Inductances

Inductance is a property of electrical conductors and components that causes an electromotive force to be induced in proportion to the rate of change of current through them. It is measured in henries (H). An inductor is a component designed to provide inductance, typically consisting of a coil of wire that creates a magnetic field when current passes through it.

The defining relationships are based on flux linkage. The inductance L is equal to the flux linkage per unit current, L = λ / I, where λ = NΦ is the total flux linkage (N is the number of turns and Φ is the magnetic flux in each turn). In a simple self-inductance scenario, the voltage across the inductor satisfies v = L di/dt. When two coils are magnetically linked, mutual inductance M describes the induced voltage in one coil due to the current in the other: v1 = M di2/dt and v2 = M di1/dt. The coupling coefficient k, ranging from 0 to 1, relates M to the self-inductances L1 and L2 via M = k sqrt(L1 L2).

Inductance depends on geometry and magnetic material. For a long solenoid with a core of permeability μ, L = μ N^2 A / l, where A is cross-sectional area and l is length. Materials range from air to ferrites and laminated or powdered iron; cores affect saturation and losses. Energy stored in an inductor is E = (1/2) L I^2.

Inductors have parasitics that affect high-frequency behavior, such as equivalent series resistance (ESR), equivalent series inductance (ESL), and a self-resonant frequency where parasitic capacitance dominates. Applications include filters, chokes to block AC or noise, energy storage in power supplies, and transformers that rely on mutual inductance to transfer energy between windings.