Transcript Lecture_6

Chapter 25
Electric Currents and
Resistance
Copyright © 2009 Pearson Education, Inc.
25-7 Alternating Current
Current from a battery
flows steadily in one
direction (direct current,
DC). Current from a
power plant varies
sinusoidally (alternating
current, AC).
Copyright © 2009 Pearson Education, Inc.
25-7 Alternating Current
The voltage varies sinusoidally with time:
,,
as does the current:
Copyright © 2009 Pearson Education, Inc.
25-7 Alternating Current
Multiplying the current and the voltage gives
the power:
Copyright © 2009 Pearson Education, Inc.
25-7 Alternating Current
Usually we are interested in the average power:
.
Copyright © 2009 Pearson Education, Inc.
25-7 Alternating Current
The current and voltage both have average
values of zero, so we square them, take the
average, then take the square root, yielding the
root-mean-square (rms) value:
Copyright © 2009 Pearson Education, Inc.
25-7 Alternating Current
Example 25-13: Hair dryer.
(a) Calculate the resistance and the peak current
in a 1000-W hair dryer connected to a 120-V line.
(b) What happens if it is connected to a 240-V line
in Britain?
Copyright © 2009 Pearson Education, Inc.
25-8 Microscopic View of Electric
Current: Current Density and Drift
Velocity
Electrons in a conductor have large, random
speeds just due to their temperature. When a
potential difference is applied, the electrons
also acquire an average drift velocity, which is
generally considerably smaller than the
thermal velocity.
Copyright © 2009 Pearson Education, Inc.
25-8 Microscopic View of Electric
Current: Current Density and Drift
Velocity
We define the current density (current per
unit area) – this is a convenient concept
for relating the microscopic motions of
electrons to the macroscopic current:
If the current is not uniform:
.
Copyright © 2009 Pearson Education, Inc.
25-8 Microscopic View of Electric
Current: Current Density and Drift
Velocity
This drift speed is related to the current in the
wire, and also to the number of electrons per unit
volume:
and
Copyright © 2009 Pearson Education, Inc.
25-8 Microscopic View of Electric
Current: Current Density and Drift
Velocity
Example 25-14: Electron speeds in a wire.
A copper wire 3.2 mm in diameter carries a 5.0A current. Determine (a) the current density in
the wire, and (b) the drift velocity of the free
electrons. (c) Estimate the rms speed of
electrons assuming they behave like an ideal
gas at 20°C. Assume that one electron per Cu
atom is free to move (the others remain bound
to the atom).
Copyright © 2009 Pearson Education, Inc.
25-8 Microscopic View of Electric
Current: Current Density and Drift
Velocity
The electric field inside a current-carrying
wire can be found from the relationship
between the current, voltage, and resistance.
Writing R = ρ l/A, I = jA, and V = El , and
substituting in Ohm’s law gives:
Copyright © 2009 Pearson Education, Inc.
25-8 Microscopic View of Electric
Current: Current Density and Drift
Velocity
Example 25-15: Electric field inside a wire.
What is the electric field inside the wire of
Example 25–14? (The current density was
found to be 6.2 x 105 A/m2.)
Copyright © 2009 Pearson Education, Inc.
25-9 Superconductivity
In general, resistivity
decreases as
temperature decreases.
Some materials,
however, have
resistivity that falls
abruptly to zero at a
very low temperature,
called the critical
temperature, TC.
Copyright © 2009 Pearson Education, Inc.
25-9 Superconductivity
Experiments have shown that currents, once
started, can flow through these materials for
years without decreasing even without a
potential difference.
Critical temperatures are low; for many years no
material was found to be superconducting above
23 K.
Since 1987, new materials have been found that
are superconducting below 90 K, and work on
higher temperature superconductors is
continuing.
Copyright © 2009 Pearson Education, Inc.
Summary of Chapter 25
• A battery is a source of constant potential
difference.
• Electric current is the rate of flow of electric
charge.
• Conventional current is in the direction that
positive charge would flow.
• Resistance is the ratio of voltage to current:
Copyright © 2009 Pearson Education, Inc.
Summary of Chapter 25
• Ohmic materials have constant resistance,
independent of voltage.
• Resistance is determined by shape and
material:
• ρ is the resistivity.
Copyright © 2009 Pearson Education, Inc.
