The Henry (H): SI Unit of Inductance

The henry (H) quantifies how effectively a conductor stores magnetic energy when current flows. This article connects formal SI definitions with engineering intuition, from analytical coil models to modern power-electronic converters. Use it alongside the weber guide, the tesla overview, and calculators like the LC resonant frequency solver when translating inductance targets into hardware.

Definition and Dimensional Form

ISO 80000-6 defines inductance L via the relation between flux linkage Λ and current I:

Λ = L · I.

Flux linkage is the total magnetic flux Φ linked by all turns of a conductor. For a single-turn loop, Λ = Φ. The SI unit of inductance is the henry, symbol H. Expressed through base units,

1 H = 1 Wb·A⁻¹ = 1 kg·m²·s⁻²·A⁻².

A component has an inductance of 1 H if a current change of 1 A per second induces an electromotive force of 1 V. This equivalently describes energy storage E = ½ L I². Maintaining SI notation and consistent symbols keeps multi-domain simulations—electrical, magnetic, and thermal—internally coherent.

Historical Context and Standardization

Origins of inductance measurement

Joseph Henry and Michael Faraday independently discovered electromagnetic induction in the early 1830s. Henry’s studies of self-inductance in long wire coils and telegraph relays informed the eventual naming of the unit in his honour. By the late 19th century, AC power systems demanded accurate inductance values for reactance calculations, prompting precision bridge circuits that compared inductors against capacitors and resistors.

Adoption into the SI

The International Electrotechnical Commission formalized the henry in the 1930s within the MKSA framework. Its inclusion in the 1960 SI launch cemented the henry as a derived unit coherent with the weber, volt, and ampere. Modern realizations rely on calculable inductors, coaxial resistors, and quantum-accurate voltage and resistance standards. The 2019 SI update reinforced these links by fixing the elementary charge and Planck constant, ensuring that inductance dissemination aligns with the ISO terminology adopted globally.

Conceptual Foundations

Magnetomotive force and reluctance

Magnetic circuits often analogize inductors to resistors: magnetomotive force (mmf) F = N·I drives flux through reluctance ℛ. The flux is Φ = F / ℛ, with ℛ determined by path length ℓ, permeability μ, and area A:

ℛ = ℓ / (μ A).

Combining these yields L = N² / ℛ. The henry therefore encapsulates geometry, material properties, and turn count. This framework supports quick design iteration: adjust ℓ, A, or μ to achieve target inductance while respecting saturation limits described in the tesla article.

Energy and dynamics

Inductors resist changes in current. The governing differential equation for a series RL circuit is V = L (dI/dt) + R I. Solving yields exponential current build-up with time constant τ = L / R, analogous to the RC constant in capacitive systems. In sinusoidal steady state, inductive reactance is XL = ωL. These relationships highlight why the henry is central to filter design, resonant converters, and electromagnetic interference mitigation.

Mutual inductance and coupling

Two circuits exhibit mutual inductance M when current in one induces flux linking the other. The induced voltage is U₂ = −M (dI₁/dt). The coupling coefficient k = M / √(L₁ L₂) quantifies linkage quality. Transformers and wireless power transfer devices engineer M via core materials and coil geometry. Expressing M and L in henries clarifies efficiency targets, leakage inductance budgets, and resonance tuning.

Measurement and Realization

Primary standards

  • Calculable coaxial inductors: Precisely machined coaxial cylinders produce an inductance determined by geometry and permeability of free space. These standards anchor national measurement systems.
  • AC bridges: Maxwell-Wien and Hay bridges compare unknown inductors to resistors and capacitors whose values trace to quantum Hall and Josephson standards.
  • Impedance analyzers: Vector network analyzers calibrated with traceable standards measure L across frequency, enabling characterization of parasitic capacitance and core losses.

Practical measurement techniques

  • Time-domain methods: Apply a current ramp and integrate the resulting voltage to recover L via L = V / (dI/dt). Ensure the ramp avoids core saturation and respects the volt-second limits detailed in the weber article.
  • Resonant techniques: Form an LC tank with a known capacitor, measure resonant frequency, and compute L = 1 / (ω² C). The LC calculator streamlines this approach for laboratory and classroom use.
  • Impedance spectroscopy: Frequency sweeps reveal where core losses or skin effect alter effective inductance. Document conditions—temperature, excitation amplitude, frequency range—to maintain reproducibility.

Conditioning measurement signals often relies on resistor networks and buffering. The Ohm's law voltage calculator converts sensed currents and resistances into usable voltages, while the Ohm's law power calculator ensures that measurement resistors and shunts dissipate heat safely.

Applications and Case Studies

Power electronics

DC-DC converters rely on inductors to temporarily store energy. Designers choose L to shape current ripple ΔI = VL · Δt / L. High-frequency operation shrinks inductance requirements but magnifies core and copper losses. Selecting materials with high saturation flux density and low coercivity balances efficiency with compactness.

Signal integrity and filtering

Inductors in radio-frequency filters, matching networks, and chokes suppress interference and shape spectra. Accurate henry-level values ensure filter poles land where intended. Surface-mount inductors include parasitics—series resistance, inter-winding capacitance—that must be modeled when approaching gigahertz frequencies.

Electromechanical systems

Solenoids, relays, and actuators convert electrical energy into mechanical motion. Inductance dictates response time and force: higher L smooths current but slows actuation. Designers simulate coupled electrical and mechanical domains, aligning henry-based models with flux distributions discussed in the weber companion article.

Metrology and research

Laboratories developing superconducting magnets or qubit control lines require inductance measurements with parts-per-million accuracy. Documenting L, its uncertainty, and temperature coefficients allows reproducibility across facilities. Reporting results in henries, millihenries (mH), or nanohenries (nH) with SI prefixes maintains clarity.

Importance and Best Practices

Treat the henry as the anchor linking magnetic, electrical, and energetic viewpoints. Always specify operating frequency, current range, temperature, and waveform when publishing inductance values. Provide uncertainty budgets and measurement methods so colleagues can replicate results. Cross-reference voltage, flux, and current analyses—using the volt, weber, and ampere articles—to maintain a holistic view. Doing so supports robust designs, compliance with ISO standards, and the creation of educational resources that future engineers can trust.