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Through the Looking Glass – Duality – The Inductor

The Inductor circuit.

The Inductor circuit.

Whenever you are learning something new it is best to compare and contrast with something you already know.  Tonight we are going to talk about the inductor, the crazy sister to the capacitor.   In a few ways this is similar, but being that she is crazy everything is different and she has a few tricks her sister doesn’t.  I am going to build this story by taking a small side trip… It is for a reason.

Current coming out of the page

Magnetic field of a wire with conventional current flowing out of the page toward us.

Electromagnetism:

The picture to the right of this shows a wire, the hatched area, with conventional current flowing through the wire toward us.  This direction is represented by the dot in the middle of the wire.  Imagine the dot as the point of an arrow pointing toward us.   The concentric circles represent the magnetic field around the wire and the arrows represent the field direction from North magnetic pole to the South pole.

Magnetic field of wire with current flowing into page.

Magnetic field around a wire with the conventional current flowing into the page.

Now imagine the direction of the current is reversed and in the picture to the left it is shown flowing into the page.  Again the direction is shown by an arrow on the wire, but this time we are looking at the backside of the arrow, the feather end, represented by the black cross.  Since the current is the opposite direction it makes sense that the magnetic field would also be in the opposite direction.   The direction of the field can be determined by “the right hand rule”.  If the thumb of the right hand is placed in the direction of conventional current flow, folding the fingers show the direction of the magnetic field.   Please be aware that in many places this is taught as the “left hand rule”… that is because those places are talking about electron flow.  In actual use it very seldom matters. The important point to remember is when the current direction is reversed the magnetic field direction is reversed.

Intuition and logic are correct if you assume that as the current increases the magnetic field also increases.  This becomes important in electrical power work.   If short circuits develop and a large current flows before the circuit breaker trips or the fuses blow a strong field develops around conductors.  If the current is flowing in opposite directions in two wires next to each other, the fields are such that two North or two South poles are opposing each other.   The wires will attempt to separate violently.   If the conductors are bare bus bars this can cause even more short circuits and a catastrophic  failure.  It is an important part of power engineering to know the amount of current available during a short circuit and make sure the bus work inside enclosures are braced for this force.

The magentic field around a coil of wire.

The magnetic field around a cross section of a coil of wire.

To increase this field we can wind the wire into a coil.  The picture to the right shows a cross section view of a coil of wire with current flowing through it.  All of the fields around each turn of the conductor add together to make a strong magnet when the current flows.   The coil could be short and fat by having many layers of winding or tall and skinny like the one I drew.  The point is the windings all add and concentrate the field.  This can be expressed mathematically as: Field Strength = Number of turns X the current.

Some materials allow magnetism to flow easily though them.  Think of these as magnetic conductors.  Iron is a good example of such a material.   If the path for the magnetic field has less resistance to the flow of magnetism then the field will be stronger.  Many coils are wound around ferrous materials to increase the magnetic strength.  Things start to get strange here, because the materials are friendly to the field up to a point and then become saturated.  Once the material becomes saturated, the strength of the field is no longer a nice equation like shown above.  This becomes very important in things such as motors.   There are other factors to consider in the case of AC but we will deal with those later.

The Twisted Sister’s first trick:

The magnetic field we have been talking about is developed because of moving charges in a wire also known as current.  What happens if we have a coil just setting there with no power source connected and we put a magnetic field inside it?   The answer is nothing…unless that magnetic field is moving.   Imagine we are inserting a U shaped magnet with the North pole inside the coil and we are pushing it from top to bottom in the coil.  The coil would develop a voltage and would attempt to produce a current.   If we were to do the same thing with but with the South pole inside the coil the voltage would be in the opposite direction.  ( It is possible to know the voltage direction, but it would require some research for me and it is not really important to know at this time.  In real life, if it was really important we would just swap the wires.)   If the magnet is moved in the opposite direction again the voltage would reverse.  Our kind of loose equation at this point is:  The voltage of the coil is proportional to the   change in magnetic field X the Number of turns.   So as you can see the twisted sister is bipolar.  She will produce a magnetic field from moving charges and she will produce a voltage from a changing magnetic field.

Here is looking back at you — In the looking glass: 

Now imagine the circuit in the first diagram.   The device marked L in the diagram is our coil and it is just setting there because we have yet to throw the switch.   If we throw the switch and connect the coil and resistor to the battery, the battery will attempt so flow a current through the coil and the coil will attempt to build a field.  BUT.. an increasing magnetic field will create a voltage on the coil.  The voltage being created is in a direction opposite of the battery voltage so at the start very little current will flow.

Counter Electromotive Force (CEMF) created by the inductor after the switch is closed.

Counter Electromotive Force (CEMF) created by the inductor after the switch is closed.

The diagram to the left shows a way of thinking of what happens at the first moments.   If you remember the other term for Voltage is Electromotive Force.  The coil in the first moments develops a Counter Electromotive Force or CEMF that opposes the battery voltage.  Because the battery has a constant voltage and there is resistance in the circuit the battery eventually wins and current starts to flow.  As you can probably guess this will end up with our old friend an exponential function.   However, this post is becoming long so we will continue with the story of the twisted sister in a post in the near future.

I have chosen to tell this story this way because coils are a very important things not only as inductors, but also for almost all electromechanical devices such as motors,solenoids and relays.   It is probably a little while before we get to those but the ideas presented here will be very important when we do.  The rest of inductors will probably go quickly.

Thank you for your time. It is my desire to make it worth the effort.

Gary.

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