Electric Resistance
Discussion
introduction
Yech! What a mess this is.
Conduction: S. Gray, 1729 — Resistance: Georg Simon Ohm, 1827.
Regular version…
I ∝ ΔV
| I = | V | ⇒ | V = IR | ⇒ | R = | V |
| R | I |
quantity: resistance R
unit: ohm [Ω] Georg Ohm (1787–1854) Germany
| ⎡ ⎢ ⎣ |
Ω = | V | = | J/C | = | J/A s | = | J | = | kg m2/s2 | = | kg m2 | ⎤ ⎥ ⎦ |
| A | C/s | A | A2 s | A2 s | A2 s3 |
Reciprocal version…
I ∝ ΔV
| I = GV | ⇒ | V = | I | ⇒ | G = | I |
| G | V |
quantity: conductance G
unit: siemens [S] Werner von Siemens (1816–1892) Germany
| G = | 1 |
| R |
| ⎡ ⎢ ⎣ |
S = | A | ⎤ ⎥ ⎦ |
| V |
| ⎡ ⎢ ⎣ |
S = | 1 | ⎤ ⎥ ⎦ |
| Ω |
Fancy version (the magnetohydrodynamic version?)…
J ∝ E
| J = σ E | ⇐ |
|
⇒ | E = ρ J |
Welcome to symbol hell…
| quantity | symbol | SI unit | symbol | property of… |
|---|---|---|---|---|
| resistance | R | ohm | Ω | objects |
| conductance | G | siemens | S | |
| resistivity | ρ | ohm meter | Ω m | materials |
| conductivity | σ | siemens per meter | S/m |
Ohm's law isn't a 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.
| color | digit | multiplier | tolerance | tcr (10−6/K) | |
|---|---|---|---|---|---|
| none | ±20% | ||||
| pink | 10−3 | ||||
| silver | 10−2 | ±10% | |||
| gold | 10−1 | ±5% | |||
| black | 0 | 100+ | ±250 | ||
| brown | 1 | 101+ | ±1% | ±100 | |
| red | 2 | 102+ | ±2% | ±50 | |
| orange | 3 | 103+ | ±0.05% | ±15 | |
| yellow | 4 | 104+ | ±0.02% | ±25 | |
| green | 5 | 105+ | ±0.50% | ±20 | |
| blue | 6 | 106+ | ±0.25% | ±10 | |
| violet | 7 | ±0.10% | ±5 | ||
| gray | 8 | ±0.01% | ±1 | ||
| white | 9 | ||||
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.
(Note the difference in units between metals and nonmetals.)
| metals | ρ (nΩ m) |
|---|---|
| aluminum | 26.5 |
| brass | 64 |
| chromium | 126 |
| copper | 17.1 |
| gold | 22.1 |
| iron | 96.1 |
| lead | 208 |
| lithium | 92.8 |
| mercury (0 °C) | 941 |
| manganese | 1440 |
| nichrome | 1500 |
| nickel | 69.3 |
| palladium | 105.4 |
| platinum | 105 |
| plutonium | 1414 |
| silver | 15.9 |
| solder | 150 |
| steel, plain | 180 |
| steel, stainless | 720 |
| tantalum | 131 |
| tin (0 °C) | 115 |
| titanium (0 °C) | 390 |
| tungsten | 52.8 |
| uranium (0 °C) | 280 |
| zinc | 59 |
| nonmetals | ρ (Ω m) |
|---|---|
| aluminum oxide (14 °C) | 1 × 1014 |
| aluminum oxide (300 °C) | 3 × 1011 |
| aluminum oxide (800 °C) | 4 × 106 |
| carbon, amorphous | 0.35 |
| carbon, diamond | 2.7 |
| carbon, graphite | 650 × 10−9 |
| indium tin oxide, thin film | 2000 × 10−9 |
| germanium | 0.46 |
| pyrex 7740 | 40,000 |
| quartz | 75 × 1016 |
| silicon | 640 |
| silicon dioxide (20 °C) | 1 × 1013 |
| silicon dioxide (600 °C) | 70,000 |
| silicon dioxide (1300 °C) | 0.004 |
| water, liquid (0 °C) | 861,900 |
| water, liquid (25 °C) | 181,800 |
| water, liquid (100 °C) | 12,740 |
| foods | ρ (Ω m) |
|---|---|
| apple | 17.9–26.3 |
| beer | 5.56–7.7 |
| bread crumb | ~57 |
| butter | ~12.5 |
| cucumber | 43.5 |
| fruit juices | 2.5–5.0 |
| milk, fresh | 1.67–2.75 |
| milk, sour | 1.25–1.60 |
| pear | 37.0–71.4 |
| potato | 26.3–27.0 |
| root vegetables | 24.4–66.7 |
| syrups | 16.7–25.0 |
| tomato | 35.7 |
| wheat, 10% moisture | ~108 |
| wheat, 24% moisture | ~104 |
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 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.
see also: superconductivity
miscellaneous
magnetoresistance
photoconductivity
liquids
electrolytes
gases
dielectric breakdown
plasmas
microphones
A carbon microphone is a backward nothing
| 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 |