I was trying to learn the way basic guitar circuits work, the other day, and I stumbled upon a thing that I couldn't fully understand.
According to this site, a simple guitar circuit can be made as shown on the image below.
As i understand the tone knob is represented by an LP filter with a variable cutoff frequency changed by the variable resistor, where higher the resistance is the brighter the tone is(higher frequencies in the signal). The volume knob on the other hand is a simple voltage divider represented by a potentiometer, regulating the voltage levels of the output signal.
Considering the way the tone RC filter is wired, it should only work if the pickup behaves as an AC current generator. I did AC analysis in LTSpice and the results came out positive.
The thing is that it is quite counter intuitive to me since I have always thought that EMF is induced in the coil according to Faraday's law: $$EMF = -N\frac{d\phi}{dt}$$ and then the current in the circuit depends on the load connected to the induction coil. According to this I should replace the pickup with an AC voltage generator but then the RC filter would not work.
Could anyone help me explain the way induction works in this process because clearly I have a mistake somewhere in my way of thinking.