The carrier frequency of a transmitter is provided by a tank circuit of a coil of inductance 49 `muH` and a capacitance of 2.5 nF It is modulated by an audio signal of 12 kHz The frequency range occupied by the side bands is :

Options

A. 18kHz-30kHz
B. 63kHz-75kHz
C. 442kHz-466kHz
D. 13482kHz-13494kHz

Answer

C

Explanation

Given: Inductance , `L= 49 mu H = 49 xx 10^(-6)`H , capacitance `C= 2.5 nF = 2. 5 xx 10^(-9) F `
Using `omega= (1)/( sqrt(LC))`
`=(1)/( sqrt( 49 xx 10^(-6) xx (2.5)/(10) xx 10^(-9)))=(1)/( 7 xx 5 xx 10^(-8)) = (10^(8))/( 7 xx 5)`
`or , (10^(8))/( 7 xx 5) = 2pi xx f= 2 xx (22)/(7) xx f ( :. omega=2 pi f)`
`or f= (10^7)/( 22 ) = (10^4)/( 22) kHz= 454. 54 kHz `
Therefore frequency range ` 454.54 pm 12 kHz `
i.e., 442 kHz- 466 kHz