Hello Aspirant,

This question can be solved in the following way-

Given- Amplitude of carrier wave, Ac= 12 V

Modulating frequency = 1kHz

To find- equation of the modulated wave.

Solution - Amplitude was modulated to 50 %.

So, modulation index, m= 50/100 = 0.5

We know that m= Am / Ac => Am = m× Ac

= (0.5 × 12 )V = 6V

Hence the equation is

Cm ( t) = 12sin ωc t + 0.5×12 sin ωm t × sin ωc t

= 12 sin ωc t + 6 sinωm t × sin ωc t

The m and c will be subscript.

I hope it helps.

Thank you