A transistor oscillator using a resonant circuit with an inductor L (of negligible resistance and a capacitor C in series produce oscillation of frequency f. If L is doubled and C is changed to 4C, then what will be the resonance frequency ?

Options

A. `f/(2sqrt2)`
B. `f/(3sqrt2)`
C. `f/(4sqrt2)`
D. `f/(1sqrt2)`

Answer

A

Explanation

`omega=1/sqrt(LC)`
`therefore 2pif=1/sqrt(LC)`
`therefore f=1/(2pisqrt(LC))`…(1)
If we double the value of L and value of C is 4 C then,
`f_0=1/(2pisqrt(2Lxx4C))`
`=1/(2pixx2sqrt2xxsqrt(LC))`
`f_0=1/(2sqrt2xx2pisqrt(LC))`..(2)
`therefore (f_0)/f = 1/(2sqrt2)`
`therefore f_0=f/(2sqrt2)`