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Transformers and AC

The Circuit

Applying an ac voltage to a transformer.

Because an inductor operates by building a magnetic field around itself, we can take a second inductor and place it inside the same magnetic field. This gives us a transformer. In the case of the circuit shown to the right, the two solid lines between the symbols of the two coils indicate that the coils are wrapped around an iron core. The iron serves to concentrate the magnetic field and to help make sure that the field fully envelopes both coils. This greatly increases the inductance of each coil as well as the magnetic coupling between them.

Because the transformer is built with the two coils of wire wound around the commmon core, each coil is sometimes also called a "winding." The winding to which the original voltage is applied is designated the primary winding, while the other winding is designated the secondary winding. A transformer can have multiple secondary windings, but except for a very special circumstance, it only has one primary winding.

That special circumstance has to do with power transformers designed to operate from houshold line voltage in either North America (120 volts, 60 Hz) or Europe (240 volts, 50 Hz). These transformers have two primary windings each rated at 120 volts. They are connected in parallel for a 120 volt system, or in series for a 240 volt system. Thus, each winding serves as half of the required primary winding. This arrangement makes it possible to use that piece of equipment in many different places in the world without requiring special adapters.

Remember that any inductor consists of a coil of wire. We can count the number of turns of wire that make up that coil. When a voltage appears across the coil as a whole, that voltage is shared equally by the individual turns of wire in the coil. Thus, if a coil contains 1200 turns of wire and has a voltage of 120 volts across it, each individual loop or turn of wire has 0.1 volt across itself.

Another point to keep in mind is that the inductor itself generates this voltage in its effort to prevent the current through the coil from changing. The changing magnetic field induces that voltage and shares it across the entire coil. Therefore, that same magnetic field also induces the same voltage in each turn of the secondary winding or windings.

Thus, if our example transformer has a secondary winding of 100 turns, it will generate a total voltage of 10 volts across itself. This will be the voltage appearing across the resistor.

If the resistor is removed and the secondary winding left unconnected to any load, no current flows in the secondary winding. In this case, it might as well not be there, and current through the primary winding is determined by the inductance, and inductive reactance, of the primary winding. This is made sufficiently high that the no-load current is very small. For example, a power transformer with a 120 volt, 60 Hz primary winding might have a primary inductance of 15 Henries. This gives us:

XL = 2πfL = 6.2831853 × 60 × 15 = 5654.8668 ohms
iL = 120/5654.8668 = 0.021220659 A = 21.220659 mA

21 mA is generally a negligible amount of current to drain from your wall socket, so it is reasonable to simply pretend that no current is drawn if there is no load on the secondary winding.

Now let's put R back into the circuit, as shown in the schematic diagram above. Now we have a load, which will draw current from the secondary winding. This current derives from the changing magnetic field as its lines of force move across the turns of wire in the secondary winding. Therefore, the secondary current draws energy from the magnetic field and reduces its strength.

The reduced magnetic field cannot oppose changes in primary current as readily as it did before, so the primary winding draws more current, which restores the magnetic field the full strength. However, with more turns of wire, the primary winding doesn't have to draw as much current as the secondary supplies, to restore the magnetic field. In the final analysis, the amount of power drawn by the load on the secondary is essentially equal to the amount of power required by the primary winding, except for very small loss due to imperfect efficiency.

If we ignore those losses for the moment (a reasonable approximation), then we can specify the behavior of the transformer by defining a few variables as follows:

I1  =  V2  =  N2

I2 V1 N1

The transformer basically behaves as if it were an independent ac generator whose output voltage is equal to the secondary voltage, and which can be electrically isolated from the wall power source. This can be very important with some types of electrical equipment.

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