# 18.21 Inductors and inductance

Before you read this, I suggest you read post 17.44.

In post 16.25, we saw that an electric current produces a magnetic field. So, a current that changes with time produces a changing magnetic field. This effect was observed experimentally by the British scientist Michael Faraday (1791-1867). He also observed the inverse effect – a changing magnetic field causes a current to flow in a conductor. He called this effect electromagnetic induction.

Now let’s think about what happens when the current in a conductor increases. The increase creates a changing magnetic field which causes an additional current to flow in the conductor. This additional current must flow in the opposite direction to the original, increasing current, otherwise the electrical energy (post 17.45) would spontaneously increase which is contrary to the principle of conservation of energy, also called the first law of thermodynamics (post 16.21). The ability of a conductor to oppose changes in the flow of current is called inductance or self-inductance (to distinguish it from the concept of mutual-inductance, that we will meet in a later post).

The potential difference required to counter this effect is proportional to the rate of change of current. In other words, in a conductor, if the rate of change of current doubles, the voltage required to overcome the inductance doubles. And if the rate of change of the current halves, the voltage required to overcome the inductance halves. We can represent this effect by the equation

V = L(dI/dt) = L(d2Q/dt2).

Here, dI/dt represents the rate of change of current with time (post 17.4) and the right-hand side follows because current is defined by I = dQ/dt (post 17.44). L is a constant for a given conductor and is called its inductance. You might expect that inductance would have the units V.s.A-1, since potential difference is measured in volts (V), current is measured in amps (A) (see post 17.44) and time is measured in seconds (s) (see post 16.12 for more details on these SI units). However, the unit of inductance has a special name – the henry (abbreviated to H). The unit is named after the American scientist Joseph Henry (1797-1878) who independently discovered electromagnetic induction at about the same time as Faraday.

The inductance of an ordinary conducting wire is very low, but the effect can be increased by winding it into a coil, as shown in the picture above. If the coil is wound around a cylinder of something with a high permeability (post 16.25), the inductance increases because the high permeability increases the magnetic field. For example, if the coil is wound around a cylinder of iron, the magnetic field and, therefore, the inductance, is increased by about five thousand times. At this point I should make it clear that I am thinking about a conducting wire that is insulated (usually with a plastic coating). It is this insulated wire that is wound into a coil.

The device that I have described in the previous paragraph is called an inductor. Together with a capacitor (post 18.19), an inductor can influence the way in which the behaviour of a conducting path depends on the frequency (post 16.14) of the time-dependent potential difference between its ends. In practice, the inductance of an inductor is much less that 1 H; in electronic circuits, inductances commonly range from 0.1 μH to 1 mH (see post 16.12 for an explanation of the prefixes used here).

As we shall see, in the next post, inductors are important because they contribute to the impedance (post 18.20) of an electrical circuit.

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