Capacitors remember the past, resistors don't. The voltage across a capacitor is proportional to the total charge that has passed through it, since it last had zero volts across it. Or mathematically, V=Q/C. 1/C is just the constant of proportionality between voltage and charge.
If you look at this as a process, in time, rather than as a result, you can say that the rate of change of the voltage across a capacitor is proportional to the current passing through it. I=C*(dv/dt), where dv/dt means rate of change of voltage with respect to time, with units like "volts per second".
Think of a resistor as a device that enforces a fixed proportionality between voltage and current. Another way to look at ohms is to call them volts per ampere. Double the volts (electromotive force across the resistor) and the amperes through it (amount of charge per second) also doubles.
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An inductor also remembers the past, but instead of having a voltage in proportion to total charge, it has a current proportional to total volt seconds. So it remembers how much voltage for how long has been applied to it, and that memory is represented by its current.
A capacitor and inductor in combination act something like a spring and mass act, mechanically to produce a resonance. When the spring is at maximum distortion and the mass is changing directions, but momentarily at rest, all the energy is stored in the spring. But when the mass hits peak velocity and the spring is passing through its relaxed state, all the energy is stored in the kinetic energy of the mass. The energy sloshes back and forth between spring and mass, twice per cycle, and the value of spring stiffness and mass determine the resonant frequency.
I'm not following the question. I think you are trying to combine several processes into one, and skipping too many steps. It is sort of like saying that if you can run a mile on one hamburger, how fast can you run if you eat a gallon of gasoline.
The FM transmitter combines radio frequency energy with audio by varying the frequency of a fixed energy carrier in proportion to the amplitude of the audio signal. Replacing the audio with something else does not change the power of the carrier.
The receiver separated the modulated carrier from all other frequencies (if it receives enough energy from the transmitter) and then discards all information about how strong the carrier is, and just responds to the frequency variations to recreate the audio signal in proportion to the frequency shifts. Doubling the power of the transmitter carrier allows this process to work over a longer distance, but does not change the volume of the audio at the receiver.