Real circuit elements
When looked at from any one pair of terminals, any arbitrary circuit made up of ideal impedances and generators is, at any given frequency, equivalent to a generator $\emf$ in series with an impedance $z$. That comes about because if we put a voltage $V$ across the terminals and solve all the equations to find the current $I$, we must get a linear relation between the current and the voltage. Since all the equations are linear, the result for $I$ must also depend only linearly on $V$. The most general linear form can be expressed as \begin{equation} \label{Eq:II:23:1} I=\frac{1}{z}(V-\emf). \end{equation}  In general, both $z$ and $\emf$ may depend in some complicated way on the frequency $\omega$. Equation (23.1), however, is the relation we would get if behind the two terminals there was just the generator $\emf(\omega)$ in series with the impedance $z(\omega)$. There is also the opposite kind of question: If we have any electromagnetic device at all with two terminals and we measure the relation between $I$ and $V$ to determine $\emf$ and $z$ as functions of frequency, can we find a combination of our ideal elements that is equivalent to the internal impedance $z$? The answer is that for any reasonable—that is, physically meaningful—function $z(\omega)$, it is possible to approximate the situation to as high an accuracy as you wish with a circuit containing a finite set of ideal elements. We don’t want to consider the general problem now, but only look at what might be expected from physical arguments for a few cases. If we think of a real resistor, we know that the current through it will produce a magnetic field. So any real resistor should also have some inductance. Also, when a resistor has a potential difference across it, there must be charges on the ends of the resistor to produce the necessary electric fields. As the voltage changes, the charges will change in proportion, so the resistor will also have some capacitance. We expect that a real resistor might have the equivalent circuit shown in Fig. 23–1. In a well-designed resistor, the so-called “parasitic” elements $L$ and $C$ are small, so that at the frequencies for which it is intended, $\omega L$ is much less than $R$, and $1/\omega C$ is much greater than $R$. It may therefore be possible to neglect them. As the frequency is raised, however, they will eventually become important, and a resistor begins to look like a resonant circuit. A real inductance is also not equal to the idealized inductance, whose impedance is $i\omega L$. A real coil of wire will have some resistance, so at low frequencies the coil is really equivalent to an inductance in series with some resistance, as shown in Fig. 23–2(a). But, you are thinking, the resistance and inductance are together in a real coil—the resistance is spread all along the wire, so it is mixed in with the inductance. We should probably use a circuit more like the one in Fig. 23–2(b), which has several little $R$’s and $L$’s in series. But the total impedance of such a circuit is just $\sum R+\sum i\omega L$, which is equivalent to the simpler diagram of part (a). As we go up in frequency with a real coil, the approximation of an inductance plus a resistance is no longer very good. The charges that must build up on the wires to make the voltages will become important. It is as if there were little condensers across the turns of the coil, as sketched in Fig. 23–3(a). We might try to approximate the real coil by the circuit in Fig. 23–3(b). At low frequencies, this circuit can be imitated fairly well by the simpler one in part (c) of the figure (which is again the same resonant circuit we found for the high-frequency model of a resistor). For higher frequencies, however, the more complicated circuit of Fig. 23–3(b) is better. In fact, the more accurately you wish to represent the actual impedance of a real, physical inductance, the more ideal elements you will have to use in the artificial model of it. Let’s look a little more closely at what goes on in a real coil. The impedance of an inductance goes as $\omega L$, so it becomes zero at low frequencies—it is a “short circuit”: all we see is the resistance of the wire. As we go up in frequency, $\omega L$ soon becomes much larger than $R$, and the coil looks pretty much like an ideal inductance. As we go still higher, however, the capacities become important. Their impedance is proportional to $1/\omega C$, which is large for small $\omega$. For small enough frequencies a condenser is an “open circuit,” and when it is in parallel with something else, it draws no current. But at high frequencies, the current prefers to flow into the capacitance between the turns, rather than through the inductance. So the current in the coil jumps from one turn to the other and doesn’t bother to go around and around where it has to buck the emf. So although we may have intended that the current should go around the loop, it will take the easier path—the path of least impedance. If the subject had been one of popular interest, this effect would have been called “the high-frequency barrier,” or some such name. The same kind of thing happens in all subjects. In aerodynamics, if you try to make things go faster than the speed of sound when they were designed for lower speeds, they don’t work. It doesn’t mean that there is a great “barrier” there; it just means that the object should be redesigned. So this coil which we designed as an “inductance” is not going to work as a good inductance, but as some other kind of thing at very high frequencies. For high frequencies, we have to find a new design.