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Transformers and mutual inductance, but probably no mutual admiration.



Tonight’s post is about two coils tightly coupled on a common iron core. When the fields of two (or more) coils affect each other it is said they have mutual inductance. I thought seriously of embedding an old song by Teresa Brewer called “Mutual Admiration Society” but in the case of a transformer there is a constant give and take going on.  It would better be described as  “The constant bickering society.”  Enough joking, back to the task at hand!

Before we start this post it is very important that you have read and fully understand the first several posts about inductance.  These are listed from the first one to the most recent one:


Transformer physical

One way a transformer could be created.

The picture to the right is a cross section view of one way to create a transformer.  Two separate windings are wound on a common Iron core.  As you will see later, usually this is done differently but the concept is exactly the same.  In a transformer, it is assumed the field produced by each coil is completely felt by the other coil.  Usually one coil is connected to an AC power source and the other coil is connected to the load.  (Why AC and not DC?  I am not going to answer that at this time, the previous Inductor Posts should provide you with that answer.)  The coil connected to the power source is called the primary winding and the coil feeding the load is called the secondary winding.

If only the primary winding is connected and the secondary wires are not connected to anything then the primary winding is acting like a pure inductor.  A simple inductor in a power circuit is often given some descriptive names.  In most modern language it is called a reactor coil because it is creating inductive reactance.  An older term, and one that in many ways I like better is a choke coil, because it chokes the flow of electricity.  In the transformer I drew in the 2nd picture, assume the primary coil is the coil on the left side and it has twice as many windings as the secondary coil on the right side.   If, as we have stated, the secondary coil is disconnected and the primary is drawing almost zero current then the primary is producing a CEMF (counter voltage) equal to the power voltage.  Because we have 100% coupling between the two coils the secondary coil is also producing a EMF (voltage), but since this coil only has 1/2 as many turns as the primary coil the EMF will also only be 1/2 as much as the primary coil.

This leads to one of the formulas always presented when talking about transformers:

N1/N2 = V1/V2   where N1 is the number of windings or “turns” on the primary coil and N2 is the turns on the secondary coil.  This ratio N1/N2 is called the turns ratio.

The second formula presented is the inverse relationship is true for the current in the primary and secondary.    N1/N2 = I2/I1.   The argument usually presented is the VA (Volts X Amperes — which probably is greater than the actual power) has to be the same in the primary and secondary.  The formula is true, but I have a couple of problems with the argument.  First, I have yet to talk about VA and power.  That is coming very soon, but my goal is to give you a feel for what is happening before I “throw the math at you”… then you have a reason to learn the math.   My more serious problem with just using that argument without any explanation  is “How does the current in the secondary winding affect the current in the primary winding?”

The understanding of this will take you a long way in understanding in the future about how motors, generators, and devices like loud speakers operate.

Once the secondary coil is connected to a load, a current will start flowing in the secondary winding.  This current will create a CEMF in that winding that will be counter to the EMF being created in the secondary by the field being created in the primary winding.  This will have the effect of countering the field of the primary winding so the primary winding will be producing less CEMF and will start to draw more current.   (If  you followed all that in the first reading you are a better person than me.)

Another way of looking at is:  The secondary is now absorbing some of the field created by the primary windings and turning it into energy.   This energy is no-longer available to create a CEMF in the primary winding so the primary will draw more current.

This will  take you a little while to really make your own.  If necessary glue four drinking straws together and pretend they are the core of the transformer and use your fingers of your right had as if they are wires and your your thumb as the direction of the field.  Once smoke starts to come out of your ears: relax, listen to some music, and come back to it later, until you make it your own.   It is a lot more fun than just memorizing formulas.

old smokey's windings

Old Smokey’s windings

This post is getting a little long so I will complete it on the next post.   For now I will show you the insides of a real transformer.  I call this transformer, “Old Smokey”, because that is what happened to it.   The transformer was designed for a primary of 120 Vac but was installed by the factory into a 480 Vac circuit.  It was not happy and let everyone know it had a problem.  This is a small transformer used in a control circuit.

The main reason I am showing this picture is to show how the coils are not on opposite sides of a box shaped iron core but that both are on the center leg of an E frame core.  Often the two windings are wound directly on top of each other, but in this case the two windings are wound next to each other.   I will continue to do a postmortem on this transformer because there is more to show, and actually I have some big questions on how it is constructed.

I hope you got a lot out of this post. it actually was a fun one for me to write.   Warning, make sure you relax awhile after you think of the Counter, of the Counter EMF.  It is probably not safe to drive for a while.   Seriously, it is a very important concept to understand once we go into electromechanical devices such as motors, generators, and even loudspeakers.

The next post to finish up transformers will be much much easier…. I promise.


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