Hi,
When we try to understand things it is best to look at the basic theory behind what makes something work. It is often just one particular aspect that reveals what it is that makes something work the way it does.
In the case of two coils, it's none other than the principle of "mutual inductance". Mutual inductance in its most basic form is the phenomenon where a changing magnetic field in one wire produces a changing current flow in another wire when the second wire is reasonably close to the first wire. The changing magnetic field in the first wire comes about because there is a changing current in that first wire, and so we see a changing current in the first wire result in a changing current in the second wire. This is known as mutual inductance.
There is much written on this subject over the years even a long time ago when people started coming up with ways to calculate this so that they could predict the behavior of circuits that contain mutual inductances.
The simplest form of this phenomenon comes to us in the form of a transformer. The transformer has at least two coils and many times they are individual coils that are not directly connected to each other, so the only way we can see current in the secondary change is if we see current in the primary change. The calculated value of the mutual inductance, along with the other inductances, tells us how much energy will transfer from one coil to the next.
The simplest model of this is probably the T equivalent model, where we see a modified primary inductance in series with a modified secondary inductance, and a third inductance usually called simple "M" from the center tap of the two to ground. The shape of the three inductors forms a T shape and that's where it gets it's name.
The analysis then proceeds just like any other circuit analysis, where we can calculate input voltage, output voltage, etc.
Since the key point in all this is the mutual inductance, you need to read up on how to calculate that with different coil arrangements. You may even find some approximate formulas on line to use. Once you do that, you can calculate output voltage with or without load, output current, and of course output power, which here would be the amount of power that actually made it to the output (transferred) and of course the all important efficiency.
I happened to take an interest in this because there were a lot of things coming out that are using wireless energy transfer in the form of wireless charging. Since in the typical application the efficiency is not very high, we may be hearing some negative arguments coming up in the near future from government agencies against the use of wireless power transfer unless the efficiency can be raised. That's because one of the goals these days is to reduce energy consumption as much as possible.
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