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 / 2
B. f / 4
C. 8 f
D. `f//2sqrt2`

Answer

D

Explanation

Initial resonant frequency
`f=1/(2pisqrt(LC))`
Final resonant frequency
`f'=1/(2pisqrt(L'C'))`
`therefore (f')/f = sqrt("LC"/"L'C'")="LC"/(2L xx 4C) = 1/8 =1/(2sqrt2)`
`therefore f'=f/(2sqrt2)`