Transcript Lecture_7

Chapter 24
Capacitance, Dielectrics, Electric
Energy Storage
Recap:
Q  CV
C pp 
C para
1
C series
0 A
d
 C1  C 2 
1
1



C1 C 2
(all capacitors same V)
(all capacitors same Q)
1 Q2 1
1
2
UE 
 CV  QV
2 C 2
2
0E2
uE 
2 0
C K  KC 0
ConcepTest 24.3c
How does the charge Q1 on the first
Capacitors III
1) Q1 = Q2
2) Q1 > Q2
capacitor (C1) compare to the
charge Q2 on the second capacitor
3) Q1 < Q2
(C2)?
4) all charges are zero
C2 = 1.0 mF
10 V
C1 = 1.0 mF
C3 = 1.0 mF
ConcepTest 24.3c
How does the charge Q1 on the first
Capacitors III
1) Q1 = Q2
2) Q1 > Q2
capacitor (C1) compare to the
charge Q2 on the second capacitor
3) Q1 < Q2
(C2)?
4) all charges are zero
We already know that the
C2 = 1.0 mF
voltage across C1 is 10 V
and the voltage across both
C2 and C3 is 5 V each. Since
Q = CV and C is the same for
all the capacitors, we have
V1 > V2 and therefore Q1 > Q2.
10 V
C1 = 1.0 mF
C3 = 1.0 mF
24-6 Molecular Description of
Dielectrics
The molecules in a dielectric, when in an
external electric field, tend to become oriented
in a way that reduces the external field.
24-6 Molecular Description of
Dielectrics
This means that the electric field within the
dielectric is less than it would be in air, allowing
more charge to be stored for the same potential.
This reorientation of the molecules results in an
induced charge – there is no net charge on the
dielectric, but the charge is asymmetrically
distributed.
The magnitude of the induced charge depends on
the dielectric constant:
Summary of Chapter 24
• Capacitor: nontouching conductors carrying
equal and opposite charge.
• Capacitance:
• Capacitance of a parallel-plate capacitor:
Summary of Chapter 24
• Capacitors in parallel:
• Capacitors in series:
Summary of Chapter 24
• Energy density in electric field:
• A dielectric is an insulator.
• Dielectric constant gives ratio of total field to
external field.
• For a parallel-plate capacitor:

Chapter 25
Electric Currents and
Resistance
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Units of Chapter 25
• The Electric Battery
• Electric Current
• Ohm’s Law: Resistance and Resistors
• Resistivity
• Electric Power
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Units of Chapter 25
• Power in Household Circuits
• Alternating Current
• Microscopic View of Electric Current: Current
Density and Drift Velocity
• Superconductivity
• Electrical Conduction in the Nervous System
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25-1 The Electric Battery
Volta discovered that
electricity could be
created if dissimilar
metals were
connected by a
conductive solution
called an electrolyte.
This is a simple
electric cell.
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25-1 The Electric Battery
A battery transforms chemical energy into
electrical energy.
Chemical reactions within the cell create a
potential difference between the terminals by
slowly dissolving them. This potential
difference can be maintained even if a current is
kept flowing, until one or the other terminal is
completely dissolved.
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25-1 The Electric Battery
Several cells connected together make a
battery, although now we refer to a single cell
as a battery as well.
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25-2 Electric Current
Electric current is the rate of flow of charge
through or past a point:
The instantaneous current is given by:
Unit of electric current: the ampere, A:
1 A = 1 C/s.
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25-2 Electric Current
A complete circuit is one where current can
flow all the way around. Note that the
schematic drawing doesn’t look much like the
physical circuit!
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25-2 Electric Current
Example: Current is flow of charge.
A steady current of 2.5 A exists in a wire
for 4.0 min. (a) How much total charge
passed by a given point in the circuit
during those 4.0 min? (b) How many
electrons would this be?
In a hydrogen atom, an electron circles a
nucleus. Given that it takes a minimum
of 13.6 eV to remove an electron from a
hydrogen atom, what current is circling
the nucleus?
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Hydrogen atom
2
1
ke
E0  13.6 eV  K  U E  mv 2 
2
r
mv 2 ke 2
ke 2 ke 2
ke 2
Orbit circular, so
 2  E0 


