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.]
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.