The maximum amplitude of an AM wave is found to be 15 V while its minimum amplitude is found to be 3 V.What is the modulation index?

Explanation

Let `A_(c )` and `A_(m)` be the amplitudes of carrier wave and modulating wave respectively. So,
Maximum amplitude `rarr A_("max")=A_(c ) + A_(m) = 15 V" ....(i)"`
Maximum amplitude `rarr A_("min")=A_(c ) - A_(m) = 3 V" ....(ii)"`
Adding Eqs. (i) and (ii), we get `2 A_(c ) = 18`
or `A_(c ) = 9 V`
and `A_(m) = 15 - 9 = 6 V`
Modulating index of wave `mu = (A_(m))/(A_(c ))=(6)/(9) = (2)/(3)`