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 `200muH` , 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 radio wave.]

Explanation

`v = (1)/(2pi sqrtLC) ` for 800 kHz ` C = (1)/(4pi^2 v^2 L)= (1)/(4pi^2 xx 200 xx 10^(-6) xx (800 xx 10^2)^2) = 197.8 pF`
when `v 1200 kHz , C = (1)/(4pi^2 (200 xx 10^(-6) ) (1200 xx 10^3)^2) = 87.9 pF`
hence range of the capacitor is from 88pF to 198 pF