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Circuit Components: The Transformer

In our discussions of inductors in series and in parallel, we noted that the mutual inductance between coils could have a profound effect on the total inductance, depending on how much of the magnetic field of each coil overlaps the other coil. However, it is also possible to have two coils with interacting magnetic fields, but not connected electrically in the same circuit. The question then is, how does such a construction behave?

Before we address that question, however, we must consider that the amount of interaction between coils is not fixed. Therefore we must introduce the concept of coupling between coils. Coupling is the extent to which the magnetic field of each coil overlaps the other coil. Coupling can range from 0% (no interaction at all) to 100% (full interaction). In practice, 100% coupling is not possible, as some of the magnetic field will remain outside of the opposite coil. However, we can get close to it.

Qualitatively, coils with more than 50% coupling are said to be tightly coupled, while coils with less than 50% coupling are loosely coupled.



The schematic symbol for an iron-core transformer.

The schematic symbol for an iron-core transformer is shown to the right. It shows two coils sharing a common iron core. Because of the core, coupling between the two coils is as close to 100% as it can get. This is the standard arrangement for power transformers.

It is also possible to have two coils with a ferrite core, or with no core at all. These are still transformers and have the same basic properties. Only their design and construction varies, in accordance with their intended application.



A basic transformer-coupled circuit.

Because the two coils are not electrically connected, only the magnetic field between them has any effect here. Therefore, let's take a look at what the magnetic field does.

In this circuit, the lefthand coil in the transformer is connected to the source of energy. Therefore, it is known as the primary or primary winding of the transformer. ("Winding" because the coils are wound around the core.) The righthand coil receives energy magnetically, so it is known as the secondary winding.

As long as switch S is open, the battery is not connected to the lefthand winding and no current flows. Therefore, there is no magnetic field around either coil of the transformer, and nothing happens.

When the switch closes, current begins to flow through the primary winding. This creates an expanding magnetic field around the primary winding, which also affects the secondary winding. The expanding magnetic field induces a voltage across the secondary winding, which causes current to flow through resistor R. The magnitude of the current depends on the induced voltage and the value of R, in accordance with Ohm's Law.

As switch S remains closed, the circuit current eventually reaches its maximum value and remains there, no longer changing. Therefore the magnetic field stops expanding and remains constant. Since the induced voltage in the secondary winding depends on a changing magnetic field, that has now ended and no current flows through resistor R.

Finally, when switch S is opened again, current stops flowing through the primary. The magnetic field collapses as it induces a voltage in both windings that tries to keep current flowing. Therefore current again flows through R, this time in the opposite direction from when S was first closed.

Once the magnetic field has completely collapsed, all current stops flowing, and the circuit remains in its original quiescent state as long as S remains open.



Since a transformer only works with changing currents, you may be wondering why we would even use a circuit like this one. However, there's a very practical application that people use every day. The number of turns of wire in the secondary does not have to be the same as the number of turns in the primary, and indeed generally is not the same. If the secondary has more turns of wire, it will step up the voltage generated in the secondary winding (and use up the energy in the magnetic field faster). This makes for an easy way to generate the high-voltage impulse needed to fire the spark plugs in your car's engine. It requires only a very slight adaptation of the above circuit to accomplish this.


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