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Mutual Inductance and Inductive Reactance

I promised no more math in the last session, and it was difficult. We could have covered the number of turns to inductance:
but we didn't. We could have covered the math behind inductors in parallel:
but we didn't. But we will cover just a little math in this lesson.

When AC is applied to a coil, a varying magnetic field will be produced around it. When another coil is placed within that magnetic field, it will induce a current flowing in that coil. This principle is called MUTUAL INDUCTANCE The amount of mutual inductance between the two coils depends on the distance between the two coils, and the angle between the two coils. When two coils are linked together via mutual inductance in this manner, we say that the coils are inductively COUPLED. When the mutually inductive coils are close to each other, we say that they are closely, or tightly coupled. When they are far apart, we say that they are loosely coupled. The greatest amount of coupling occurs when the coils are wound one directly over the other and on a closed iron core. The quantity of coupling between two coils is sometimes referred to as the Coefficient of Coupling. The formula for Coefficient of Coupling is:

Whew! Now that we've got the math out of the way, let's move on to the magic of electronics. We have already discussed that inductance is an opposition to the flow of current in an AC circuit by a coil. This is caused by the expanding and collapsing of the magnetic field. More important though, as the field expands and collapses, it generates a counter- electromotive force, by way of mutual inductance within the same coil. We call this SELF INDUCTANCE. Simply put, self inductance is when a coils magnetic field, produces an electric current within the same coil. This self inductance causes a resistance to AC current. But this resistance is not measured in Ohms, as normal resistance is. This resistance isn't even called resistance, it's called REACTANCE, because of the way it reacts with AC. In the case of a coil, it is specifically called INDUCTIVE REACTANCE, and its symbol is XL.

XL is a very special number in electronics. Let me say this another way:

XL is a very special number!

get the idea?

Now that I have your attention. XL is the variable number that we use while expressing the AC resistance of a coil. You will see this number in your sleep. You will eat with this number, you will go out on dates with this number and you will

XL = 2πfL

  • f = the FREQUENCY in Hz
  • L= the inductance of the coil in henries
  • and
  • π= 3.1415926536..... (or 3.14 for short)
  • It has been quite prominently established that I hate math as much as you do. However, as you have also found, in order to have a CLEAR understanding of how electronic circuits and components work - a fairly decent grasp of the basic math functions is required. I absolutely promise you that the math is almost done. We've covered MOST of the math important to basic electronic components, and we will cover more - but I won't push it. That isn't to say that if you are using this as a supliment to classroom study - that your teacher won't give you a MAJOR math test right after you read this! That being said - I wouldn't want you to fail the test - so another review of the more important formulae may be in order:
    In Review, the formula for finding Resistance, Voltage, and Current within a circuit (Ohm's Law) is:

    or or

    Much Akin to it is "Ohm's Watts Law" for finding POWER

    The Formula for finding the TOTAL RESISTANCE (or inductance in the case of a coil) in series is
    R1+R2+R3... = RTotal

    The Formula for finding the TOTAL CURRENT in series is

    which we haven't covered because it is not a very important formula. Not so important because of the following formula which is also true:

    I1=I2=I3... = ITotal

    CURRENT NEVER CHANGES in a series circuit!!! In short - if you can measure the current ANYWHERE within the series circuit - you know the current in the whole circuit! (Very handy when checking Christmas lights)

    The Formula for finding the TOTAL RESISTANCE in a parallel circuit is

    The Formula for finding the TOTAL CURRENT in parallel is
    I1+I2+I3... = ITotal

    CURRENT IS ADDITIVE in parallel.

    The formula for Time and Frequency is
    F=1/T (or T=1/F)

    The formula for Peak vs Effective voltage is:
    EPeak=1.41xEEff or EEff=.707xEPeak
    What is the formula for Inductive Reactance?

    XL = 2πfL

    RED? REALLY? Ok, perhaps I have stressed this point a bit too far, but then again, in electronics, and especially in radio electronics, you will see this formula again and again. Inductive reactance constitutes the resistance seen by an AC circuit when it runs into a coil. Sometimes, an inductor is called a CHOKE, because it chokes an alternating current flow. In power supplies, you may find a FILTER CHOKE, which opposes any ac frequencies, while allowing DC to pass through unharmed. Its purpose is to clean up the power supply voltages, so that no noise is seen on the power - just a clean DC source. There are both audio frequency chokes (AFC) and radio frequency chokes (RFC).

    Another point, which I passed over previousely, is that there are several types of "RESISTANCE" found in AC electronics, some of which will be negligable, others you will find fascinating and extremely important to the study of electronics. I will try to cover in detail the important ones. I will also, (when I remember to) mention the lesser important ones, as I will at this time.

    RELUCTANCE is a form of resistance which we have not discussed yet. The reason for not discussing it, is that in most electronic applications, you can pretend that it doesn't exist. Reluctance is actually the resistance, not to the flow of current, but to any MAGNETIC FIELD which cuts through any pre-existing magnetic field. To some small extent, this happens in all coils operating at AC, due to Self Inductance, or by way of Mutual Inductance. Mathematically speaking (oh no!) we say that it is equal to the MAGNETOMOTIVE FORCE / MAGNETIC FLUX, or that it is the reciprocal of PERMEANCE. Now, don't you feel safer? Isn't your life better, since you have learned that bit of trivia?
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