Electric Current, Resistance & Ohm's

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?

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

1 Electric Current • Current Flow – Consider a simple circuit diagram • What direction does the current flow? – Electron flow vs. conventional current • Curse you Ben Franklin!

Electric Current ΔQ • Definition: I = Δt • Unit: The ampere (A) – “amps” • 1 A =€ 6.25 x 1018 electrons/s

The Water Pump Analogy

2 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

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)

3 Resistivity • Resistivity is a measure of how well a material conducts electricity. – Resistance also depends on the material dimensions of the conductor. ρL R = A

• Further define conductivity as € 1 σ = 11 ρ

€

Table of Resistivities 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

How about a real 12 copper wire?

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

4 Superconductors • Type 1 – Pb, Hg, Sn, Cr, Al

– For Pb, Tc = 7.2 K • Type 2 – 1986: Superconducting oxocuprates

– Tc > 100K

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 V 2 P = VI = = I 2R R 15

€

Electric Pie Chart Calculator

5 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 ⎛ ⎞2 2 Psupplied 2 R Ploss = I R = ⎜ ⎟ R = Psupplied ⎜ V ⎟ V 2 ⎝ ⎠ • P = I2 R, so should heaters have high resistance or low resistance? €

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

AC vs. DC

V V sin2 ft20 = o π

€ 6 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?

Home Electricity

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

7 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

Limiting Current in Circuits • Fuses and Circuit Breakers

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?

8 Frequency Dependance • The lower the current value, the more sensitive the body is at that frequency.

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

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

9 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