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A radio can tune over the frequency rang...

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 mu H`, what must be the range of its varialbe capacitor ?

Text Solution

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Here, `v_(1) = 800 kHz = 8 xx 10^(5) Hz, v_(2) = 1200 k Hz = 12 xx 10^(5) Hz`
`L = 200 mu H = 200 xx 10^(-6) H = 2 xx 10^(-4) H`
`C_(1) = ? C_(2) = ?`
From `v_(1) = (1)/(2 pi sqrt(LC_(1)))`
`C_(1) = (1)/(4 pi^(2) L v_(1)^(2)) = (1)/(4 xx (22)/(7) xx (22)/(7) xx 2 xx 10^(-4) (8 xx 10^(5))^(2)) = 197.7 xx 10^(-12) F = 197.7 pF`
Similarly, `C_(2) = (1)/(4 pi^(2) L v_(2)^(2)) = (1)/(4 xx (22)/(7) xx (22)/(7) xx 2 xx 10^(-4) (12 xx 10^(5))^(2)) = 87.8 xx 10^(-12) farad = 87.8 pF`
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