Identify the mathematical expression for amplitude modulated wave:

Options

A. `A_(c)sin[{omega_(c)+KV_(m)(t)}t+phi]`
B. `A_(c)sin[{omega_(c)t+phi+KV_(m)(t)}t]`
C. `{A_(c)+KV_(m)(t)}sin(omega_(c)t+phi)`
D. `A_(c)V_(m)(t)sin(omega_(c)t+phi)`

Answer

C

Explanation

modulating signal `m(t)=A_(m)sinomega_(c)t`
carrier signal `c(t)=A_(c)sinomega_(c)t`
modulated signal
`c_(m)(t)=(A_(c)+A_(m)sinomega_(m)t)sinomegat`
`c_(m)(t)=A_(c)[1+(A_(m))/(A_(c))sin omega_(m)t]sinomega_(c)t`
`c_(m)(t)=(A_(c)+muA_(c)sinomega_(c)t)` as `k=muA_(c)`
`c_(m)(t)=(A_(c)+ksinomega_(m)t)sinomega_(m)t`