Introduction

An inductor is a device -- typically a coil, a solenoid, or a toroid -- used specifically to store energy in a magnetic field when an electric current flows through it, playing a role in circuits parallel to how a capacitor stores energy in an electric field. Inductance is the general property of such inductors to generate an emf in response to a changing current: either the change of current in the SAME circuit (self-induction) or a change of current in a magnetically-linked NEIGHBOURING circuit (mutual induction), both developed formally in the sections that follow.

An electric current flowing through a coil sets up its own magnetic field, and since this field's lines pass back through the same coil, the coil's magnetic flux is linked with itself. If this self-linked flux is changed (by changing the current), an emf is induced right there in the very coil carrying that changing current -- this is self-induction, and the emf induced is the self-induced emf. Because the total flux linkage $N\Phi_B$ of a coil is directly proportional to the current i flowing in it, $N\Phi_B\propto i$, i.e.

where the constant of proportionality L is called the self-inductance (or coefficient of self-induction) of the coil, given by $L=N\Phi_B/i$. Setting $i=1$ A shows that self-inductance equals the flux linkage produced by unit current: the self-inductance of a coil is the flux linkage with the coil when a current of 1 A flows through it.

When the current i changes with time, Faraday's law (with Lenz's minus sign) gives the self-induced emf as $\varepsilon = -d(N\Phi_B)/dt = -d(Li)/dt$; if L itself is constant (as it is for a rigid coil of fixed geometry), this simplifies to

The negative sign shows that the self-induced emf always opposes the change in current with respect to time -- setting $di/dt=-1\ \text{A/s}$ gives $L=-\varepsilon$, so inductance is also defined as the opposing emf induced when the current through the coil changes at the rate of 1 A/s.

The SI unit of inductance (a scalar quantity) is the henry (H): $1\ \text{H} = 1\ \text{Wb A}^{-1} = 1\ \text{V s A}^{-1}$, with dimensional formula $\text{M L}^2\text{T}^{-2}\text{A}^{-2}$. Combining the two defining relations, a coil has inductance exactly 1 H if a current of 1 A produces a flux linkage of 1 Wb-turn in it, and equally if a current changing at 1 A/s induces an opposing emf of exactly 1 V. …