Abohm: CGS Electromagnetic Resistance Unit
The abohm (abΩ) is the unit of electrical resistance in the CGS electromagnetic (EMU) system. It is defined so that a potential difference of one abvolt drives a current of one abampere through a conductor. Because 1 abvolt equals 10−8 volt and 1 abampere equals 10 ampere, the abohm corresponds to 10−9 ohm.
Converting abohm values to ohms is essential when digitising historical circuit schematics or comparing early telegraph resistance measurements with modern instrumentation. Multiply abohm values by 10−9 to obtain ohms, or multiply ohms by 109 to express them in abohm.
Definition and Conversion
Resistance in CGS-EMU adheres to Ohm’s law formulated as V = I × R, where V is in abvolt, I in abampere, and R in abohm. Translating to SI units gives:
1 abΩ = 10−9 Ω.
This scaling reveals why practical engineers quickly favoured the ohm: most everyday resistances are far larger than 10−9 Ω, making abohm inconveniently small for routine work. Nevertheless, the unit remains useful when studying very low-resistance contacts or superconducting transitions in legacy literature.
Historical Development
The abohm was formalised during the late nineteenth-century International Electrical Congresses. Researchers sought a coherent set of electromagnetic units tied to mechanical dimensions, leading to the CGS-EMU system. While practical units (ohm, volt, ampere) soon dominated industrial applications, laboratories and theorists continued to publish in CGS terms well into the twentieth century.
Standards laboratories maintained conversion tables so that resistances calibrated with mercury columns or manganin coils could be compared across unit systems. Understanding abohm nomenclature remains important when reading early metrology reports and telegraph design manuals.
Conceptual Foundations
Relationship with Abampere and Abvolt
Because CGS-EMU defines resistance via abampere and abvolt, converting to SI always involves scaling both current and voltage. For example, a circuit described as 5 abΩ with 3 abA flowing experiences 15 abV (1.5 × 10−6 V) of drop. Translating these values ensures compatibility with SI instrumentation.
Magnetic Interpretation
CGS electromagnetism emphasises the magnetic effects of currents. Expressing resistance in abohm keeps Maxwell’s equations symmetric when written with centimetre and gram base units, simplifying certain theoretical derivations.
Connection to Conductivity
The reciprocal of abohm is absiemens, equivalent to 109 siemens. Converting conductivity data therefore requires the same scaling factors. The siemens explainer elaborates on how conductance links to resistance units.
Applications
Telegraphy and Early Power Systems
Nineteenth-century telegraph engineers documented line resistances in abohm, particularly when comparing very short or heavy-gauge conductors. Modern historians convert those values into ohms to evaluate signal attenuation and copper usage.
Low-Resistance Measurements
Some superconductivity and cryogenic research papers adopt CGS-EMU to simplify theoretical expressions. Translating abohm to ohm clarifies how near-zero resistance states compare to modern measurement capabilities.
Education and Standards History
Comparing abohm with ohm helps students appreciate why the international community transitioned to SI. Examining conversion factors highlights the benefits of base units tied to invariant constants, as demonstrated by the 2019 SI redefinition.
Importance Today
Although rarely used in practice, the abohm persists in archival documents and in theoretical discussions that favour CGS formulations. Professionals digitising heritage schematics or comparing textbooks should be comfortable with the 10−9 conversion to maintain accuracy.
Revisiting CGS-EMU units like the abohm also underscores the interconnectedness of current, voltage, and resistance definitions. This historical perspective enriches modern work with SI-based instrumentation and modelling.