Download Chapter 18 Notes

Chapter 18
Electric Currents
© 2002, B.J. Lieb
Ch 18
1
Simple Electric Cell
Carbon
Electrode
(+)
Zn
_ Electrode
(-)
+
+
+
_
_
Zn+ Zn+
Zn+ Zn+
Sulfuric acid
•Two dissimilar metals or carbon rods in acid
•Zn+ ions enter acid leaving terminal negative
•Electrons leave carbon leaving it positive
•Terminals connected to external circuit
•‘Battery’ referred to several cells originally
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Electric Current
•If we connect a wire between the two
terminals electrons will flow out of the
negative terminal and toward the positive
terminal we have an electric current.
•Electric current I is defined as the net
amount of charge that flows past a given
point per unit time.
Q
I 
t
1 C/s = 1A (ampere)
An ampere is a large current and
often currents are mA (10-3 A) or
A (10-6 A).
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Electric Circuit
• It is necessary to have a complete circuit
in order for current to flow.
• The symbol for a battery in a circuit
diagram is:
+
_
“Conventional” current
direction is opposite to
actual electron flow
direction which is – to
+.
Current
Device
9 volts
+
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Ohm’ Law
• For wires and other circuit devices, the
current is proportional to the voltage
applied to its ends:
IV
• The current also depends on the amount of
resistance that the wire offers to the
electrons for a given voltage V. We define
a quantity called resistance R such that
V = I R (Ohm’s Law)
• The unit of resistance is the ohm which is
represented by the Greek capital omega
().
V
• Thus
1 
A
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Resistors
• A resistor is a circuit device that has a fixed
resistance.
Resistor
Circuit symbol
Resistors obey Ohm’s law but not all circuit
devices do.
I
I
0
V
Resistor
0
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non-ohmic device
6
Example 1
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Resistivity
• In most electronic circuits we ignore the
resistance of the wires because it is small in
comparison to the other circuit components
• If we need to calculate the resistance of a
given wire we can use its resistivity ()
which is defined by:
L
R  
A
where L is the length of the wire and A is
the cross sectional area.
A
L
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Resistivity and Temperature
•Resistivity usually depends on temperature.
For most metals the resistivity increases with
temperature.
•Often the flow of current through a wire is the
cause of the temperature change.
T  0 1   (T  T0 )
where T0 is usually 20o and 0 is the resistivity
at that temperature.
Material
0 ( m)
0 (Co)-1
Silver
1.59 x 10-8
0.0061
Aluminum
2.65 x 10-8
0.00429
Hard Rubber (insulator)
1013 - 1015
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Example 2
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Superconductivity
• The resistivity of certain metals and
compounds becomes zero at low
temperatures near absolute zero- this state
is called superconducting.
• Occurs only below a critical temperature
TC which is usually close to absolute zero
• Materials require liquid helium for cooling.
• Since 1987 a new class of “high TC”
materials have been discovered that are
superconducting up to 160 K.
• Would be many practical applications if
some of the difficulties can be overcome.
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Power in Electric Circuits
• Electrical circuits can transmit and
consume energy.
• When a charge Q moves through a
potential difference V, the energy
transferred is QV.
• Power is energy/time and thus:
energy QV  Q 
P  power 

   V  IV
time
t
t
and thus:
P  IV
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Notes on Power
•The formula for power applies to devices
that provide power such as a battery as well
as to devices that consume or dissipate
power such as resistors, light bulbs and
electric motors.
J
C  J 
P  IV      
 W  watt
s
 s C 
•The formula for power can be combined with
Ohm’s Law to give other versions:
2
V
P  IV  I 2 R 
R
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Example 3
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Household Power
•Electric companies usually bill by the
kilowatt-hour which is the energy
consumed by using 1.0 kW for one hour.
•Thus a 100 W light bulb could burn for 10
hours and consume 1.0 kWh.
•Electric circuits in a building are protected
by a fuse or circuit breaker which shuts
down the electricity in the circuit if the
current exceeds a certain value. This
prevents the wires from heating up when
carrying too much current.
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Current
Alternating Current
1.5
1
0.5
0
-0.5 0
-1
-1.5
5
10
15
Time
•Electrical power is distributed using
alternating current (ac) in which the
current reverses direction with a
frequency of 60 Hz (in the USA).
•The current and voltage varies as a sin
function as shown above. Thus
V  V0 sin 2 ft
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Average Power
•Even though the electron motion in ac circuits is back
and forth they can still deliver power.
•Because the current and voltage change greatly over a
cycle, we have to average over a cycle to get an
accurate value for the average power consumed in the
circuit
•The correct way to calculate this average is to use
calculus to average the square of the current over a
cycle and then take the square root of the result. This is
called a root-mean-square (rms) average:
I rms
I0

2
2
V
2
P  I rms R  rms
R
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Voltage
Alternating Current in U.S.
1.5
1
0.5
0
-0.5 0
-1
-1.5
5
10
15
Time
V  V0 sin 2 ft
•In the U.S.: f = 60 Hz
V0  170 V
Vrms 120 V
•In Europe: f = 50 Hz
V0  310 V
Vrms  220 V
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Example 4
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Microscopic View of Current
•Read Example 18-13. It studies a 5.0A current
in a copper wire that is 3.2 mm in diameter. It
finds that the average “free” electron moves
with a velocity of 4.7 x 10-5 m/s in the direction
of the current. This is called the drift velocity.
•It also assumes the “free” electrons behave like
an ideal gas and calculates that the thermal
velocity of the average electron is 1.2 x 105 m/s.
•Thus in a wire carrying a current, the electron
motion is largely random with a slight tendency
to move in the direction of the current. Thus if
you could see electrons in a wire carrying
current they would appear to be moving
randomly.
Ch 18
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