# Self Inductance

### - basic information about self-inductance, how it occurs, the basic self-inductance formula and associated calculations.

### In this section

Inductance is defined as the magnetic induction of a voltage in a current carrying wire when the current in a wire changes. This can occur in the same wire and additionally in another wire.

In the case of self-inductance, the magnetic field created by a changing current in the circuit induces a voltage in the same wire or circuit - in other words any voltage is self-induced.

## Self-inductance definition

Self-inductance can be defined as:

- the phenomenon in which a change in electric current in a circuit produces an induced electro-motive-force in the same circuit.

In terms of the units the following self-induction definition may be applied:

- The self-inductance of a coil is said to be one henry if a current change of one ampere per second through a circuit produces an electro-motive force of one volt in the circuit.

## Self-inductance basics

When current passes along a wire, and especially when it passes through a coil or inductor, a magnetic field is induced. This extends outwards from the wire or inductor and could couple with other circuits. However it also couples with the circuit from which it is set up.

The magnetic field can be envisaged as concentric loops of magnetic flux that surround the wire, and larger ones that join up with others from other loops of the coil enabling self-coupling within the coil.

When the current in the coil changes, this causes a voltage to be induced the different loops of the coil - the result of self-inductance.

In terms of quantifying the effect of the inductance, the basic formula below quantifies the effect.

Where:

VL = induced voltage in volts

N = number of turns in the coil

dφ/dt = rate of change of magnetic flux in webers / second

The induced voltage in an inductor may also be expressed in terms of the inductance (in henries) and the rate of change of current.

## Lenz's law and self-induction

It can be seen from the formula that the voltage induced by a change in current is in the opposite sense to the change in current. Any current induced in a conductor will oppose the change in current that caused the change in flux.

This is effectively what Lenz's law states because an induced current has a direction such that its magnetic field opposes the change in magnetic field that induced the current.

Lenz's law states that an induced electromotive force, EMF gives rise to a current whose magnetic field opposes the original change in magnetic flux.

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