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Question

A radio can tune overthe frequency range of a portion of MW broadcast band: (800 kHz to1200 kHz). If its LC circuit has an effective inductance of200 μH, what must be therange of its variable capacitor?

[Hint: Fortuning, the natural frequency i.e., the frequency of freeoscillations of the LC circuit should be equal to thefrequency of the radiowave.]

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Solution

The range of frequency(ν) of a radio is 800 kHz to1200 kHz.

Lower tuning frequency,ν1 = 800 kHz =800 × 103 Hz

Upper tuning frequency,ν2 = 1200 kHz =1200× 103 Hz

Effective inductance ofcircuit L = 200 μH =200 × 10−6 H

Capacitance of variablecapacitor for ν1 isgiven as:

C1

Where,

ω1 =Angular frequency for capacitor C1

Capacitance of variablecapacitor for ν2,

C2

Where,

ω2 =Angular frequency for capacitor C2

Hence, the range of thevariable capacitor is from 88.04 pF to 198.1 pF.


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