A radio can be tuned into a particular station frequency by adjusting the capaci

Question

A radio can be tuned into a particular station frequency by adjusting the capacitance in an L-C circuit. Suppose that the minimum capacitance of a variable capacitor in a radio is 4.13 pF. Part A What is the inductance L of a coil connected to this capacitor if the oscillation frequency of the L-C circuit is 1.65 MHz, corresponding to one end of the AM radio broadcast band, when the capacitor is set to its minimum capacitance? Part B The frequency at the other end of the broadcast band is 0.543 MHz. What is the maximum capacitance C_max of the capacitor if the oscillation frequency is adjustable over the range of the broadcast band?

Explanation / Answer

oscillation frequency f = 1/(2*pi*sqrt(LC))

f = 1.65*10^6 Hz

C = 4.13*10^-12 F

L = 1/(4*pi^2*f^2*C)

L = 1/(4*pi^2*(1.65*10^6)^2*4.13*10^-12)

L = 2.25*10^-3 H

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part B

Cmax = 1/(4*pi^2*f^2*L)

Cmax = 1/(4*pi^2*(0.543*10^6)^2*2.25*10^-3)

Cmax = 3.82*10^-11 F

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