Question 6A382

When an Amplitude Modulated (AM) signal is 100% modulated by a sinusoidal waveform, the total radiated power increases by 50% compared to the unmodulated carrier power. Since power ($P$) is proportional to the square of the antenna current ($I$), i.e., $P \propto I^2$, we can relate the new current to the original current. If $P_{total} = 1.5 \times P_{carrier}$, then $I_{total}^2 = 1.5 \times I_{carrier}^2$. Therefore, $I_{total} = \sqrt{1.5} \times I_{carrier}$. Given the unmodulated antenna current is 8 amps: $I_{total} = \sqrt{1.5} \times 8 \text{ amps}$ $I_{total} \approx 1.2247 \times 8 \text{ amps} \approx 9.7976 \text{ amps}$. Rounding this value gives approximately 9.8 amps, which corresponds to option A. To find the percentage increase: Percentage increase $= ((\sqrt{1.5} \times I_{carrier} - I_{carrier}) / I_{carrier}) \times 100\%$ Percentage increase $= (\sqrt{1.5} - 1) \times 100\%$ Percentage increase $\approx (1.2247 - 1) \times 100\% \approx 0.2247 \times 100\% \approx 22.47\%$. Rounding this gives approximately 22.5%, which corresponds to option B. Since both option A and option B are correct representations of the same calculation, the answer is C.