A radio can tune over the frequency range of a portion of MW broadcasr band: 800kHz to 1200kHz. IF its LC circuit has an effective inductance of 200`muH`, what must be the range of the variable capacitor?
[Hint: for tuning, the natural frequency of the LC circuit should be equal to the frequency of the radio wave.]

Explanation

`f=1/(2pisqrt(LC))`or,`C=1/(4pi^2f^2L)`
when L=`200muH` and f=800 kHz,
`C_1=1/(4pi^2times800times800times10^8times200times10^-6)`
=197.8pF
when f=1200 kHz,
`C_2=1/(4pi^2times1200times1200times10^6times200times10^-6)`
`=87.9pF`
`therefore` The range of the capacitance should be between 87.9 pF ad 197.8 pF, i.e., between 88pF and 198 pF.