The Physics
Opus in profectus

Electric Resistance

search icon



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


Fancy version (the magnetohydrodynamic version?)…

J ∝ E

J = σE  ⇐ 
ρ = 1
 ⇒  E = ρ J

Welcome to symbol hell…

Electrical properties
quantity symbol unit symbol property of…
resistance R ohm Ω objects
conductance G siemens S
resistivity ρ ohm meter Ωm 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.


Bad booze rots our young guts but vodka goes well.

Better build roof over your garage before van gets wet.

Marking codes for resistors and capacitors
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      


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

R = ρℓ

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 =  ne2


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]


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

Conducting polymers.

Resistivity of selected materials (~300 K)
(Note the difference in units between metals and nonmetals.)
metals ρ (nΩ m) nonmetals ρ (Ω m)
aluminum 26.5 aluminum oxide (14 °C) 1 × 1014
brass 64 aluminum oxide (300 °C) 3 × 1011
chromium 126 aluminum oxide (800 °C) 4 × 106
copper 17.1 carbon, amorphous 0.35
gold 22.1 carbon, diamond 2.7
iron 96.1 carbon, graphite 650 × 10−9
lead 208 indium tin oxide, thin film 2000 × 10−9
lithium 92.8 germanium 0.46
mercury (0 °C) 941 pyrex 7740 40,000
manganese 1440 quartz 75 × 1016
nichrome 1500 silicon 640
nickel 69.3 silicon dioxide (20 °C) 1 × 1013
palladium 105.4 silicon dioxide (600 °C) 70,000
platinum 105 silicon dioxide (1300 °C) 0.004
plutonium 1414 water, liquid (0 °C) 861,900
silver 15.9 water, liquid (25 °C) 181,800
solder 150 water, liquid (100 °C) 12,740
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    


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))

Scatterplot showing the resistivity of copper at various temperatures with a line of best fit added

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

Scatterplot showing the resistivity of tungsten at various temperatures with a power curve fit added

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







dielectric breakdown



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