2r
r
2r
r
r
 ke
r

2 E0
2
v
2
ke

mr



 9  109 1.6  1019 e
2  13.6  e V
 0.53  1011 m
 9  10  1.6  10   6.9  10
 9.11  10  0.53  10 
19
9
31
2
11
Q
e
1.6  1019
I 

 33mA
11
6
T 2 r v 2 0.53  10
6.9  10

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
6
m s
ConcepTest 25.1
Which is the correct way to
light the lightbulb with the
Connect the Battery
4) all are correct
5) none are correct
battery?
1)
2)
3)
ConcepTest 25.1
Which is the correct way to
light the lightbulb with the
Connect the Battery
4) all are correct
5) none are correct
battery?
1)
2)
3)
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).
25-2 Electric Current
By convention, current is defined as flowing
from + to -. Electrons actually flow in the
opposite direction, but not all currents consist
of electrons.
Thanks,
Ben!
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25-3 Ohm’s Law: Resistance and
Resistors
Experimentally, it is found that the
current in a wire is proportional to
the potential difference between its
ends:
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25-3 Ohm’s Law: Resistance and
Resistors
The ratio of voltage to current is called the
resistance (R):
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25-3 Ohm’s Law: Resistance and
Resistors
In many conductors, the
resistance is independent
of the voltage; this
relationship is called
Ohm’s law. Materials that
do not follow Ohm’s law
are called nonohmic.
Unit of resistance:
the ohm, Ω:
1 Ω = 1 V/A.
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(Diode)
25-3 Ohm’s Law: Resistance and
Resistors
Conceptual Example 25-3: Current and
potential.
Current I enters a resistor R as shown. (a)
Is the potential higher at point A or at point
B? (b) Is the current greater at point A or at
point B?
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25-3 Ohm’s Law: Resistance and
Resistors
Example 25-4: Flashlight bulb
resistance.
A small flashlight bulb draws 300
mA from its 1.5-V battery. (a) What
is the resistance of the bulb? (b) If
the battery becomes weak and the
voltage drops to 1.2 V, how would
the current change?
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25-3 Ohm’s Law: Resistance and
Resistors
Standard resistors are
manufactured for use
in electric circuits;
they are color-coded
to indicate their value
and precision.
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25-3 Ohm’s Law: Resistance and
Resistors
This is the standard resistor color code. Note
that the colors from red to violet are in the
order they appear in a rainbow.
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25-3 Ohm’s Law: Resistance and
Resistors
Some clarifications:
• Batteries maintain a (nearly) constant
potential difference; the current varies.
• Resistance is a property of a material or
device.
• Current is not a vector but it does have a
direction.
• Current and charge do not get used up.
Whatever charge goes in one end of a circuit
comes out the other end.
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25-4 Resistivity
The resistance of a wire is directly
proportional to its length and inversely
proportional to its cross-sectional area:
The constant ρ, the resistivity, is
characteristic of the material.
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25-4 Resistivity
This table gives the resistivity and temperature
coefficients of typical conductors, semiconductors,
and insulators.
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25-4 Resistivity
Example 25-5: Speaker wires.
Suppose you want to connect
your stereo to remote
speakers. (a) If each wire must
be 20 m long, what diameter
copper wire should you use to
keep the resistance less than
0.10 Ω per wire? (b) If the
current to each speaker is 4.0
A, what is the potential
difference, or voltage drop,
across each wire?
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ConcepTest 25.2
You double the voltage
across a certain conductor
and you observe the current
increases three times. What
can you conclude?
Ohm’s Law
1) Ohm’s law is obeyed since the
current still increases when V
increases
2) Ohm’s law is not obeyed
3) this has nothing to do with Ohm’s
law
ConcepTest 25.2
You double the voltage
across a certain conductor
and you observe the current
increases three times. What
can you conclude?
Ohm’s Law
1) Ohm’s law is obeyed since the
current still increases when V
increases
2) Ohm’s law is not obeyed
3) 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.
Follow-up: Where could this situation occur?
ConcepTest 25.3b
Wires II
A wire of resistance R is
1) it decreases by a factor of 4
stretched uniformly (keeping its
2) it decreases by a factor of 2
volume constant) until it is twice
3) it stays the same
its original length. What happens
4) it increases by a factor of 2
to the resistance?
5) it increases by a factor of 4
ConcepTest 25.3b
Wires II
A wire of resistance R is
1) it decreases by a factor of 4
stretched uniformly (keeping its
2) it decreases by a factor of 2
volume constant) until it is twice
3) it stays the same
its original length. What happens
4) it increases by a factor of 2
to the resistance?
5) it increases by a factor of 4
Keeping the volume (= area x length) constant means
that if the length is doubled, the area is halved.
Since R  
factor of 4.
A
, this increases the resistance by a
25-5 Electric Power
Power, as in kinematics, is the energy
transformed by a device per unit time:
or
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25-5 Electric Power
The unit of power is the watt, W.
For ohmic devices, we can make the
substitutions:
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25-5 Electric Power
Example 25-8: Headlights.
Calculate the resistance of a 40-W
automobile headlight designed for 12 V.
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25-4 Resistivity
For any given material, the resistivity
increases with temperature:
Semiconductors are complex materials, and
may have resistivities that decrease with
temperature.
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25-4 Resistivity
Example: Resistance thermometer.
A nichrome heater dissipates 500 W when
the applied potential difference is 110 V
and the wire temperature is 800 oC. What
would the dissipation rate be if the wire
temperature were held at 200 oC by
immersing the wire in a bath of oil while
the applied potential difference remains
the same?
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25-5 Electric Power
What you pay for on your electric bill is
not power, but energy – the power
consumption multiplied by the time.
We have been measuring energy in
joules, but the electric company
measures it in kilowatt-hours, kWh:
1 kWh = (1000 W)(3600 s) = 3.60 x 106 J.
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25-5 Electric Power
Example: Electric light.
A 100 W light bulb is plugged into a standard
120 V outlet. a) At $0.08/kW-hr, how much
does it cost to have the bulb on 24 hrs/day for
a 31-day month? b) What is the resistance of
the bulb? c) What is the current in the bulb?
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Electric light


