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Question -

A radio can tune over thefrequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). Ifits LC circuit has an effective inductance of 200 μH, whatmust be the range of its variable capacitor?



Answer -

The range of frequency (ν) of aradio is 800 kHz to 1200 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

Capacitanceof variable capacitor for νis given as:
C1

Where,

ω1 = Angularfrequency for capacitor C1

Capacitance of variable capacitorfor ν2,

C2 

Where,

ω2 = Angularfrequency for capacitor C2

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

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