Discussion
An AM signal has a carrier of \( 500 \ \mathrm{W} \) and total power of \( 650 \ \mathrm{W} \). The modulation index is
Answer: B
Inverting the power relation:
\[ \begin{aligned} 1 + \frac{\mu^{2}}{2} &= \frac{650}{500} = 1.30 \\ \mu &= \sqrt{0.60} = 0.77 \end{aligned} \]
so about 0.77. 0.30 is the excess power ratio taken as the index directly. 0.55 halves the excess before rooting it. 1.30 is the power ratio itself, which would imply over-modulation and shows how easily the ratio and the index are confused. Working backwards from measured powers like this is the standard way a transmitter's modulation is verified.
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