Oscillating Circuit: LC Charging & Discharging

• July 16, 2024
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After implementing Low-Pass and High-Pass filter mappings last week on the global and local scope, I took the time to focus more on coils and capacitors.

Because this entire topic is already quite complex, let me explain its importance in simple terms:

• Capacitors, Coils, and Resistors are the three main building blocks of electronics. There are about two dozen other components, but these three are fundamental. Together with chips, they account for over 90% of the action on any circuit board.

• Said electronics run bottomline our entire civilization as you may have noticed (Fridge,TV,PC,Phone,Lights etc.). You got to be aware of how key they really are.

• Resistors are a topic on their own, but we will focus here on the two other big ones, coils and capacitors.

• Both coils and capacitors store energy: capacitors store it as static potential energy, and coils store it dynamic (as a variant of) kinetic energy in their magnetic field. Both can charge and discharge said energy. We make use of this property in numerous ways. Additionally, they have other properties; for example, a coil can function as an electromagnet or antenna, and a capacitor can smooth signals. The importance of these components cannot be overstated – without them, we’d be living in the age of Queen Victoria and the steam engine at best.

• Coils, also called inductors, relate to capacitors as addition relates to subtraction, division relates to multiplication, or integration relates to differentiation.

One takeaway is that there is a natural symmetry between these two. At first glance, you wouldn’t suspect this because they look completely different as physical components and also behave differently. However, the math clearly shows that one is “somehow” the opposite of the other.

Now with the WTF, it becomes a little clearer “why”: On a fundamental level, a coil is nothing more than concentrated curvature, and a capacitor is essentially a cut in the wire or a temporary disconnect (it’s a stretch, but we are focusing on the most primitive property).

So one stems from an interruption and the other from curvature. In the WTF, curvature is the identifying property of the periphery, and the interruption within infinity is that of the center. We can therefore map these to the center and periphery, but even more to the local and the global scope. A concentration of curvature indicates the position of the inductor in the center. So we have a global scope and center position for the inductor. For the capacitor, we infer a local scope and peripheral position. Align their charging and discharging behavior to the Cycle of the WTF, and voilà – there’s almost what’s called in German a ‘Schwingkreis’ or oscillating circuit:

I say almost because the charge in the WTF mapping is not swapping back and forth between different plates, yet the illustration is rather close: You have charge and discharge for both the coil and the capacitor. That 2D .GIF is good enough to convey the idea. It’s further mapped onto the WTF in the video below, see specifically the lower right corner:

Notice that I have also added the general characteristics of parallelism and sequentialism as a second descriptive overlay (lower left corner): As we move to the periphery (and thus become more parallel), capacity increases and inductance decreases. Capacitance in parallel adds up, and inductance in parallel diminishes. That relation is inverted towards the center (everything becomes more serial) where capacity decreases and inductance increases.

This gives some deeper insights when we do further matching with, for example, the BPM Notation, Economic Bubble, or the Four Stroke Engine. But that would exceed the scope of this post and will be a future topic.

I doubt many people will already understand this, as it is too complex without proper context – which I have failed to provide so far. I need to create a short introduction to the WTF in the near future, as this take on the LC-Circuit is an interesting building block, but without the big picture, people won’t understand how this relates. I’ll try to manage that soon, as well as the recently promised release – and that will likely be a cold one that I put on the web without any sort of accompanying fanfare anyway.