Ohm
Georg Ohm taught mathematics at a gymnasium in Cologne and measured currents in wires in the evenings. The batteries of the time ran down quickly, so in 1826 he took a thermocouple: one junction in boiling water, the other in melting ice. It gave a steady voltage. Ohm swapped wires of different lengths and watched how far the magnetic needle above the wire was deflected.
In 1827 he described the law: the current is proportional to the voltage and inversely proportional to the resistance. The book was received coldly; recognition came to Ohm only some fifteen years later. One ohm is the resistance at which a voltage of 1 V drives a current of 1 A. A kettle element is about 26 Ω, a resistor on a circuit board thousands of ohms.
| Notation | Ω |
| Definition | volt per ampere · V/A · kg·m²·s⁻³·A⁻² |
| Reference values | R_K — 25 812.807 45 Ω · international ohm — 1.000 49 Ω · impedance of free space — 376.73 Ω |
| Introduced | 1861, British Association · international ohm 1881 · in the SI since 1960 |
| Standards | ISO 80000-6 · IEC 60062 · SI Brochure 9th ed. |
| Typical values | 17 mΩ — a metre of 1 mm² copper wire · 26 Ω — a kettle element · 4.7 kΩ — a resistor on a board |
01 · Definition
A volt for every ampere
Resistance R shows what voltage is needed to drive a current of one ampere through a conductor. One ohm is one volt per ampere. Electrons in a metal keep colliding with the vibrating atoms of the lattice and give them energy. That is why a wire carrying current heats up.
The resistance of a wire grows with its length and falls with its thickness. It also depends on the material: nichrome resists 65 times more than copper. In metals resistance rises when heated, while in carbon it falls slightly.
How to read a resistor by its bands
Digits cannot be printed on a tiny resistor, so the value is painted as rings. The first two bands are digits, the third is the multiplier, the fourth, set apart, is the tolerance. Black means 0, brown 1, red 2, and so on through the rainbow to white 9. Choose the colours, and the value with its tolerance limits appears below.
The resistance of a wire equals the resistivity of the material multiplied by the length and divided by the cross-section. A hundred metres of copper wire with a 1 mm² cross-section is 1.7 Ω. A 2 kW kettle element at 230 V is about 26 Ω: it is made of nichrome, thin and short.
When Ohm's law holds, and when it does not
On the left is a laboratory power supply: up to 24 V, with the current limited to ten amperes. A wire is stretched between two clamps. The current heats it, and the heat makes it sag, glow red, then yellow, and it may melt. On the right a magnifier shows what is inside: the violet dots are lattice atoms, which shake harder the hotter the metal is; the turquoise ones are electrons, and a flash is a collision. You can lower the wire into water: there it will not heat above 100 °C. Time in the scene runs four times faster.
Move the voltage and watch the wire heat up.
02 · Conversion
| Unit | Value | Where it is met |
|---|---|---|
| {n} | {v} | {note} |
A 60 W lamp filament resists about 880 Ω when hot, and thirteen times less when cold.
The siemens is the reciprocal: a conductance of 1 S means a resistance of 1 Ω, and 1 mS means 1 kΩ.
A superconductor has exactly zero resistance: a current in a ring made of it flows for years with no source.
03 · Orders of magnitude
04 · Measuring instruments
05 · Writing rules
06 · Neighbouring units
07 · Historical section
The international ohm of 1893 is the resistance of a column of mercury 106.3 cm long with a mass of 14.4521 g at 0 °C, that is, with a cross-section of about 1 mm². Mercury was used because it is easy to purify and to fill into a tube in the same way in any laboratory. It later turned out that this ohm was 0.049 % larger than today's.
Since 1990 the ohm has been kept with the quantum Hall effect. In a thin film in a strong magnetic field and at deep cold, the Hall resistance settles on even steps R_K/i. The von Klitzing constant R_K = h/e² equals 25 812.807 45 Ω, and since 2019 this number has been exact.
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