1.

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 ?

Answer»

`f/(2SQRT2)`
`f/(3sqrt2)`
`f/(4sqrt2)`
`f/(1sqrt2)`

Solution :`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)`


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