A radio tunes in to a broadcasting station by matching the resonant frequency of

Question

A radio tunes in to a broadcasting station by matching the resonant frequency of the radio's LC circuit to the station's broadcast frequency. An electronics hobbyist is building a radio set to receive the AM band with frequencies from 520 kHz to 1700 kHz. The antenna, which also serves as the inductor in an LC circuit, has an inductance of 230 mu H. She needs to add a variable capacitor whose capacitance she can adjust to tune the radio. What range of capacitance (minimum and maximum) must the capacitor have?

Explanation / Answer

w = 1/ sqrt(LC)

for f = 520 kHz

2 x pi x 520 x 10^3 = 1 / sqrt(230 x 10^-6 x C)

C = 407.3 x 10^-12 F

when f = 1700 kHz

2 x pi x 1700 x 10^3 = 1 / sqrt( 230 x 10^-6 x C)

C = 38.1 x 10^-12 F

range = 38.1 pF to 407.2 pF ........Ans

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