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.]
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:
ω1 = Angular frequency for capacitor C1
Capacitance of variable capacitor for ν2,
ω2 = Angular frequency for capacitor C2
Hence, the range of the variable capacitor is from 88.04 pF to 198.1 pF.