Question 6A378

When an Amplitude Modulated (AM) transmitter is 100% modulated by a sinusoidal waveform, the total power output increases. The total power ($P_T$) is related to the carrier power ($P_C$) by the formula $P_T = P_C (1 + m^2/2)$, where $m$ is the modulation index. At 100% modulation, $m=1$. So, $P_T = P_C (1 + 1^2/2) = P_C (1 + 0.5) = 1.5 P_C$. This means the total power transmitted increases by 50%. Since power is proportional to the square of the current ($P = I^2 R$), the antenna current ($I_A$) will change as the square root of the power change. $I_A \propto \sqrt{P_T}$. Therefore, $I_{A, modulated} / I_{A, unmodulated} = \sqrt{P_T / P_C} = \sqrt{1.5}$. Calculating $\sqrt{1.5} \approx 1.2247$. This means the antenna current increases to approximately 122.47% of its unmodulated value. The percentage increase is $(1.2247 - 1) \times 100\% = 22.47\%$, which rounds to 22.5%. Options B and D are incorrect because modulation adds power to the sidebands, thus increasing the total power and consequently the antenna current. Option C, 12.25% increase, is not the correct calculated value for current increase.