An electronic hobbyist is building a radio set to receive an

An electronic hobbyist is building a radio set to receive an AM band, with frequencies from 520kH_2, to 1700kH_2. The antenna, which also serves as the inductor in an LC circuit, has an inductance of 230mu H. She needs to add a variable capacitor whose capacitance she can adjust to tune the radio between the frequencies above. What is the minimum capacitance the capacitor must have and v/hat is the maximum capacitance the capacitor must have?

Solution

f = 1 / [ 2 pi * (L x C)^1/2 ]

C = 1 / [ (f²) * 4 * (pi²) * L ]

L = 230 muH = 230 * 10^-6 H

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f = 520 kHz = 520 * 10³ Hz

C = 1 / [ (520 * 10³)² * 4 * (pi²) * 230 * 10^-6 ]

C = 4.07 * 10^-10 F

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f = 1700 * 10³ Hz

C = 1 / [ (1700 * 10³)² * 4 * (pi²) * 230 * 10^-6 ]

C = 3.81 * 10^-11 F