The amplitude modulated voltage E is given by :
` E = 100 [ 1 + 0.6 sin 3000 t] sin ( 5 xx 10^(5) ) t` .
Calculate :
(i) Modulation index .
(ii) Modulating frequency .
(iii) Carrier frequency .
(iv) Carrier frequency .
(iv) Total power fed to the antenna of `100 Omega ` resistance .

Explanation

Given equation is
`E = 100 [ 1 + 0.6 sin 3000 t] sin ( 5 xx 10^(5)) t…..(1)`
Equation for amplitude modulated wave is `E = E_(c) [1 + m_(a) sin w_(m) t] sin w_(c) t…..(2)`
On comparing (1) and (2) ,
(i) Modulation index ` = m_(a) = 0.6`
(ii) `w_(m) = 3000`
` 2 pi v_(m) = 3000`
` V_(m) = (3000)/(2pi) = 477.71 Hz`
Modulating frequency ` = v_(m) = 477.71 Hz`
(iii) `w_(c) = 5 xx 10^(5)`
` 2pi v_(c) = 500000`
`V_(c) = (500000)/(2pi) `
` = 79617.8 Hz = 7.96 xx 10^(4) Hz`
(iv) Total power fed to the antenna ` = p = (E_(rms)^(2))/(R)`
`E_(rms) = (E)/(sqrt(2)) = (100)/(sqrt(2))`
`P = ((100// sqrt(2))^(2))/(100) = 50 W `