The Ohm (Ω): Unit of Electrical Resistance

Overview

The ohm (Ω) is the SI derived unit of electrical resistance. In ISO 80000‑6 the quantity symbol is R (or Z for complex impedance), with the unit symbol Ω. Resistance quantifies how strongly a component opposes current for a given voltage. Formally,

1 Ω = 1 V·A⁻¹ = 1 kg·m²·s⁻³·A⁻².

The reciprocal unit is the siemens (S) for conductance. Use the Ohm's Law Resistance calculator and the parallel resistance tool to see how these reciprocal relationships play out in practice.

Historical Development and Formalization

From empirical law to quantum standard

Georg Simon Ohm established the proportionality U = IR in the 1820s, enabling resistance as a measurable quantity. The practical “ohm” emerged in 19th‑century telegraphy and standardization efforts. In modern SI, resistance is realized via the quantum Hall effect (QHE): in two-dimensional electron systems at low T and high B, the Hall resistance is quantized

R_H = R_K / i,   R_K = h / e²,

with integer i. Since 2019 h and e are fixed constants, R_K is exact, making QHE devices the primary standard of the ohm. This ended the era of artifact-based standards and earlier “conventional” values. Compare this traceability ladder with the Josephson-based volt to understand how electrical units align around fixed constants.

Conceptual Foundations

DC resistance, AC impedance, and materials parameters

• Ohmic behavior: For linear elements, R = U/I. Power P = I²R = U²/R sets thermal management limits. Validate these relationships with the Ohm's Law Power calculator and the watts to amps converter.
• Impedance: In AC, Z = R + jX combines resistance and reactance; magnitude |Z| = U/I with phase defines dynamics. Explore impedance breakdowns using the RC time constant tool and motor-focused calculators on the tesla page.
• Resistivity and geometry: R = ρ·L/A (Ω·m); conductivity σ = 1/ρ (S·m⁻¹). Temperature coefficients (TCR) and magnetoresistance describe dependence on T and B. Link these parameters with the resistor color code calculator to select components accurately.
• Johnson–Nyquist noise: A resistor at temperature T has voltage-noise spectral density S_V = 4k_BTR, linking resistance to thermodynamic noise floors.

Coherence with SI

Ohm’s law couples the ohm tightly to volt and ampere; derived quantities such as time constants (τ = RC), skin depth, and power dissipation follow without extra conversion factors when SI is used consistently. Reference the volt explainer and the ampere guide whenever you propagate units through circuit calculations.

Realization, Calibration, and Traceability

Primary and dissemination routes

• Quantum Hall standards: Provide exact values of R = R_K/i.
• Transfer standards: Wire-wound and thin-film standard resistors (1 Ω, 10 kΩ, etc.) disseminate the unit; stability and low TCR are critical.
• Cryogenic current comparators (CCC): Achieve sub-ppm comparisons and build resistor networks (Hamon dividers) with minimal ratio error.

Measurement techniques

• Low-ohm (µΩ–mΩ): Four-terminal (Kelvin) connections remove lead/contact resistance; high currents and thermal EMF cancellation improve accuracy.
• High-ohm (MΩ–TΩ): Guarded electrometers and high-resistance bridges mitigate leakage; humidity and surface contamination dominate errors.
• AC impedance: Bridge methods and vector network analysis require modeling parasitic L/C and frequency dependence.

Pair these methods with tools like the USB voltage drop calculator and the voltage divider calculator to anticipate measurement loading and wiring losses.

Applications

Power and energy systems

Shunt resistors enable accurate current measurement in converters and battery systems. Grounding and bonding specifications (mΩ) ensure safety. Resistive losses (I²R) drive efficiency and thermal design across grids and vehicles. Use the battery charge time calculator and horsepower to watts converter to translate resistance data into system-level planning.

Electronics and sensing

Precision RTDs (e.g., Pt100) convert temperature to resistance; strain gauges transduce mechanical strain via resistive changes; mixed-signal ICs rely on matched on-chip resistors for gain accuracy and linearity. Reinforce these practices with the resistor color code helper and by cross-referencing the Kelvin explainer when relating resistance to temperature.

Materials and physics

Characterizing semiconductors, superconductors, and quantum materials hinges on resistivity vs temperature and field; four-probe and Hall measurements reveal carrier densities and mobilities. Link these explorations to the tesla unit discussion and to the ISO 80000-10 summary where electromagnetic constants intersect.

Good Practice and Common Pitfalls

• Use four-wire methods for low-ohm work; avoid 2-wire errors from lead/contact resistance.
• Control self-heating and thermoelectric EMFs; reverse current for DC measurements.
• Specify temperature, frequency, and measurement bandwidth; resistance is not monolithic across conditions.
• For precision networks, consider tolerance, drift, TCR, and voltage coefficient.

Why the Ohm Matters

The ohm translates voltage limits and current demands into tangible power, heat, and signal integrity constraints. ISO 80000‑6’s unified symbols and the SI’s quantum realization make resistance measurements traceable from national labs to production lines, ensuring that a “1 kΩ” part or a “100 mΩ” shunt means the same thing everywhere—in design equations, compliance tests, and field performance. Use this wrap-up with the volt, ampere, and tesla guides plus calculators like the Ohm's Law Voltage solver to maintain SI coherence from component selection to field diagnostics.