REACTANCE, IMPEDANCE AND PHASE

We are now nearly ready to splice inductance and capacitance together into that blissful state known as "the turned circuit."  But before the actual wedding takes place, we ought to make sure the union can withstand any and all strains that may be placed upon it.  It is true that we have observed how both an inductance and  a capacitance behave under the influence of a direct current, but do we know what they will do when an a.c. voltage starts pushing and tugging at them?   Perhaps it would be well to investigate this angle before we bestow our blessing on the marriage.

You cannot penetrate very far into the a.c. woods without having a clear understanding of phase;  so we may as well get that at straight right now.  Phase simply means  comparative time of occurrence as applied to actions, changes, or events. If two things happen together, we say they are in phase.  If one happens first, we say that it has a leading phase.  the thing that happens second is said to have a lagging phase  with respect to the first.

Consider the case of you and your one-and-only doing a dance step.  If the feet of both are in phase, her foot moves back at the same instant your foot moves forward.  If your foot has a leading phase, it will move forward before hers is out of the way, and you will probably step on her toes and be told you are a poor dancer. If your foot has a lagging phase, she is doing the leading, and you are going to be a henpecked man!

As applied to electricity, phase usually means a comparison between similar changes in two or more different voltages or between a single voltage and its accompanying current.  For example,  Fig.601 shows what happens when and a.c. voltage is applied across a pure resistance.  Don't be surprised if you don't see it; Fig 601 has probably balled up more students than any other diagram in the science of radio!  It's supposed to show the life  history of a cycle of alternating current.  In our figure, having chosen the standard 60-cycle current, our base line is laid off in fractions of 1/60 second.  This makes it a time chart, just like the rolls that record the temperature for a day, with a thermometer-controlled pen making a continuous track.  Any point on the voltage curve on the chart will tell you just what the voltage is at that instant - the curve is simply a combination of all those instantaneous voltages.

No, alternating current really does not wiggle as the chart might lead you to believe.  What happens is that current from the alternator starts to flow through the resistor, staring with very low  (zero, to be exact)  voltage and current.  Both current and voltage rise until, at the end of 1/240 second, we have maximums of 170 volts (dashed line) and 2½ amperes (solid line).

The exact quantities are unimportant; in many radio circuits we have alternating currents of some hundreds of volts at only a few milliamperes, and in some welding circuits there may be hundreds of amperes with only a few volts.  In most a.c. diagrams, voltage and current curves are arbitrarily drawn the same height - see Fig. 602 and 603.  The only reason we didn't do it here is that the two curves would then be on top of each other, and you couldn't tell them apart.  Neither is the frequency important; we have used 60 cycles because it's common, but the story would equally true at radio frequencies.

But now - because of the way an alternator is built - our voltage and current start to drop, and at the end of 1/120 second there is no voltage across the resistor and no current flowing through it.  Then the current starts to flow through the resistor in the opposite direction.  Our clever mathematicians represent these volts and amps in the reverse direction by just drawing the voltage and amperage curves in the opposite direction to the first ones.  Neat, eh?   

Following the chart, we find that vltage and current in this direction again rise to a maximum in 1/240

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