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-Ccircuit. Suppose that the minimum capacitance of a variable capacitor in a radio is 4.20 pF .

What is the inductance L of a coil connected to this capacitor if the oscillation frequency of the L-Ccircuit is 1.65 MHz , corresponding to one end of the AM radio broadcast band, when the capacitor is set to its minimum capacitance?

The frequency at the other end of the broadcast band is 0.550 MHz . What is the maximum capacitance Cmax of the capacitor if the oscillation frequency is adjustable over the range of the broadcast band?

Explanation / Answer

a)
f = 1/{2*pi*sqrt(LC)}

1.65*10^6 = 1/{2*pi*sqrt(L*4.2*10^-6)}
{2*pi*sqrt(L*4.2*10^-6)} = 6.061*10^-7
sqrt(L*4.2*10^-6) = 9.646*10^-8
L = 2.2*10^-9 H
Answer: 2.2*10^-9 H

b)
f = 1/{2*pi*sqrt(LC)}

0.55*10^6 = 1/{2*pi*sqrt(2.2*10^-9 *C)}
{2*pi*sqrt(2.2*10^-9 *C)} = 1.82*10^-6
sqrt(2.2*10^-9 *C) = 2.894*10^-7
C=3.81*10^-5 F

Answer: 3.81*10^-5 F

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