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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 uH, 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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Answer» Solution :We know that natural frequency `v_(0) =1/(2PI sqrt(LC))` `rArr C = 1/(4pi^(2) Lv_(0)^(2))` and here L = 200 `mu` H `=2 xx 10^(-4)` H (i) To tune radio station broadcasting at 1200 kHz (i.e. `v_(0) =1.2 xx 10^(6) Hz)`,. We have `C = 1/(4 xx (3.14)^(2) xx (2 xx 10^(-4)) xx (1.2 xx 10^(6))^(2)) = 8.79 xx 10^(-11)`F or 87.9 pF and (ii) to tune radio station broadcasting at 800 kHz (i.e. `v_(0) = 8 xx 10^(5)` Hz) `C = 1/(4 xx (3.14)^(2) xx (2 xx 10^(-4)) xx (8 xx 10^(5))^(2)) = 1.978 xx 10^(-10)` F or 197.8 pF. Thus, the variable capacitor should have a range of about 88 pF to 198 pF. |
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