
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17.1 Batteries and Direct CurrentThe actual terminal voltage of the battery is
always less than the emf, due to internal
resistance. Usually the difference is very
small.
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17.1 Batteries and Direct Current
When batteries are
connected in
series, the total
voltage is the sum
of the individual
voltages.
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17.1 Batteries and Direct Current
When batteries of
equal voltage are
connected in parallel,
the total voltage does
not change; each
battery supplies part
of the total current.
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17.1 Batteries and Direct Current
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17.2 Current and Drift Velocity
Current is the time rate of flow of charge.
SI unit of current: the ampere, A
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17.2 Current and Drift Velocity
Historically, the direction of current has been
taken to be from positive to negative; this is
opposite to the way electrons flow. However,
this seldom matters.
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How long would it take for a net charge
of 2.7 C to pass a location in a wire if it
is to carry a steady current of 4.0 mA?
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17.2 Current and Drift Velocity
Electrons do not flow like water in a pipe. In
the absence of voltage, they move randomly
at high speeds, due to their temperature.
When a voltage is
applied, a very small
drift velocity is added
to the thermal
motion, typically
around 1 mm/s; this
is enough to yield the
observed current.
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17.3 Resistance and Ohm’s Law
If there is a potential difference across a
conductor, how much current flows?
The ratio between the voltage and the
current is called the resistance.
SI unit of resistance: the ohm, Ω
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17.3 Resistance and Ohm’s Law
An ohmic material is one whose resistance
is constant.
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17.3 Resistance and Ohm’s Law
Ohm’s law is valid only for ohmic materials:
The resistance of a
particular object
depends on its
length, cross-
sectional area,
material, and
temperature.
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17.3 Resistance and Ohm’s Law
As expected, the resistance is proportional
to the length and inversely proportional to
the cross-sectional area:
The constant ρ is called the resistivity,
and is characteristic of the material.
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a) Ohm’s law is obeyed since the
current still increases when V
increases
b) Ohm’s law is not obeyed
c) this has nothing to do with Ohm’s
law
Question 17.2 Ohm’s Law
You double the voltage
across a certain conductor
and you observe the current
increases three times. What
can you conclude?
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a) Ohm’s law is obeyed since the
current still increases when V
increases
b) Ohm’s law is not obeyed
c) this has nothing to do with Ohm’s
law
Ohm’s law, V = IR, states that the
relationship between voltage and
current is linear. Thus, for a conductor
that obeys Ohm’s law, the current must
double when you double the voltage.
Question 17.2 Ohm’s Law
You double the voltage
across a certain conductor
and you observe the current
increases three times. What
can you conclude?
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Question 17.3a Wires I
Two wires, A and B, are made of the
same metal and have equal length,
but the resistance of wire A is four
times the resistance of wire B. How
do their diameters compare?
a) dA = 4dB
b) dA = 2dB
c) dA = dB
d) dA = 1/2dB
e) dA = 1/4dB
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The resistance of wire A is greater because its area is less than
wire B. Since area is related to radius (or diameter) squared, the
diameter of A must be two times less than the diameter of B.
Question 17.3a Wires I
R ρA
,
Two wires, A and B, are made of the
same metal and have equal length,
but the resistance of wire A is four
times the resistance of wire B. How
do their diameters compare?
a) dA = 4dB
b) dA = 2dB
c) dA = dB
d) dA = 1/2dB
e) dA = 1/4dB
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Question 17.3b Wires II
A wire of resistance R is
stretched uniformly (keeping its
volume constant) until it is twice
its original length. What happens
to the resistance?
a) it decreases by a factor of 4
b) it decreases by a factor of 2
c) it stays the same
d) it increases by a factor of 2
e) it increases by a factor of 4
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Keeping the volume (= area x length) constant means
that if the length is doubled, the area is halved.
Since , this increases the resistance by a
factor of 4.
Question 17.3b Wires II
RA
,
A wire of resistance R is
stretched uniformly (keeping its
volume constant) until it is twice
its original length. What happens
to the resistance?
a) it decreases by a factor of 4
b) it decreases by a factor of 2
c) it stays the same
d) it increases by a factor of 2
e) it increases by a factor of 4
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17.3 Resistance and Ohm’s LawIn this table, you can easily see the
differences between the resistivities of
conductors, semiconductors, and insulators.
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17.3 Resistance and Ohm’s Law
For many materials, the temperature
dependence of the resistivity is approximately
linear, as long as the temperature change is
not too large.
The constant α is called the temperature
coefficient of resistivity. Some values of α
are listed in the table on the previous page.
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17.3 Resistance and Ohm’s Law
Some materials exhibit a curious
phenomenon: at a very low temperature called
the critical temperature, their resistivity drops
abruptly to zero.
These are called superconductors; they have
a number of unique properties. They are
impractical for everyday home use, however,
as they must be cooled to cryogenic
temperatures.
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17.4 Electric Power
Power, as usual, is the rate at which work is
done. For work done by electricity:
Rewriting,
For ohmic materials, we can write:
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17.4 Electric Power
So, where does this power go? It is changed
to heat in resistive materials.
