The Physics
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Opus in profectus

Electric Resistance

Discussion

introduction

Yech! What a mess this is.

Conduction: S. Gray, 1729 — Resistance: Georg Simon Ohm, 1827.

Regular version…

I ∝ V

 I = V ⇒ V = IR ⇒ R = V R I

variableogy…

• quantity: resistance R
unit: ohm [Ω] Georg Ohm (1787–1854) Germany

Fancy version (the magnetohydrodynamic version?)…

J ∝ E

J = σE  ⇐
 ρ = 1 σ
⇒  E = ρ J

Symbol hell…

 quantity symbol unit symbol property of… resistance R ohm Ω objects conductance G siemens S resistivity ρ ohm meters Ω materials conductivity σ siemens per meter S/m

Ohm's law isn't a very serious law. It's the jaywalking of physics. Sensible materials and devices obey it, but there are plenty of rogues out there that don't.

resistors

Bad Booze Rots Our Young Guts But Vodka Goes Well.

Better Build Roof Over Your Garage Before Van Gets Wet.

Resistor color code
first & second bands
(first & second digits)
black   0
brown   1
red   2
orange   3
yellow   4
green   5
blue   6
violet   7
gray   8
white   9
third band
(multiplier)
black   100+
brown   101+
red   102+
orange   103+
yellow   104+
green   105+
blue   106+
silver   10−2
gold   10−1
fourth band
(tolerance)
none   ±20%
silver   ±10%
gold   ±05%

materials

Resistance and resistivity. Factors affecting resistance in a conducting wire.

 R = ρℓ A

Conductors vs. insulators

Best electrical conductors: silver, copper, gold, aluminum, calcium, beryllium, tungsten

Resistivity and conductivity are reciprocals.

Conductivity in metals is a statistical/thermodynamic quantity.

Resistivity is determined by the scattering of electrons. The more scattering, the higher the resistance.

 σ = ne2ℓ mevrms

Where…

 σ = electrical conductivity [S/m] n = density of free electrons [e/m3] e = charge of an electron (1.60 × 10−19 C) me = mass of an electron (9.11 × 10−31 kg) vrms = root-mean-square speed of electrons [m/s] ℓ = mean free path length [m]

Graphite

Where does this idea belong? Nichrome was invented in 1906, which made electric toasters possible.

Conducting polymers.

metals ρ (nΩ m) nonmetals ρ (Ω m)
aluminum 26.5 aluminum oxide (14 ℃) 1 × 1014
brass 64 aluminum oxide (300 ℃) 3 × 1011
chromium 126 aluminum oxide (800 ℃) 4 × 106
copper 17.1 carbon, amorphous 0.35
gold 22.1 carbon, diamond 2.7
iron 96.1 carbon, graphite 650 × 10−9
lithium 92.8 pyrex 7740 40,000
mercury (0 ℃) 941 quartz 75 × 1016
manganese 1440 silicon 640
nichrome 1500 silicon dioxide (20 ℃) 1 × 1013
nickel 69.3 silicon dioxide (600 ℃) 70,000
palladium 105.4 silicon dioxide (1300 ℃) 0.004
platinum 105 water, liquid (0 ℃) 861,900
plutonium 1414 water, liquid (25 ℃) 181,800
silver 15.9 water, liquid (100 ℃) 12,740
solder 150
steel, plain 180
steel, stainless 720
tantalum 131
tin (0 ℃) 115
titanium (0 ℃) 390
tungsten 52.8
uranium (0 ℃) 280
zinc 59
Resistivity of selected materials (~300 K)
(Note the difference in units between metals and nonmetals.)

temperature

The general rule is resistivity increases with increasing temperature in conductors and decreases with increasing temperature in insulators. Unfortunately there is no simple mathematical function to describe these relationships.

The temperature dependence of resistivity (or its reciprocal, conductivity) can only be truly understood with quantum mechanics. In the same way that matter is an assembly of microscopic particles called atoms and a beam of light is a stream of microscopic particles called photons, thermal vibrations in a solid are a swarm of microscopic particles called phonons. The electrons are trying to drift toward the positive terminal of the battery, but the phonons keep crashing into them. The random direction of these collisions disturbs the attempted organized motion of the electrons against the electric field. The deflection or scattering of electrons with phonons is one source of resistance. As temperature rises, the number of phonons increases and with it the likelihood that the electrons and phonons will collide. Thus when temperature goes up, resistance goes up.

For some materials, resistivity is a linear function of temperature.

ρ = ρ0(1 + α(T − T0))

The resistivity of a conductor increases with temperature. In the case of copper, the relationship between resistivity and temperature is approximately linear over a wide range of temperatures.

For other materials, a power relationship works better.

ρ = ρ0(T/T0)μ

The resistivity of a conductor increases with temperature. In the case of tungsten, the relationship between resistivity and temperature is best described by a power relationship.

miscellaneous

magnetoresistance

photoconductivity

liquids

electrolytes

gases

dielectric breakdown

plasmas

microphones

A carbon microphone is a backward nothing

Microphones and how they work
type sounds produce
changes in…
which cause
changes in…
which result in
changes in…
carbon granule density resistance voltage
condenser plate separation capacitance voltage
dynamic coil location flux voltage
piezoelectric compression polarization voltage