Chapter 20: Electric Current, Resistance & Ohm s Law Brent Royuk Phys-112 Concordia University
The Minds of Our Own Challenge Light a bulb with a battery and a wire. Could you do it? 2
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 3
Electric Current Current Flow Consider a simple circuit diagram What direction does the current flow? Electron flow vs. conventional current Curse you Ben Franklin! 4
Definition: Electric Current Unit: The ampere (A) amps I = ΔQ Δt 1 A = 6.25 x 10 18 electrons/s 5
The Water Pump Analogy 6
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 7
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 8
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) 9
Resistivity Resistivity is a measure of how well a material conducts electricity. Resistance also depends on the material dimensions of the conductor. R = ρl A Further define conductivity as σ = 1 ρ 11
Table of Resistivities Substance ρ (Ω m) Substance ρ (Ω m) Quartz 7.5 x 10 17 Iron 9.71 x 10-8 Rubber 1 to 100 x 10 13 Tungsten 5.6 x 10-8 Glass 1 to 1000 x 10 11 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 How about a real copper wire? 12
Temperature Dependence For most materials, resistivity increases with temperature. Approximate relationship: ρ = ρ o (1 + αδt) Semiconductors actually lower their resistivity as they heat up. Thermistors 13
Type 1 Superconductors Pb, Hg, Sn, Cr, Al For Pb, T c = 7.2 K Type 2 1986: Superconducting oxocuprates T c > 100K 14
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 2 R 15
Electric Pie Chart Calculator 16
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 loss = I 2 R = P supplied P = I 2 R, so should heaters have high resistance or low resistance? V 2 R = P supplied 2 R V 2 17
Energy Bills What is a kilowatt-hour (kwh)? How much does it cost to light a 100-W bulb for a month? 19
AC vs. DC V = V sin2πft 20 o
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? 21
Home Electricity 22
Human Shock Risk Three Conditions for Danger 1. 2. 3. Enough Voltage to Cause Current Enough Charge/Current to Cause Damage Electrical Path Through Body 23
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 24
Limiting Current in Circuits Fuses and Circuit Breakers 25
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? 26
Frequency Dependance The lower the current value, the more sensitive the body is at that frequency. 27
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 28
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% 31
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 32