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Question

A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200 μH, what must be the range of its variable capacitor?
[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radiowave.]

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Solution

Lower tuning, f1=800×103 Hz
Upper tuning, f2=1200×103 Hz
L=200×106 H
Capacitance of the variable capacitor for f1 is,
C1=1/(ω21L)
where, ω1=2πf1
so, C1=198.1 pF
similarly, C2=88.04 pF
C[88.04 pF,198.1 pF]

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