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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

## The range of frequency (ν) of a radio 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 of circuit L = 200 μH = 200 × 10−6 H Capacitance of variable capacitor for ν1 is given as: C1 Where, ω1 = Angular frequency for capacitor C1 Capacitance of variable capacitor for ν2, C2 Where, ω2 = Angular frequency for capacitor C2 Hence, the range of the variable capacitor is from 88.04 pF to 198.1 pF.

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