Why Is Instantaneous Value Used in Amplitude Modulation?

[rahuld.exe]

In the amplitude modulation equation,
V=(Ec+Ei*coswt)coswt

I don't understand why the instantaneous value of information signal is used. Shouldnt it be peak value as that would give the maximum value (amplitude)?

 

[sophiecentaur]

In the amplitude modulation equation,
V=(Ec+Ei*coswt)coswt

I don't understand why the instantaneous value of information signal is used. Shouldnt it be peak value as that would give the maximum value (amplitude)?

There is an error here. There are two frequencies (ω) involved. ω_c and ω_i, where the suffices correspond to Carrier and Input (?) / Modulating signal (the same as the E suffices).
The equation tells you the value (in volts) of the signal, V at all times. It's what you will see on an oscilloscope. The maximum amplitude, for your equation, would be E_c + E_i and doesn't involve any Cos functions.
"Ei*coswt" is the shape of the envelope (the cosinusoidal modulating signal). If you want undistorted AM, E_i must be no greater than E_c. If it gets bigger then the phase of the carrier undergoes an abrupt change and this will involve a 'splash' which generates a large number of sidebands both in and out of band. (Not to be recommended)