1 Chapter 20: Electric Current, Resistance & Ohm’s Law Brent Royuk Phys-112 Concordia University 2 The “Minds of Our Own” Challenge • Light a bulb with a battery and a wire. Could you do it? 3 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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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?
3
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
2
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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
€
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”
analogy
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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
€
R =ρLA
€
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
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
€
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?
€
Ploss = I2R =Psupplied
V
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
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
€
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%
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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