# 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.

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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) I Obeys the passive sign + - convention V if I > 0 then V > 0 R = or V = I∙R This is Ohm’s Law! Voltage Current

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 http://www.elexp.com/t_resist.htm 56 * 10 k  = 560 k  237 * 1  = 237 

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 0 o Kelvin

Conductor Animation http://micro.magnet.fsu.edu/electromag/java /filamentresistance/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 ·10 2 ohm-m 6 Glass – An insulator – ρ=10 12 ohm-m

Example A round wire has a radius of 1 mm = 10 -3 m The wire is 10 meters long The wire is made of copper R= (1.72 · 10 -8 Ω·m · 10 m) /( π ·(10 -3 m) 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 = I 2 ∙ R Or since I = V /R, then P = V 2 / 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 mm 2 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 mm 2 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 +-+- r∙Ix K∙Vx or g∙Vx K∙Ix or

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 Drain Source

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 Light Sensor Is = K amps +-+- Room Lights Vs =120v -VL/5 100Ω + VL _

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