29 Inductance
Inductance is the ability of an inductor to store energy and it does this in the magnetic field that is created by the flow of electrical current. Energy is required to set up the magnetic field and this energy is released when the field falls. As a result of the magnetic field associated with the current flow, inductors generate an opposing voltage proportional to the rate of change in current in a circuit. Inductance is caused by the magnetic field generated by electric currents flowing within an electrical circuit. Typically coils of wire are used as a coil increases the coupling of the magnetic field and increases the effect.
There are two ways in which inductance is used:
Self-inductance: Self-inductance is the property of a circuit, often a coil, whereby a change in current causes a change in voltage in that circuit due to the magnetic effect caused by the current flow. It can be seen that self-inductance applies to a single circuit — in other words it is an inductance, typically within a single coil. This effect is used in single coils or chokes.
Mutual-inductance: Mutual inductance is an inductive effect where a change in current in one circuit causes a change in voltage across a second circuit as a result of a magnetic field that links both circuits. This effect is used in transformers.
29.1 Unit Definition
When indicating an inductor on a circuit diagram or within an equation, generally the symbol “L” is used. On circuit diagrams, inductors are generally numbered, L1, L2, etc.
The SI unit of inductance is the henry, H which can be defined in terms of rate of change of current and voltage. The inductance of a circuit is one henry if the rate of change of current in a circuit is one ampere per second and this results in an electromotive force of one volt. \(1\mathrm{H} = 1 \mathrm{Wb}/\mathrm{A}\).
29.2 Phenomena
When a current flows within a conductor, whether it be straight or in the form of a coil, a magnetic field builds up around it and this affects the way in which the current builds up after the circuit is made.
In terms of how inductance affects and electrical circuit, it helps to look at the way the circuit operates, first for a direct current (DC), and then for an alternating current (AC). Although they follow the same laws and the same effects result, it helps the explanation, the direct current example is simpler, and then this explanation can be used as the basis for the alternating current case.
29.2.1 Direct current
As the circuit is made the current starts to flow. As the current increases to its steady value the magnetic field it produces builds up to its final shape. As this occurs, the magnetic field is changing, so this induces a voltage back into the coil itself, as would be expected according to Lenz’s Law.
The time constant \(T\) in seconds of the circuit which will include the inductor value \(L\) Henries and the associated circuit resistance, \(R\) Ohms can be calculated as \(T = L/R\). \(T\) is the time for the current \(I\) amps to rise to 0.63 of its final steady state value of V/R. The energy stored in the magnetic field is \(\frac{1}{2}L\,I^2\).
When the current is switched off this means that effectively the resistance of the circuit rises suddenly to infinity. This means that the ratio \(L / R\) becomes very small and the magnetic field falls very rapidly. This represents a large change in magnetic field and accordingly the inductance tries to keep the current flowing and a back electromagnetic force (EMF) is set up to oppose this arising from the energy stored in the magnetic field.
When the back EMF is set up, the very high voltages generated mean that sparks can appear across the switch contact, especially just as the contact is broken. This leads to pitted contacts and wear on any mechanical switches. In electronic circuits this back EMF can destroy semiconductor devices and therefore ways of reducing this back EMF are often employed.
29.2.2 Alternating current
For the case of the AC passing through an inductor, the same basic principles are used, but as the waveform is repetitive, we tend to look at the way the inductor responds in a slightly different way as it is more convenient.
By its very nature, an alternating waveform is changing all of the time. This means that the resulting magnetic field will always be changing, and there will always be an induced back EMF produced. The result of this is that the inductor impedes the flow of the alternating current through it as a result of the inductance. This is in addition to the resistance caused but the Ohmic resistance of the wire.
It means that if the Ohmic resistance of the inductor is low, it will pass DC with little loss, but it can present a high impedance to any high frequency signal. This characteristic of an inductor can be used in ensuring that any high frequency signals do not pass though the inductor.
A further aspect of inductance is that the reactance of an inductor and that of a capacitor can act together in a circuit to cancel each other out. This is known as resonance, and it is widely used in bandpass filters.
29.3 Inductors
Inductors are electronic components that use inductance in an electronic circuit. These inductors are normally wound components having many turns of wire to increase the level of inductance. They may also be would on ferromagnetic cores to further increase the level of inductance.
29.3.1 Inductance of Wires and Coils
Straight wires and coils have an inductance. Normally coils are used for inductors because the linking of the magnetic field between the different turns of the coil increases the inductance and enables the wire to be contained within a smaller volume.
If the wire was not coiled, then very long lengths of wire would often be needed making electronic components of this nature not viable. By coiling the wire the inductance is maximised enabling inductors to be incorporated into many electronic circuits.
However, even the inductance of a straight wire can affect some electronic circuits. For most low frequency applications, the inductance of a straight wire can be ignored, but as the frequency increases into the VHF region and beyond, the inductance of the wire itself can become significant, and interconnections need to be kept short to minimise the effects.
Calculations are available to enable the inductance of wires to be calculated quite accurately, but the inductance of coils is a little more complicated and depends upon a variety of factors including the shape of the coil and the constant of the material in and around the coil.
29.3.2 Applications
Inductance is a very important aspect of electronic circuit design. Although inductors are not so widely used in low frequency electronic circuit designs because the size of the electronic components required to give the levels of inductance needed is large, they are widely used for much higher frequencies in radio frequency designs, as well as within EMC — where filtering is used, often using inductors to ensure that any interference is not able to pass along wires and cables. For example a simple form of inductor is often seen on computer cables where a ferrite is added around a cable to add inductance and prevent the signals from travelling along the cable and being transmitted, thereby giving rise to the possibility of interference to other systems.