Resistance Conversion — mΩ · Ω · kΩ · MΩ · GΩ

Georg Simon Ohm (1789-1854) was a Gymnasium physics teacher in Cologne when he performed the experiments that would become Ohm's law. Working with thermoelectric piles (the only stable voltage sources available before Daniell's 1836 cell) and copper wires of various lengths, he discovered the linear relation V = I × R between current, voltage and resistance. His 1827 book Die galvanische Kette, mathematisch bearbeitet ("The galvanic circuit, mathematically treated") laid out the proof — and was initially rejected by the German physics establishment.

Ohm was forced to resign his Cologne teaching post over the controversy and lived in poverty for several years. The Royal Society of London awarded him the Copley Medal in 1841, vindicating his work; Munich appointed him professor in 1849. The unit ohm was adopted at the International Electrical Congress in Chicago in 1893 alongside the volt, ampere, coulomb, farad and henry. The 9th General Conference on Weights and Measures (CGPM) in 1948 codified the ohm as the SI derived unit Ω = V/A = kg·m²·s⁻³·A⁻².

Practical resistance spans 12 orders of magnitude. The lowest values — battery sense shunts at 1 mΩ — require 4-wire Kelvin sensing to remove the few mΩ of lead and contact resistance. Riedon SSA and Vishay LVK foil shunts achieve 0.1% tolerance and 2 ppm/°C TCR. The next decade — copper wire and connectors at Ω level — is tabulated in NEC Chapter 9 Table 8 (resistivity 1.724 × 10⁻⁸ Ω·m for copper, 2.65 × 10⁻⁸ for aluminum at 20 °C).

Pull-up and pull-down resistors at kΩ scale dominate digital logic. The NXP UM10204 I²C specification calls for 10 kΩ pullups on SDA/SCL at 100 kHz (4.7 kΩ for 400 kHz fast mode, 1.5 kΩ for 1 MHz fast-mode-plus). The 100 kΩ MOSFET gate pulldown preset comes from Texas Instruments app-note SLVA642 — safe-off the gate when the driver is high-impedance.

DMM input impedance sits at 10 MΩ on every standard 3½ digit meter (Fluke 87V, Keysight U1233A, Brymen BM857) — high enough to avoid loading 9 V battery circuits but low enough that an ungrounded probe tip floats at ~50 V (Wilson's ghost voltage). High-end 6½-digit instruments (Keysight 34465A, Keithley 2002) offer >10 GΩ input on low-voltage ranges for source-impedance-sensitive measurements.

Insulation resistance enters the GΩ regime. IEEE 43-2013 specifies megger tests at 500 V DC for 600 V class equipment and 1000-5000 V for higher voltages; a pass is ≥1 GΩ for new installations and ≥100 MΩ for in-service equipment. NFPA 70E Article 120 requires verification of de-energized state and absence of ground faults before authorized work begins; the megger turret on the ohmmeter widget links voltage-staircase work to the resistance domain.

Quantum-Hall metrology fixed the ohm exactly in 1990 via the von Klitzing resistance R_K = h / e² = 25,812.80745 Ω. The 2019 SI redefinition turned R_K into a derived exact value, anchoring every resistance reading on this page through h and e to natural constants. From Ohm's 1827 Cologne galvanic-pile experiments through the Weston 280 vintage galvanometer ohmmeter to the modern Keysight 3458A 8½-digit DMM, every ohm on the dial traces back to the same fundamental physics.