Electronic – a sine wave


This came up when a student asked me. A simple question one might think. Except… how to define one without tautology? That is, without using the word "sine" (or cosine for that matter). Wikipedia does not help, although the moving disc might be of relevence.

In short, I suspect his teacher has given him a severely hard problem, though I may be wrong.

This came up as part of an electronics course. So presumably any answers can be derived from the characteristics of various components/circuits.

Best Answer

Start with this:


simulate this circuit – Schematic created using CircuitLab


we have the inductor L1. We charge C1 separately, and then quickly connect it as shown, so that the top side of this circuit is at +1V potential relative to the lower side.

Ask yourself (or the student(s)):

What will happen next?

Clever students will say: yeah, well, it's a fast change of voltage across L1, so it will take some time until things look more "DC-y", and current starts flowing through L1 and discharge C1, so that the overall potential will be 0V.

But what about the magnetic field in the inductor

Oh yeah, that now stores the energy from the capacitor

So the current flow will stop forever once the voltage across C1 (and L1) is 0 V?

No, the magnetic field energy has to go somewhere. So the Capacitor charges again.

Can we put formulas to that? Yes, we can; enter the differential equations describing current and voltage across capacitors and inductors. Show that you need a function whose second derivative is itself, negated.

Now comes the hard part, and I'm afraid you'll be able to do nothing about it: You need to say: hey, this is a sine, it fulfills that condition.

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