The minimum capacitance of a variable capacitor in a radio is 4.20 pF . Part A W

Question

The minimum capacitance of a variable capacitor in a radio is 4.20 pF .

Part A

What is the inductance of a coil connected to this capacitor if the oscillation frequency of the L-C circuit is 1.66 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 0.550 MHz . What is the maximum capacitance of the capacitor if the oscillation frequency is adjustable over the range of the broadcast band?

Explanation / Answer

(A)
Cmin = 4.20 pF
At resonance,
^2 = (2**f)^2 = 1/LC
L = 1/ ( C * (2**f)^2 )
L = 1/ ( 4.2*10^-12 * (2**1.66*10^6)^2 )
L = 2.19 * 10^-3 H

(B)
C =  1/ ( L * (2**f)^2 )
C = 1/ ( 2.19 * 10^-3 * (2**0.55 * 10^6)^2 )
C = 3.82 * 10^-11 F

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