Q.RMS value of a RF voltage after amplitude modulation to a depth of 60% by a sinusoidal voltage is 50 V. Calculate the rms value of modulated voltage when modulated to depth of 80%.

Because the modulated rms voltage relates to the carrier rms voltage as $V_T = V_C\sqrt{1 + m_a^2/2}$, the fixed carrier voltage is found from the 60% data and then reused to get the 80% value. …

[!TLDR]

From the 60% data, $V_C = 50/\sqrt{1 + 0.6^2/2} = 46.03$ V; at 80% depth, $V_T = 46.03\sqrt{1 + 0.8^2/2} = 52.88$ V.

The rms value of a modulated RF voltage is larger than the carrier rms voltage because the sidebands add power. Since $P_T/P_C = (V_T/V_C)^2 = 1 + m_a^2/2$, the modulated and carrier rms voltages are related by

The carrier voltage $V_C$ is a fixed property of the transmitter, so it is first extracted from the 60%-modulation data and then used to find the modulated voltage at 80%.

Given $V_T = 50$ V at $m_a = 0.60$: …