Suppose the antenna in your car can pick any signal in the radio frequency spectrum without loss (fradio ∈ [3 kHz, 300 GHz]). Further suppose that if you were to look at Vantenna on a scope, you would see a signal that is a superposition of all these frequencies. To mitigate this, we can send Vantenna through an RLC resonant circuit that has a very narrow resonance curve (high Q factor, ?f very small). This causes all frequencies other than a particular one at fres to attenuate, effectively tuning the radio to the "fres" channel. In order to tune the radio to listen to a particular channel, the RLC circuit has a variable capacitor in it whose capacitance changes as the radio tuning knob it turned.
1) What range of capacitance must the variable capacitor need to be tunable over to be able to listen to the entire radio frequency spectrum, assuming the inductance in the circuit is L = 1 mH? In reality, most of the RF spectrum is reserved for specific purposes such as radiolocation, space research, the federal government, amongst other purposes. The FM radio spectrum ranges from 88 MHz to 108 MHz.
Instead imagine now that the RLC circuit is composed of a single value capacitor (1μF) and a variable inductor.
2) What is the inductance range necessary to tune into just the FM band?