Discussion of the article "Displacement Current"

Figure 1 depicts a capacitor as it is drawn in circuit diagrams, and is misleading. Similarly, Figure 2 is misleading in its depiction of a battery.

The leads to a capacitor (or battery) enter at one end, not at the centre. Thus, the two lines at the right of Figure 2  represent a capacitor more properly then  Figure 1 , drawn even better in Figure 4 . We then see that a capacitor is a transmission line, its peculiarity as a transmission line being its extremely low characteristic impedance. This is due to (1) its very wide plates, (2) their closeness to each other, and (3) the very high dielectric constant of the dielectric. (3) also causes the time taken to traverse the capacitor from end to end very long.

To get a thorough grasp of the reality of charging a capacitor, it would be better to move to Figure 4, where a long length has been interposed between battery and capacitor. We will assume that the characteristic impedance of the two wires is equal to the value of the resistor on the left.

We now close the two switches. A voltage step advances at the speed of light (in the vacuum between the conductors) towards the capacitor. When it reaches the capacitor, some of the step enters the capacitor and most reflects, according to the laws of reflection at Figure 3.4 in one book and Figure 11 in another book. The much smaller step (equal to half the first step in  Figure 3 ), continues to the right inside the capacitor, while a large step returns towards the left, towards resistor and battery. This large step is properly terminated by the resistor, and so does not reflect from the left. The small step continues to the right, and reflects at the end, giving the appearance of a voltage doubling. After an equal delay, it returns to the left and is seen by the monitor at the left hand end of the capacitor, and shows as the first step in the graph in Figure 3 . (Note that the graph must be showing the voltage at thee right hand end of the capacitor. The Work here was done by6 Dr. David Walton.) At this point, where the returning step collides with the left hand end of the capacitor, a small amount leaks out into the leftwards transmission line, but most of it, slightly reduced, returns towards the right, representing the second step in Figure 3 .



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