A radio can be tuned into a particular station frequency by adjusting the capaci
ID: 3897434 • Letter: A
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 4.20pF .
A)What is the inductance
L of a coil connected to this capacitor if the oscillation frequency of the L-C circuit is 1.54MHz , corresponding to one end of the AM radio broadcast band, when the capacitor is set to its minimum capacitance?
B)The frequency at the other end of the broadcast band is 0.539
MHz . What is the maximum capacitance Cmax of the capacitor if the oscillation frequency is adjustable over the range of the broadcast band?
Q2:A 7.0
mH inductor is connected in parallel with a variable capacitor. The capacitor can be varied from 180pF to 320pF .
A)What is the minimum oscillation frequency for this circuit?
Explanation / Answer
1.
Given
C=4.2 pF =4.2*10^-12 F
Resonant frequency
f=1.54 MHz =1.54*10^6 Hz
Resonant frequency
f=1/2pi*sqrt(LC)
=>L=1/4pi^2*f^2*C
L=1/4pi^2*(1.54*10^6)^2*(4.2*10^-12)
L=2.543*10^-3 H or 2.543 mH
b)
Now resonant frequency
f=0.539 MHz =0.539*10^6 Hz
f=1/2pi*sqrt(LC)
=>C=1/4pi^2*f^2*L
C=1/4pi^2*(0.539*10^6)^2*(2.543*10^-3)
C=3.43*10^-11 F or 34.3 pF
2.
a)
minimum oscillation frequency occurs at C=320 pF
f=1/2pi*sqrt[7*10^-3*320*10^-12]
f=106,339.9 Hz or 106.34 Khz
b)
Maximum oscillation frequency at C=180 pF
f=1/2pi*sqrt(LC) =1/2pi*sqrt(7*10^-3*180*10^-12)
f=141,786.5 Hz or 141.786 KHz
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