In a radio receiver, the short wave and medium wave station are tuned by using the same capacitor but coils of different inductance `L_(s)` and `L_(m)` respectively then

Explanation

The value of inductance is more while tuning a radio receiver at midium wave station than that at short wave station. We know that the short wave station emit radiowaves of short wavelength `(lambda_(s))` and medium wave station emit rediowaves of longer wavelength `(lambda_(m))`, i.e.,
`lambda_(m)gtlambda_(s)`.
Let `v_(s),v_(m)` be the frequencies of short wave and medium wave signals.
Then `v_(s)=c//lambda_(s)` and `v_(m)=c//lambda_(m)`
or `v_(s)/v_(m)=lambda_(m)/lambda_(s)` .....(i)
If `L_(s),L_(m)` be the self inductance of the short wave and the medium wave coils respectively and C be the capacitance of capacitor used, then
`v_(s)=(1)/(2pisqrt(L_(s)C))` and `v_(m)=(1)/(2pisqrt(L_(m)C))`
`:. v_(s)/v_(m)=sqrt(L_(m)/L_(s))` or `v_(s)^(2)/v_(m)^(2)=L_(m)/L_(s)` ...(ii)
From (i) and (ii),
`L_(m)/L_(s)=(lambda_(m^(2)))/(lambda_(s^(2)))gt 1 (As lambda_(m)gtlambda_(s)) :. L_(m) gt L_(s)`