henry

SI coherent derived unit with special name and symbol

Name

Symbol

Derived quantity

Expressed in terms of SI base units

henry

inductance

kg m² s⁻² A^-2

Definition

The henry, symbol H, is the SI coherent derived unit of electrical inductance.

One henry is the inductance of an electric circuit when an electric current, that is changing at one ampere per second, results in an electromotive force of one volt across the inductor.

The henry is named after the American scientist Joseph Henry (1797 – 1878).

Inductance

Inductance is a measure of the tendency of an electrical conductor, such as a coil, to oppose a change in the electric current passing through it.

The inductance of a coil depends on its size, the number of turns, and the permeability of the material within and surrounding the coil.

If a current of one ampere flowing through a coil produces flux linkage of one weber turn, the coil has a self inductance of one henry.‌

Faraday’s law of induction

Faraday’s law of induction states that an electromotive force, EMF, or voltage, is induced in a circuit whenever relative motion exists between a conductor and a magnetic field, and that the magnitude of this voltage is proportional to the rate of change of the magnetic flux.

Lenz’s law

Lenz’s law states that the direction of an induced EMF is such that it will oppose the change that is causing it. In other words, the direction of an induced current will oppose the motion or change which caused the induced current. The induced voltage is described as a “back EMF”.

$\mathcal{E} \propto \dfrac{dI}{dt}$

Using SI coherent units, the proportionality constant is the inductance:

$\mathcal{E} = -L \dfrac{dI}{dt}$

where:

ℰ is the back EMF, measured in volts, symbol V,
L is the inductance, measured in henries, symbol H,
^dI⁄_dt is the rate of change of current, measured in amperes per second, symbol A/s,

Thus:

$L = \dfrac {\mathcal{E}} {dI / dt}$

$1\ \text{H} = 1\ \text{V s A}^{-1}$

Faraday’s law states that the EMF is also given by the rate of change of the magnetic flux:

$\mathcal {E} = -\ \dfrac {d \Phi _{\text{B}}} {d t}$

where:

ℰ is the electromotive force, or EMF, measured in volts, symbol V,
Φ_B is the magnetic flux, measured in webers, symbol Wb.

The direction of the electromotive force is given by Lenz’s law.

Mechanical analogy

Inductance in a circuit is analogous to mass in a mechanical system:

electrical system	mechanical system
$\mathcal{E} = -L \dfrac{dI}{dt}$	$F = m \dfrac{dv}{dt}$

where the back EMF, and rate of change of current, are also analogous to force and acceleration:

system	cause of change	=	resistance to change	×	rate of change
electrical	ℰ		–L		^dI⁄_dt
mechanical	F		m		^dv⁄_dt