Inductance is a property of an electrical circuit or component that quantifies the relationship between magnetic flux linkage and current and describes the opposition to changes in current through the associated magnetic field. It is represented by L and measured in henries, H. For an ideal linear inductor, the flux linkage is proportional to current and the voltage is given by v = L di/dt under the passive sign convention.
The stored magnetic energy is U = ½LI² for an ideal linear inductor. Inductance arises because current produces a magnetic field, and changes in that field induce an electromotive effect that opposes the change responsible for it. The concept therefore links circuit theory directly to electromagnetic fields. A physical inductor can be made from a coil of wire, often with an air, ferrite, iron or other magnetic core.
Self-inductance describes the induced voltage in a circuit caused by changes in its own current, whereas mutual inductance describes coupling between two circuits through shared magnetic flux. For a simple ideal inductor, increasing current produces increasing magnetic flux linkage, and changing current produces a voltage proportional to the rate of change. The polarity of the induced voltage follows Lenz's law and acts to oppose the change in current.
This does not mean that the inductor always opposes current itself; a steady current through an ideal inductor can continue with zero voltage across it after the transient has ended. The distinction between opposing current and opposing changes in current is therefore fundamental. Mutual inductance provides the operating principle for transformers, coupled inductors and many wireless power-transfer arrangements.
The inductance of a coil depends on geometry, number of turns, dimensions, magnetic path and core properties. Increasing the number of turns generally increases inductance substantially, while a magnetic core with high effective permeability can increase inductance compared with an air-core coil. The simple formulas used for ideal solenoids assume suitable geometry and magnetic conditions and may not accurately predict practical components with leakage flux, core gaps or complex shapes.
A deliberately introduced air gap can reduce effective permeability and allow an inductor to store more magnetic energy without excessive core saturation, which is important in power inductors. Winding arrangement, conductor resistance, parasitic capacitance and core losses also affect practical performance. Inductance is therefore not determined solely by the number of turns; the entire electromagnetic geometry matters.
Inductors have a frequency-dependent impedance. For an ideal inductor, impedance is Z_L = jωL, so the magnitude of inductive reactance increases with frequency. In sinusoidal steady-state operation, current through an ideal inductor lags voltage by 90 degrees under the passive sign convention. This contrasts with a capacitor, where current leads voltage. Inductors and capacitors can therefore exchange energy between magnetic and electric fields, producing resonance in LC circuits.
At low frequencies, an inductor can appear relatively close to a short circuit after transient effects settle, while at higher frequencies its reactance becomes larger. Real inductors depart from the ideal model because winding resistance, core losses, parasitic capacitance and frequency-dependent material behaviour become important. At sufficiently high frequency, an inductor can approach or pass its self-resonant frequency and cease to behave like a simple inductance.
Inductance is particularly important in transient circuits because an inductor resists abrupt changes in current. If an ideal inductor carrying current is suddenly disconnected, maintaining the same current would require an arbitrarily large voltage in the ideal mathematical model. Real circuits limit the voltage through parasitic capacitance, arcing, semiconductor paths, snubber networks or other mechanisms. This behaviour is why relay coils, motors and other inductive loads can generate substantial voltage transients when switched off.
Flyback diodes, transient suppressors, RC snubbers and other protection circuits provide controlled paths for the stored magnetic energy. The energy stored in an inductor depends on current squared, so large-current inductors can contain significant energy even when their terminal voltage is modest during steady operation.
Inductors are used in filtering, energy conversion, power supplies, motors, transformers, radio-frequency circuits and electromagnetic interference suppression. In switching converters, inductors transfer and temporarily store energy as current changes according to the converter topology. In LC filters, inductors and capacitors interact to attenuate selected frequency ranges. Common-mode chokes use magnetic coupling to impede unwanted common-mode currents while allowing desired differential-mode current to pass with relatively low impedance.
Transformers rely on mutual inductance rather than direct electrical connection between windings and can change voltage and current levels while providing electrical isolation. Motors contain inductive windings whose magnetic fields interact with other magnetic fields to produce torque. The practical use of inductance therefore spans both low-frequency power engineering and high-frequency electronics.
Magnetic core behaviour introduces important limitations. Ferromagnetic cores can exhibit saturation, hysteresis and frequency-dependent losses. Saturation occurs when increasing current produces progressively less additional magnetic flux because the core approaches the limits of its magnetic response. Once saturation occurs, effective inductance can fall substantially, causing current to rise rapidly and potentially overheat the winding or switching device. Hysteresis represents energy loss associated with repeated magnetisation cycles, while eddy currents can produce additional heating in conductive magnetic materials.
Ferrites are widely used at higher frequencies because their electrical resistivity reduces eddy-current losses compared with many bulk conductive magnetic materials. Powdered iron and other core materials have different permeability, saturation and loss characteristics. Component selection therefore requires consideration of current, frequency, temperature and magnetic operating conditions.
Inductance should be distinguished from inductive reactance, impedance and magnetic flux. Inductance is a property measured in henries, while inductive reactance is the frequency-dependent opposition represented by ωL for an ideal inductor. Impedance includes both resistance and reactance, whereas inductance specifically describes magnetic energy storage and flux linkage behaviour. An inductor can have significant winding resistance, so a practical component is better represented by a combined model rather than an ideal L alone.
Parasitic capacitance between turns also creates a self-resonant frequency. Above that frequency, the component's behaviour can become predominantly capacitive. These distinctions matter in RF design, power electronics and measurement because a component labelled with a particular inductance value does not necessarily behave as a pure inductor across all frequencies, currents and temperatures.
