Resistance
• Section 2.4 in your book
Resistance
• Property of a device that indicates how freely it will
allow current to flow given a specific voltage
applied. If low in value, current flows more freely.
• Measured in ohms (Ω = V/A or KΩ = V/mA)
R = Voltage or V = I∙R
Current
• Obeys the passive sign
convention
This is Ohm’s Law!
I
+
V
if I > 0 then V > 0
Resistors
• Resistors are devices that are used in a
variety of circuits to make the currents and
voltages what you desire
• They are color-coded and come in various
tolerances, ± 1%, , ± 5% and , ± 10% are
most common
Resistor Color Code
56 * 10 kW = 560 kW
237 * 1 W = 237 W
http://www.elexp.com/t_resist.htm
Conductance (G)
•
•
•
•
Conductance is the reciprocal of resistance
Its unit is the siemen = amps/volts = 1/Ω
G=I/V=1/R
An equivalent measure of how freely a
current is allowed to flow in a device
Resistivity (ρ)
• Property of a material that indicates how
much it will oppose current flow
• R= (ρ · length) / (cross sectional area)
• Units are ohms · meters (Ω · m)
• As the wire gets bigger, so does the cross
section making the resistance smaller
• As the length gets longer, the resistance
goes up proportionately
Conductors
• Materials with electrons that are loosely
bound to the nucleus and move easily
(usually one electron in the outer shell)
• Their low resistance goes up as the
material is heated, due to the vibration of
the atoms interfering with the movement of
the electrons
• The best conductors are superconductors at
temperatures near 0o Kelvin
Conductor Animation
• http://micro.magnet.fsu.edu/electromag/java
/filamentresistance/
Semiconductors
• Materials with electrons that are bound
more tightly than conductors (usually 4
electrons in the outer shell)
• Impurities are added in controlled amounts
to adjust the resistivity down
• Semiconductors become better
conductors at higher temperatures
because the added energy frees up more
electrons (even though the electron flow is
impeded by the increased atomic vibration)
Insulators
• Materials that have all 8 electrons in the
outer shell tightly bound to the nucleus
• It takes high temperatures or very high
electric fields to break the atomic bonds to
free up electrons to conduct a current
• Very high resistivities and resistances
Resistivity of Materials
•
•
•
•
•
•
•
Glass
•
Gold
•
Silver
•
Silicon
•
Aluminum
•
Copper
Put a number 1 beside
the material that
is the best conductor,
a 2 next to the
material next most
conductive, etc.
Resistivity of Materials
1 Silver - A conductor - ρ=1.64 ·10-8 ohm-m
2 Copper - A conductor - ρ= 1.72·10-8 ohm-m
3 Gold – A conductor - ρ=2.45·10-8 ohm-m
4 Aluminum - A conductor - ρ= 2.8·10-8 ohm-m
5 Silicon - A semiconductor - ρ=6.4 ·102 ohm-m
6 Glass – An insulator – ρ=1012 ohm-m
Example
•
•
•
•
•
•
A round wire has a radius of 1 mm = 10-3m
The wire is 10 meters long
The wire is made of copper
R= (1.72 · 10-8 Ω·m · 10 m) /( π ·(10-3m) 2 )
R = 0.0547 Ω
This is negligible in most circuits where
resistances are often thousands of ohms
Power used by Resistors
•
•
•
•
We saw that P = I ∙ V
If by Ohm’s law, V = I ∙ R, then P = I2 ∙ R
Or since I = V /R, then P = V2 / R
Since resistance is always positive for
passive devices, then power is always
positive (meaning that power is always
absorbed or used)
Application
• Calculate the power lost in a 100 foot AWG
14 copper wire handling 20 amps.
– AWG 14 wire has a cross section of 2.08 mm2
and 2.52 ohms/1000 feet
• What current is an AWG 12 copper wire
handling if it had the same power loss as the
AWG 14 cable?
– AWG 12 wire has a cross section of 3.31 mm2
and 1.59 ohms/1000 feet
Application
• What is the voltage drop across the wire in
each case?
– For the AWG 14 wire ____________
– For the AWG 12 wire ____________
Conclusion
• When you need to handle more current, use
bigger or more conductive wire
–
–
–
–
Avoids loss of power
Lessens voltage drop
Avoids dangerous heating of wiring
But costs more
Voltage & Current Sources
Section 2.3 in your book
Independent Voltage Sources
• Most common in everyday life
• Voltage is fixed and independent of the
current required by the circuit
• Ideally is capable of providing any current
that the circuit requires
+
-
Vs is fixed
AC or DC
Indpendent Current Sources
• Current is fixed and independent of the
voltage across the source
• The voltage across the source adjusts to
whatever the circuit requires to produce the
fixed current – it does not usually have zero
volts across it
Is is fixed, AC or DC
Dependent Sources
• May be voltage or current sources
– May be AC or DC
• Are dependent on a current or voltage
somewhere in the circuit
K∙Vx
or
r∙Ix
+
-
K∙Ix
or
g∙Vx
Dependent Sources
• Used in modeling more complex devices
like transistors and operational amplifiers
– The voltage applied to the gate of a MOSFET
controls the conductivity of the channel so that
more current flows from drain to source
Gate
Source
Drain
Example
• A light sensor produces a 0 to 1 amp current
proportional to the outside illumination,
K amps
• The sensor current supplies a 100Ω resistor
to get the dependent voltage, VL
• The source powering the room lights equals
120 - VL/5 volts
• What is the voltage across the lights when
K = 0, .4, .7 or 1 amp?
Circuit Diagram
Vs =120v
-VL/5
+
-
Light
Sensor
Room
Lights
+
100Ω
VL
Is =
K amps
_
Plug-In Hybrid Electric Vehicles
IEEE – USA Position Statement
Adopted June 15, 2007
• Use PHEVs to add resilence to our
transportation fleet and increase energy
independence
– In the case of an oil shutdown or price spike, a
PHEV would allow people to make necessary
trips to work and shopping
– Although current hybrids increase mileage
between 16 and 47%, PHEVs could displace
almost all imported oil
Other Recommendations
• Increase research to improve
– Batteries, including weight, size, cost, life and
safety considerations
– Power electronics
– Controls
– Integration with the electric power grid
Final Recommendations
• Use incentives to encourage adoption of
PHEVs
• Encourage electric metering and pricing that
will help PHEVs realize their potential
– To encourage consumers to charge their vehicle
during off-peak hours
– To encourage consumers to make their vehicle
battery storage available to meet peak loads
Progressive X Prize
• http://www.youtube.com/watch?v=NT2FI0
H8CWA&feature=user