Summary of Chapter 25
• Power in an electric circuit:
• Direct current is constant.
• Alternating current varies sinusoidally:
Copyright © 2009 Pearson Education, Inc.
Summary of Chapter 25
• The average (rms) current and voltage:
• Relation between drift speed and current:
Copyright © 2009 Pearson Education, Inc.
Chapter 26
DC Circuits
Copyright © 2009 Pearson Education, Inc.
Units of Chapter 26
• EMF and Terminal Voltage
• Resistors in Series and in Parallel
• Kirchhoff’s Rules
• Series and Parallel EMFs; Battery Charging
• Circuits Containing Resistor and Capacitor
(RC Circuits)
• Electric Hazards
• Ammeters and Voltmeters
Copyright © 2009 Pearson Education, Inc.
26-1 EMF and Terminal Voltage
Electric circuit needs battery or generator to
produce current – these are called sources of
emf.
Battery is a nearly constant voltage source, but
does have a small internal resistance, which
reduces the actual voltage from the ideal emf:
Copyright © 2009 Pearson Education, Inc.
26-1 EMF and Terminal Voltage
This resistance behaves as though it were in
series with the emf.
Copyright © 2009 Pearson Education, Inc.
26-1 EMF and Terminal Voltage
Example 26-1: Battery with internal resistance.
A 65.0-Ω resistor is
connected to the
terminals of a battery
whose emf is 12.0 V and
whose internal
resistance is 0.5 Ω.
Calculate (a) the current
in the circuit, (b) the
terminal voltage of the
battery, Vab, and (c) the
power dissipated in the
resistor R and in the
battery’s internal resistance r.
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
A series connection has a single path from
the battery, through each circuit element in
turn, then back to the battery.
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
The current through each resistor is the
same; the voltage depends on the
resistance. The sum of the voltage
drops across the resistors equals the
battery voltage:
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
From this we get the equivalent resistance (that
single resistance that gives the same current in
the circuit):
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
A parallel connection splits the current; the
voltage across each resistor is the same:
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
The total current is the sum of the currents
across each resistor:
,
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
This gives the reciprocal of the equivalent
resistance:
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
An analogy using water
may be helpful in
visualizing parallel
circuits. The water
(current) splits into two
streams; each falls the
same height, and the total
current is the sum of the
two currents. With two
pipes open, the resistance
to water flow is half what
it is with one pipe open.
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
Conceptual Example 26-2: Series or parallel?
(a) The lightbulbs in the figure are identical.
Which configuration produces more light? (b)
Which way do you think the headlights of a car
are wired? Ignore change of filament resistance R
with current.
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
Conceptual Example 26-3: An illuminating surprise.
A 100-W, 120-V lightbulb and a 60-W, 120-V lightbulb
are connected in two different ways as shown. In each
case, which bulb glows more brightly? Ignore change
of filament resistance with current (and temperature).
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
Example 26-4: Circuit with series and
parallel resistors.
How much current is drawn from the
battery shown?
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
Example 26-5: Current in one branch.
What is the current through the 500-Ω resistor
shown? (Note: This is the same circuit as in the
previous problem.) The total current in the circuit
was found to be 17 mA.
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
Conceptual Example 26-6:
Bulb brightness in a circuit.
The circuit shown has
three identical lightbulbs,
each of resistance R.
(a) When switch S is
closed, how will the
brightness of bulbs
A and B compare with
that of bulb C? (b) What
happens when switch S is
opened? Use a minimum of
mathematics in your answers.
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
Example 26-7: A two-speed fan.
One way a multiple-speed ventilation fan for a
car can be designed is to put resistors in
series with the fan motor. The resistors
reduce the current through the motor and
make it run more slowly. Suppose the current
in the motor is 5.0 A when it is connected
directly across a 12-V battery. (a) What series
resistor should be used to reduce the current
to 2.0 A for low-speed operation? (b) What
power rating should the resistor have?
Copyright © 2009 Pearson Education, Inc.
26-2 Resistors in Series and in
Parallel
Example 26-8:
Analyzing a circuit.
A 9.0-V battery whose
internal resistance r is
0.50 Ω is connected in
the circuit shown. (a)
How much current is
drawn from the
battery? (b) What is
the terminal voltage of
the battery? (c) What
is the current in the
6.0-Ω resistor?
Copyright © 2009 Pearson Education, Inc.