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Question 17.4 Dimmer
When you rotate the knob of a
light dimmer, what is being
changed in the electric circuit?
a) the power
b) the current
c) the voltage
d) both a) and b)
e) both b) and c)
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The voltage is provided at 120 V from the
outside. The light dimmer increases the
resistance and therefore decreases the current
that flows through the lightbulb.
Question 17.4 Dimmer
When you rotate the knob of a
light dimmer, what is being
changed in the electric circuit?
a) the power
b) the current
c) the voltage
d) both a) and b)
e) both b) and c)
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17.4 Electric Power
Electric appliances
are rated in watts,
assuming standard
household voltage.
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Question 17.5a Lightbulbs
Two lightbulbs operate at 120 V, but
one has a power rating of 25 W while
the other has a power rating of 100 W.
Which one has the greater
resistance?
a) the 25 W bulb
b) the 100 W bulb
c) both have the same
d) this has nothing to do
with resistance
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Since P = V2 / R , the bulb with the lower
power rating has to have the higher
resistance.
Question 17.5a Lightbulbs
Two lightbulbs operate at 120 V, but
one has a power rating of 25 W while
the other has a power rating of 100 W.
Which one has the greater
resistance?
a) the 25 W bulb
b) the 100 W bulb
c) both have the same
d) this has nothing to do
with resistance
Follow-up: Which one carries the greater current?
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17.4 Electric Power
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17.4 Electric Power
The electric company
typically bills us for
kilowatt-hours (kWh),
a unit of energy.
We can reduce our
energy usage by buying
efficient appliances.
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Question 17.5b Space Heaters
Two space heaters in your living
room are operated at 120 V.
Heater 1 has twice the resistance
of heater 2. Which one will give
off more heat?
a) heater 1
b) heater 2
c) both equally
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Using P = V2 / R, the heater with the smaller resistance
will have the larger power output. Thus, heater 2 will
give off more heat.
Question 17.5b Space Heaters
Two space heaters in your living
room are operated at 120 V.
Heater 1 has twice the resistance
of heater 2. Which one will give
off more heat?
a) heater 1
b) heater 2
c) both equally
Follow-up: Which one carries the greater current?
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Review of Chapter 17
A battery produces emf; positive terminal is
the anode, negative is the cathode.
emf is measured in volts; it is the number of
joules the battery supplies per coulomb of
charge.
An electric current can exist only in a
complete circuit.
Resistance:
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Review of Chapter 17
Ohm’s law is obeyed if the resistance is
constant:
The resistance of an object depends on its
length, cross-sectional area, and
resistivity.
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Review of Chapter 17
Power is the rate at which work is done.
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To move 5.0 C of charge from one electrode to
the other, a 12-V battery must do how much
work?
60 W
5.0 C
12 J
60 J
12 V
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A car's starter motor draws 59 A from the
car's battery during startup.
If the startup time is 2.1 s, how many
electrons pass a given location in the circuit
during that time?
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How long does it take for a charge of
4.70 C to pass through the cross-
sectional area of a wire that is carrying
a current of 0.47 A?
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In a dental X-ray machine, the accelerated
electrons move to the east. The conventional
current in the machine is in what direction?
west
east
you can't tell from the data given
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Imagine that some protons are moving to the left
at the same time that some electrons are moving
to the right past the same location.
Part A: Will the net current be to the right, to the
left, zero, or none of the preceding?
A, to the right. B to the left. C. Zero. D. None of
the preceding
Part B. In 4.0 S, 6.9 C of electrons flow to the
right at the same time that 5.2 C of protons flow
to the left. What are the direction of the current
due to the protons?
to the left
to the right
Part C. What are the magnitude of the current
due to the protons?
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What is the emf of a battery with a 0.19 Ω
internal resistance if the battery delivers 1.5 A
to an externally connected 6.0 Ω resistor?
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If you double the voltage across a resistor while
at the same time cutting its resistance to one-
fourth its original value, what happens to the
current in the resistor?
it increases by 8 times
it increases by four times
it doubles
you can't tell from the data given
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A battery acquires and stores
A, energy.
B, charge & potential but not energy.
C, energy, charge, & potential.
D, potential.
E, charge.
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If you connect two identical storage batteries
together in series ("+" to "-"), and place them
in a circuit, the combination will provide
A, twice the voltage, and the same current
will flow through each.
B, zero volts.
C, the same voltage and the same current
will flow through each.
D, twice the voltage, and different currents
will flow through each.
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The resistivity of most common metals
A, remains constant over wide temperature
ranges.
B, increases as the temperature increases.
C, varies randomly as the temperature
increases.
D, decreases as the temperature increases.
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When charging a battery, the terminal voltage
is ________ the battery emf.
A, zero, as is
B, less than
C, more than
D, equal to
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During a research experiment on the
conduction of current in the human body, a
medical technician attaches one electrode to
the wrist and a second to the shoulder of a
patient.
If 120 mV is applied across the two
electrodes and the resulting current is 14.0
mA, what is the overall resistance of the
patient's arm?