A transistor -oscillator using a resonant circuit with an inductor `L` (of negligible resistance) and a capacitor `C` in series produce oscillations of frequency `f`. If `L` is doubled and `C` is changed to `4C`, the frequency will be

Options

A. `f//4`
B. `8f`
C. `f//2sqrt(2)`
D. `f//2`

Answer

C

Explanation

In series `LC` circuit, frequency of `LC` oscillations is given by
`f=1/(2pisqrt(LC))` or `f prop 1/(sqrt(LC))`
`(f_(1))/(f_(2))=sqrt((L_(2)C_(2))/(L_(1)C_(1)))`
Given, `L_(1)=L, C_(1)=C, L_(2)=2L,C_(2)=4C,f_(1)=f`
`(f_(1))/(f_(2))=sqrt((2Lxx4C)/(LC))=sqrt(8) implies f_(2)=f/(2sqrt(2))`