Tutorial 5 A  Inductor Properties 

Learning Objective 
Recall that an inductor produces a magnetic field. To understand that inductors have an inductance. To explain that inductors have a reactance due to their inductance. 
Key Questions 
What is inductance? How do we demonstrate the idea of reactance? How can we measure inductance? 
Properties of InductorsInductors are simpler components than capacitors. At its simplest an inductor is a coil of wire.
Photos from Wikipedia
Capacitors are very sensitive to changes in temperature, or exceeding the working voltage. There are no such problems with inductors.
The circuit symbols of different kinds of inductors as shown in the picture below.
The diagram shows the features in an inductor that we will use in the discussion of the Physics of inductance.
We will consider single inductors which have a selfinductance, for which the Physics code is L and the units are Henrys (H). The unit is named after Joseph Henry (1797 – 1878), an American physicist, who did a lot of pioneering work with electromagnetism.
As far as electric currents are concerned, an inductor is simply a piece of coiled wire and should not affect the flow of charge at all.
Suppose we connect an inductor in series with a bulb. The circuit is below:
The inductor has zero resistance. If we connect the circuit to a DC battery, the bulb lights up to full brightness, just as we would expect.
Now let’s connect it to an AC supply of exactly the same voltage. We would expect the bulb to light up to exactly the same brightness. But what we see is the bulb is slightly dimmer. 
Explain which AC voltage we should use: peak or RMS. 


InductanceThe inductance of an inductor is the property by which the inductor induces a voltage in itself in response to a changing current. It has the Physics code L and is measured in Henrys (H).
The simplest inductor is a solenoid and the inductance of a solenoid is worked out using the following equation:
The terms involved are:
The permeability of free space is a constant that is common in electromagnetism. Its Physics code is m_{0}, (pronounced “munought”). The symbol m is “mu”, a Greek lowercase letter ‘m’.

An inductor is made of a solenoid of 1200 turns of copper wire around a square former 2 cm × 2 cm. The length of the solenoid is 5 cm. Calculate the inductance. 
Inductance and CurrentThe selfinductance of a coil can be worked out from the equation:
The dI/dt term is the rate of change of the current:
We can determine this by measuring the gradient at any point, as shown in the diagram above. We need to take a tangent and work out its rise and run. This is not a particularly easy way of measuring L. But if we know L, we can easily work out the reverse EMF.




Energy in an inductorIf we have an inductor in a DC circuit, we find that it makes little difference. However, if we turn the current off, the magnetic field collapses. A large reverse EMF is produced that can give you a shock as the energy is released. The reverse voltage spike will wreck electronic components, but there is a simple way to get round this, which we will look at later.
The energy held in an inductor is given by the equation:
If it takes 0.1 s for the magnetic field to collapse, the 4.0 J is dissipated in 0.1 s, i.e. at a rate of 40 W.
To learn how this equation is derived, click
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Reverse voltage spikesThe reverse EMF can be reduced considerably by reducing the voltage slowly, over a period of several seconds. Another way is to have a reverse biased diode to protect rectifier packs and other electronic components. This conducts the reverse voltage spike harmlessly away. The diode is wired in parallel with the inductive component. The arrangement is shown in the diagram below:
Large DC motors have many advantages compared to AC motors. They can be easily reversed, and their speed can be controlled easily. However they have large inductances because they have lots of coils of wire and big lumps of magnetic material. So switching on and off by simply closing and opening a switch is not an option unless you like electrical sparks flying. This is why you need control gear such as this to increase and decrease the current slowly.



