In a radio tuner resonance is produced by an incoming electromagnetic wave rathe

Question

In a radio tuner resonance is produced by an incoming electromagnetic wave rather than an AC voltage source. The tuner circuit consists of an inductor (inductance coil) and a variable capacitor. Changing the station changes the value of the capacitance. Each radio station transmits electromagnetic waves at a particular frequency and all of these frequencies from the various stations reach the antenna of your radio. Only the frequency corresponding to the natural frequency of the tuner circuit will produce a large enough current to be picked up and then amplified.

An FM radio tuner is set to receive a station. The tuner has a 1.4microH inductance coil and a variable capacitor that is set to 1.8 pF. What is the frequency of the waves emitted by this station?

(Hint: FM stations broadcast from 87.5MHz to 107.5 MHz)

Explanation / Answer

Resonant frequency

f=1/2pi*sqrt(LC) =1/2pi*sqrt(1.4*10-6*1.8*10-12)

f=100.26 MHz

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