Download Electric Potential Difference

Current Electricity
Parallel Circuit
Series Circuit
What You Will Learn
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Transfer of energy in circuits.
Conversion of energy.
Electric Current – Conventional vs. Flow of
Electrons
Resistance and Ohm’s Law
Basic Circuits
What You Already Know
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You flip a switch to turn on a light, TV or
computer.
To turn on the car, you turn the ignition switch.
MP3 players, cell phones and flashlights have
on/off switches and use batteries.
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In each of these cases, you have a closed circuit in
which electricity flows.
What You Already Know
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Charge by Conduction – The process by
which electrons are transferred from one object
to another because of differences in excess
number of electrons on one surface compared
to the other.
What You Already Know Electric Potential
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the Electric Potential Difference is equal to the Work
required to move a test charge in an electric field divided
by the magnitude of the test charge.
F is constant
since the electric
field is constant
from one plate
to the other.
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A
B
qo
F = qoE
Uniform
Electric
Field
Vtotal = W/qo = Fd/qo = Ed
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Creating a Circuit
Plate with
excess number
of electrons
Two equal and
oppositely
charged plates
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Plate with
deficiency of
electrons
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What would happen if a conductor was connected
to both plates?
Creating a Circuit
The electrons would flow from the negatively charged
plate to the positively charged plate until the amount
of charge was the same for both plates and the wire.
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Conventional Current Flow
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Electron Flow
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How do we maintain the flow of charge?
Creating a Circuit
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Electron Flow
Electron Flow
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Charge pump
• Battery
•Generator
•Gas/Oil
•Nuclear
•Hydro
•Wind
•Tidal
•Solar
Circuit:
• A closed loop in which electric current can flow.
• It generally includes a device such as a light bulb that
reduces the electric potential energy.
• It also includes a device to increase potential energy (Charge
Pump).
What is Current?
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Current is the rate of flow of charge.
I = q/t = 1 Coulomb/second = 1 Ampere (A)
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Conventional Current = flow of positive charge.
(Note that positive charges do NOT flow in
metallic conductors.)
Electron flow is simply the
Conventional Current
flow of electrons.
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Electron Flow
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Ohm’s Law
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German Georg Simon Ohm discovered that the
ratio of the potential difference to current is a
constant for a given conductor.
R = V/I
Where:
R = Resistance in Ohms ()
V = Electric Potential in Volts (V)
I = Current in Amperes (A)
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Resistance is the hindrance to the flow of
charge.
Most metallic conductors obey Ohm’s Law.
Ohm’s Law
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The resistance (R) represents the slope (m) of a
curve where V is plotted against I.
What is R? 10
For Ohmic materials, the curve is a straight line.
m = R = V/I
Non-Ohmic
e.g. light bulb
Examples: Ohm’s Law
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How much current flows through a 12
flashlight bulb operating at 3.0 volts?
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What is the voltage drop in a 5 resistor
that has 2 amperes of current running
through it?
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What is the resistance of a heating
element in a toaster operating at 120
volts with a current flow of 2 amperes?
What causes resistance?
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E-field in conductor (resistor) is provided by a
battery or voltage source.
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Charges (electrons) are put in motion due to influences
of the electric field, but scatter in a very short time
from things that get in the way
defects, lattice vibrations (phonons), etc
The more collisions, the greater the resistance and the
fewer the collisions, the less the resistance.
Imagine the following two scenarios.
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2.
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Running down the hallway in between periods
Running down the hallway after the late bell when
there is nobody in them.
Under which scenario would you experience less
resistance?
Resistivity & Resistance
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Resistivity is a measure of the conductive ability of the
material.
Resistivity is an intrinsic (natural) property of a material.
The higher the resistivity, the higher the resistance and
vice versa.
For a conductor of length L (m) and cross-sectional area A
(m2), the resistance can be determined by:
R = L/A
Where
 = resistivity (•m)
L = length of the conductor
A = Cross-Sectional Area
R
L
A
Ex.: Resistance & Resistivity
1.
What would happen to the resistance in a wire if the length
were increased?
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B.
C.
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It would decrease.
It would increase.
It would remain the same.
What would happen to the resistance in a wire if the crosssectional area were increased?
A.
B.
C.
3.
It would decrease.
It would increase.
It would remain the same.
What would happen to the resistivity the length were
increased?
A.
B.
C.
It would decrease.
It would increase.
It would remain the same.
Low Resistance vs.
High Resistance
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To Summarize:
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Short fat wires make good conductors.
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Short & Fat = Low Resistance
While long skinny wires make poor
conductors.
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Long & Skinny = High Resistance
Resistance vs. Length and
Resistance vs. X-Sectional Area
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What is the relationship between:
Resistance and
Length?
Resistance and XSectional Area?
Length
X-Sectional Area
R
L
A
Resistivity vs. Temperature
Note: The Resistivity is zero at 0 K, therefore,
the resistance is also zero.
How fast do the electrons
travel?
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A simple observation would tell an
observer that the flow of electricity
appears to be instantaneous when
flipping on a light switch.
Does that mean the electrons travel
at the speed of light?
Drift Velocity
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When an electric field is applied to a conductor,
it will set the electrons in motion in an overall
direction opposite the applied field.
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While the electric field travels at nearly the
speed of light, the overall speed of the electron
from one end of the conductor to the other is
quite slow and random in direction due to
collisions.
Determining the drift
velocity in a wire.
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The total charge in a section of wire can
be determined as follows:
q  nALe
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(1)
Where:
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n = number of carriers per unit volume
A = cross-sectional area
L = length of the conductor
e = charge of an electron (the elementary charge)
Determining the drift
velocity in a wire.
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Since all the electrons move along the conductor
at the same average drift speed, the total
amount of charge that moves through a cross
section of wire is:
q
I
t
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(2)
Since v = d/t, we can find the time it takes for
the total charge to move through any cross
section by:
L
t
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vd
(3)
Where vd = drift velocity and L = length of wire.
Determining the drift
velocity in a wire.
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Substituting (1) into (2) for q, and (3) into (2)
for q, and then solving for vd gives us:
I
vd 
nAe
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The number of charge carriers per unit volume
(n) can be found as follows:
NA
n
M
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Where: NA = Avogadro's Number
M = the atomic mass number
 = density
Example – Drift Velocity
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What is the drift velocity in the copper
wires leading to a kitchen appliance that
operates at 1 Ampere?
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Note: wire in your kitchen has to be capable
of carrying 20 amps of current, therefore, it is
specified to be 12 gauge.
The cross-sectional area of 12 gauge wiring is
3.31 x 10-6 m2
Assume that 1 electron is donated by each
atom.
The density is 8.96 x 103 kg/m3.
The atomic mass is 63.546 g/mole.
Finding the Drift Velocity in
a Copper Wire
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First determine the number of charges
per unit of volume (n)
N A
n
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M
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kg
63.546 103 mole
 8.49 1028 electrons
m3
Now determine the drift velocity (vd)
vd 
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3 kg
(6.02 1023 electrons
)(
8
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96

