I have been given a question as
RMS value of an RF(Radio Frequency) voltage after amplitude modulation to a depth of $50$% by a sinusoidal voltage is $80$ Volts. Calculate the RMS value of modulated voltage when modulated to a depth of $75$%.
Now my question is that, If the modulation index$(m_a=\frac{V_m}{V_c})$ of an AM wave changes, what can be the reason? Will it be due to the change in the carrier voltage or due to the change in modulating voltage? I have proceeded like as $$P_t=P_c\left (1+\frac{m_a^2}{2}\right )$$ and also power is directly proportional to the voltage$(V_{rms})$ squared, therefore we get $$\frac{V_{rms}^2}{2}=\frac{V_c^2}{2}\left (1+\frac{m_a^2}{2}\right )$$ and I got two equations as $$(80)^2=V_c^2\left (1+\frac{(0.5)^2}{2}\right )\:\:\:\:\:\:\:\:\:\:\:\:\:...(1)$$
$$V_{rms}^2=V_c^2\left (1+\frac{(0.75)^2}{2}\right )\:\:\:\:\:\:\:\:\:\:\:\:\:...(2)$$On solving the above two, I got the required voltage $$V_{rms}=85.04\: V$$I have assumed that the change in the modulation index is not due to the change in the carrier voltage and kept the both $V_c$ same in both the equations and got the answer but I am still not sure that whether I am correct or not.
Is it the case that the modulating voltage is constant and the modulating index change is due to the change in carrier voltage? And obviously, then the answer will be different.
I am not sure, please explain it. Thanks beforehand.
