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An FM radio tuner is set to receive a station. The tuner has a 1.4 microHenry...

An FM radio tuner is set to receive a station. The tuner has a 1.4 microHenry (1uH- 1 x 10-6 H) inductance coil and a variable capacitor that is set to 1.8 picoFarad (1pF-1 x 10-12 Farad). What is the frequency of this station? (Hint: FM stations broadcast from 87.5 to 107.5 MHz. 1 MHz- 1 megaHertz 1 x 106 Hz.) Show all work. You may do this part "hand written."

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Answer #1


Given

the capacitance of the variable capacitor C = 1.8*10^-12 F
inductance of the inductor is L = 1.4*10^-6 H
we know that when the radio was tuned to a perticular station , so that the resonance frequency occurs only we can get the perticular station

at resonance the reactance of the inductor and capacitor are equal that is


   XL = XC
we know that XL = W*L = 2pi*f*L
and XC = 1/(W*C) = 1/(2pi*f*C)

writing for f , (frequency)


f = 1/(2pi*sqrt(L*C)) Hz


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

f = 100258190.32 Hz

f = 100.2582 MHz <<<<--------ANswer

which is in the range of 87.5 MHz to 107.5 Mhz)


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