10
)
mole
m3
I
(1.0 A)
5
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2
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22

10
6
2
19
nAe (8.49 1028 electrons
)(
2
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08

10
m
)(
1
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6

10
C)
3
m
That’s only 0.08 m/hr!
m
s
Power
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Power = Rate at which work is done
where:
P = VI
P = 1 Joule/second = 1 Watt
P = VI = (1 Volt)•(1 Ampere) = 1 Watt
V = W/q = 1 Joule/Coulomb
I = q/t = 1 Coulomb/second
Since V = IR and I = V/R:
P = IRI = I2R
P = V•V/R = V2/R
Example (Power)
What is the power rating of a lightbulb
in circuit where the current is 0.50 A
and the voltage is 120V?
P = VI
P = 120 V•0.50 A
P = 60 VA = 60 W
Power vs. Current and
Power vs. Voltage (Ohmic Materials)
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What is the relationship between:
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power and current?
Current
P = I2R
Power and voltage?
Voltage
P = V2/R
Energy
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Since power is the rate at which
work is done the amount of energy
required to complete a task is as
follows:
Total Energy = Power x time
W = Pt
Example (Energy)
How much energy is consumed by a
lightbulb operating in circuit where the
current is 0.50 A and the voltage is
120V for 1 hour?
W
W
W
W
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=
=
VIt
120 V•0.50 A•3600 s
216,000 J
216 kJ
Key Ideas
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A circuit is a closed path where current can flow.
Current is the flow of charge.
Resistance is the hindrance to the flow of charge.
Ohm’s Law = voltage to current ratio (V/I) = Resistance.
Resistivity is an intrinsic property of a material that is
proportional the the resistance.
An increase in length of a conductor will increase
resistance.
An increase in cross-sectional area of a conductor will
decrease resistance.
Power equals the rate at work is done and is represented
electrically by P = IV.