a) C  $   P 100 W T  31 days  24 hrs day  0.08 $ 103 W  hr 
 $5.95
b) P 
2
2
V
V
R
R
P
c ) P  IV  I 
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120 


100
2
 144 
P 100

 0.83 A
V 120
25-6 Power in Household Circuits
The wires used in homes to carry electricity
have very low resistance. However, if the current
is high enough, the power will increase and the
wires can become hot enough to start a fire.
To avoid this, we use fuses or circuit breakers,
which disconnect when the current goes above
a predetermined value.
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25-6 Power in Household Circuits
Fuses are one-use items – if they blow, the
fuse is destroyed and must be replaced.
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25-6 Power in Household Circuits
Circuit breakers, which are now much more
common in homes than they once were, are
switches that will open if the current is too
high; they can then be reset.
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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).
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25-7 Alternating Current
The voltage varies sinusoidally with time:
,,
as does the current:
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25-7 Alternating Current
Multiplying the current and the voltage gives
the power:
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25-7 Alternating Current
Usually we are interested in the average power:
1
sin  
2
1

2
2

2
0
sin  d    sin cos 
 
2
0
2

1
1  sin  d 1 
2
2
1
 sin  
2
2
 P  I 2 R  I 02 R sin 2  t
1 2
1 V02
 I0 R 
P
2
2 R
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
2
0
2
0
1

2

2
0
sin 2  d
cos 2  d
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:
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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?
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Questions?