Can an LC circuit be used to produce and receive FM signal? By simply changing the frequency of oscillation of an LC circuit (which you can do with the capacitor alone) you could emit (and receive) FM signal.
Are LC circuits actually used to do that? If not, why not?
 A: Yes, indeed, these are the basis of radio and television. Although the actual generators, modulators, and receivers are usually more complicated than a simple LC circuits, the LC is the basis of it (see, e.g., heterodyne, which is the simplest mixing device, used for the amplitude modulation.)
The field of radio wave generation, transmission, and reception has been so well established that it has been firmly divided into Radiophysics and Radioengineering, with (Radio)physicists often having only the basic knowledge about the relevant technology. It si exacerbated by the fact that most radio components are nowdays packed in a single chip, and thsu the popular hobby of assembling radio transmitters/receivers on one's tabletop has gone out of practice.
A: FM signal is modulating the frequency of the signal, i.e. 0 will be encoded to a short signal, and 1 will be encoded to a long signal.
To receive an FM signal, we can first use a bandpass to select the frequency we would like to listen to, and then simply 'read' the signal by parsing the short and long signals to 0s and 1s.
RLC circuit can be used as a bandpass, but to parse the signal, i think you will need another IC to perform this procedure.
