More on the “skin effect”

More on the “skin effect”

As previously mentioned, the skin effect is where alternating current tends to avoid travel through the center of a solid conductor, limiting itself to conduction near the surface. This effectively limits the cross-sectional conductor area available to carry alternating electron flow, increasing the resistance of that conductor above what it would normally be for direct current:

The electrical resistance of the conductor with all its cross-sectional area in use is known as the “DC resistance,” the “AC resistance” of the same conductor referring to a higher figure resulting from the skin effect. As you can see, at high frequencies the AC current avoids travel through most of the conductor’s cross-sectional area. For the purpose of conducting current, the wire might as well be hollow!

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Inductor quirks

Inductor quirks

In an ideal case, an inductor acts as a purely reactive device. That is, its opposition to AC current is strictly based on inductive reaction to changes in current, and not electron friction as is the case with resistive components. However, inductors are not quite so pure in their reactive behavior. To begin with, they’re made of wire, and we know that all wire possesses some measurable amount of resistance (unless its superconducting wire). This built-in resistance acts as though it were connected in series with the perfect inductance of the coil, like this:

Consequently, the impedance of any real inductor will always be a complex combination of resistance and inductive reactance. Compounding this problem is something called the skin effect, which is AC’s tendency to
flow through the outer areas of a conductor’s cross-section rather than through the middle.

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Parallel resistor-inductor circuits

Parallel resistor-inductor circuits

Let’s take the same components for our series example circuit and connect them in parallel:
Because the power source has the same frequency as the series example circuit, and the resistor and inductor both have the same values of resistance and inductance, respectively,they must also have the same values of impedance.

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Series resistor-inductor circuits

Series resistor-inductor circuits

The resistor will offer 5 of resistance to AC current regardless of frequency, while the inductor will offer 3.7699 of reactance to AC current at 60 Hz. Because the resistor’s resistance is a real number (5 6 0o, or 5 + j), and the inductor’s reactance is an imaginary number (3.7699  6 90o, or 0 + j3.7699 ), the combined effect of the two components will be an opposition to current equal to the complex sum of the two numbers. This combined opposition will be a vector combination of resistance and reactance. In order to express this opposition succinctly, we need a more comprehensive term for opposition to current than either resistance or reactance alone.

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AC inductor circuits

AC inductor circuits

Inductors do not behave the same as resistors. Whereas resistors simply oppose the flow of electrons through them (by dropping a voltage directly proportional to the current), inductors oppose changes in current through them, by dropping a voltage directly proportional to the rate of change of current. In accordance with Lenz’s Law, this induced voltage is always of such a polarity as to try to maintain current at its present value. That is, if current is increasing in magnitude, the induced voltage will “push against” the electron flow; if current is decreasing, the polarity will reverse and “push with” the electron flow to oppose the decrease. This opposition to current change is called reactance, rather than resistance.

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AC resistor circuits

AC resistor circuits

If we were to plot the current and voltage for a very simple AC circuit consisting of a source and a resistor (Figure 3.1).

Because the resistor simply and directly resists the flow of electrons at all periods of time, the waveform for the voltage drop across the resistor is exactly in phase with the waveform for the current through it. We can look at any point in time along the horizontal axis of the plot and compare those values of current and voltage with each other (any “snapshot” look at the values of a wave are referred to as instantaneous values, meaning the values at that instant in time). When the instantaneous value for current is zero, the instantaneous voltage across the resistor is also zero. Likewise, at the moment in time where the current through the resistor is at its positive peak, the voltage across the resistor is also at its positive peak, and so on. At any given point in time along the waves, Ohm’s Law holds true for the instantaneous values of voltage and current.

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