Why does the voltage induced in the receiver coil of this WPT circuit decrease when a load is added (in parallel)?
I think your real problem lies in understanding parallel and series circuits, and what they really mean.

If you have this:







simulate this circuit &ndash; Schematic created using CircuitLab

Then you can rightfully expect the voltage to be constant, regardless of whether the switch is opened or closed.

This is what you expect your wireless power transfer to do.

What you don't realize is that the current changes depending on whether the switch is opened or closed.  You need more current when the switch is closed - both resistors are drawing current, so your voltage source must deliver more current.

Unfortunately, it can't do that.  It can only deliver as much current as it can pull through the magnetic field between the two coils.

If they are close by, or coupled through a piece of magnetic material, then you can draw more current and everything is as you expected it.

As it is, it looks more like this:







simulate this circuit

R3 represents the current limitation of the coils.  With that in there, closing the switch causes more current to flow, which causes the voltage across R1 and R2 to change.

How limited the current is depends on how well the coils are coupled.  Better coupling (closer together, or using a core) makes the effect smaller.  Coils further apart makes the effect larger.

The same thing happen when using different sized batteries.

All batteries have some internal resistance.  The smaller the battery, the higher the resistance and the less current you can draw from it.