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Chapter 20: Electric Current,

Resistance & Ohm’s Law

Brent Royuk Phys-112

Concordia University

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The “Minds of Our Own” Challenge •  Light a bulb with a battery and a wire.

Could you do it?

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Introduction •  Batteries supply charge to produce a

current –  How? Electrochemistry stuff: oxy/redux

•  cathode and anode •  dry cell vs. battery

–  Electric current = moving charges •  dc vs. ac

•  How does this relate to electrostatics? –  Electroscope and D-cell? –  Voltage of charge strips

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Electric Current •  Current Flow

–  Consider a simple circuit diagram •  What direction does the current flow?

–  Electron flow vs. conventional current •  Curse you Ben Franklin!

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Electric Current •  Definition: •  Unit: The ampere (A)

–  “amps”

•  1 A = 6.25 x 1018 electrons/s

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I =ΔQΔt

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The Water Pump Analogy

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Drift Velocity •  Even without a potential, electrons are

in constant motion •  Electric field --> force --> drift velocity

–  How many conduction electrons are in a wire?

•  So drift velocities are often very slow, like walking speeds.

•  So why don’t we have to wait for the light when we hit the switch? –  What moves fast? –  “Marbles in a tube”

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Ohm’s Law •  Two laws for resistive circuits:

–  I α ΔV –  I α 1/R

•  Put them together and you get V = IR –  Ohm’s Law

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Ohm’s Law •  Definition of resistance: R = V/I

–  Resistance Unit: The ohm (Ω) •  Ohm’s Law doesn’t apply to all materials

–  E.g. semi-conductors, lightbulb filaments –  (Known as Ohmic & Non-Ohmic materials)

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Resistivity •  Resistivity is a measure of how well

a material conducts electricity. –  Resistance also depends on the

material dimensions of the conductor.

•  Further define conductivity as

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R =ρLA

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σ =1ρ

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Table of Resistivities

How about a real copper wire?

Substance ρ (Ω m) Substance ρ (Ω m)

Quartz 7.5 x 1017 Iron 9.71 x 10-8

Rubber 1 to 100 x 1013 Tungsten 5.6 x 10-8

Glass 1 to 1000 x 1011 Aluminum 2.65 x 10-8

Silicon 0.10 to 60 Gold 2.20 x 10-8

Germanium 0.001 to 0.5 Copper 1.68 x 10-8

Lead 22 x 10-8 Silver 1.59 x 10-8

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Temperature Dependence •  For most materials, resistivity

increases with temperature. –  Approximate relationship: –  ρ = ρo(1 + αΔT)

•  Semiconductors actually lower their resistivity as they heat up. –  Thermistors

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Superconductors •  Type 1

–  Pb, Hg, Sn, Cr, Al –  For Pb, Tc = 7.2 K

•  Type 2 –  1986: Superconducting oxocuprates –  Tc > 100K

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Electric Power •  A charge moving through a circuit

expends energy –  This is due to collisions between electrons

and resistor molecules. –  Voltage drops across a resistor

•  U = VQ, so divide by time. •  P = VI •  A standard flashlight bulb is rated at 5.2

V, 850 mA. What is its wattage? •  Combining with Ohm’s Law, we get

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P = VI =V 2

R= I 2R

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Electric Pie Chart Calculator

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Joule Heating •  Energy that heats a resistor is sometimes

called the Joule heat –  That’s how electric heaters, hair dryers, etc. work –  Sometimes this is bad, as in e.g. energy loss in

power lines

•  P = I2 R, so should heaters have high resistance or low resistance?

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Ploss = I2R =Psupplied

V

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⎝ ⎜ ⎜

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⎠ ⎟ ⎟

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R = Psupplied2 R

V 2

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Energy Bills •  What is a kilowatt-hour (kWh)? •  How much does it cost to light a 100-W bulb for a

month?

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AC vs. DC

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V = Vo sin2πft

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Home Electricity •  Three-wire system: difference

between two hot is 240 V, most appliances connect between one hot and a ground wire for a difference of 120 V –  Demo with hot wire, voltmeter

•  Appliances are wired in parallel: Why?

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Home Electricity

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Human Shock Risk •  Three Conditions for Danger

1.  Enough Voltage to Cause Current 2.  Enough Charge/Current to Cause Damage 3.  Electrical Path Through Body

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Electric Safety Two problems to prevent: 1.  Too much current can flow in a circuit,

causing Joule heating of the circuit, possibly starting fires. •  Solution: Fuses & circuit breakers

2.  Electricity can electrocute people. •  Solution: Three prong plugs, polarized

plugs, fuses & circuit breakers

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Limiting Current in Circuits •  Fuses and Circuit Breakers

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Electric Safety •  Problem: disconnected wire can make appliances “hot” •  Demo grounding plug: polarized plug vs. dedicated

grounding wire. –  adapters have grounding lugs

•  Path through body is important; hand vs. chest •  Why isn’t a car battery dangerous?

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Frequency Dependance •  The lower the current value, the more

sensitive the body is at that frequency.

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Electric Safety •  Effects of Electric Current on the Human Body

•  Current (approximate) Effect

•  0–0.5 mA none •  0.5–2 mA Threshold of feeling •  2–10 mA Pain; muscular contractions. •  10–20 mA Increased muscular effect, some

injury; above 16 mA is the'let-go' current above which a person cannot release held objects.

•  20–100 mA Respiratory paralysis •  100 mA–3 A Ventricular fibrillation; fatal unless

resuscitation occurs immediately. •  above 3 A Cardiac arrest; heart can be

restarted if shock is very brief; severe burns

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The Resistor Code color number multipier tolerance black 0 1 brown 1 10^1 red 2 10^2 orange 3 10^3 yellow 4 10^4 green 5 10^5 blue 6 10^6 violet 7 10^7 gray 8 10^8 white 9 10^9 gold 10^-1 5% silver 10^-2 10% no color 20% 32

The Resistor Code •  B B ROY of Great Britain had a Very Good

Wife •  Bad Betty runs over your garden but Violet Gray won't •  Big boys race our young girls, but violet generally wins •  Black Beetles Running On Your Garden Bring Very Good

Weather •  Big Bears Run Over Your Gladiola Bed Vexing Garden

Worms (go see now) •  Beer Bottles, Reminders Of Your Guests, Become

Voluminous Glass Waste •  Behold Brother, Rain On Your Grapes Brings Very Good

Wine •  Bad Booze Rots Our Young Guts, But Vodka Goes Well