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The total power contained in an AM signal is 1000W. Determine the power transmitted on the carrier frequency and on each of the side panels when the percentage modulation is 100%.

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Answer to a math question The total power contained in an AM signal is 1000W. Determine the power transmitted on the carrier frequency and on each of the side panels when the percentage modulation is 100%.

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Sigrid
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120 Answers
Given that the total power contained in the AM signal is 1000W and the percentage modulation is 100%.
Let P_c be the power transmitted on the carrier frequency and P_s be the power transmitted on each of the sidebands.

The total power in an AM signal can be expressed as:
P_{\text{total}} = P_c + P_s + P_s

Since the percentage modulation is 100%, the maximum amplitude of the modulated signal is twice the carrier amplitude. Therefore, the power transmitted on each sideband is half the total power in the modulated signal.
Thus, the total power can be expressed as:
1000 = P_c + \frac{1}{2}P_{\text{total}} + \frac{1}{2}P_{\text{total}}
1000 = P_c + 2\left(\frac{1}{2}P_{\text{total}}\right)

Solving for P_c:
1000 = P_c + P_{\text{total}}
P_c = 1000 - 500 = 500W

Solving for P_s:
P_s = \frac{1}{2}P_{\text{total}} = \frac{1}{2}(1000) = 500W

Therefore, the power transmitted on the carrier frequency is 500W and the power transmitted on each of the sidebands is 500W.

\boxed{P_c = 500W, \, P_s = 500W}

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