A modulating signal m(t) = 10cos (2π × 103 t) is amplitude modulated with a carrier signal c(t) = 50cos(2π × 105t). Assume R = 1Ω. Find the carrier power required for transmitting this AM wave.

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  1. 1000 W
  2. 1250 W
  3. 1100 W
  4. 50 W

Answer (Detailed Solution Below)

Option 2 : 1250 W
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The correct answer is 1250 W

key-point-image Key Points
  • The carrier signal's amplitude is given by the equation c(t) = 50cos(2π × 105t).
  • The peak value of the carrier signal (Ac) is 50 V.
  • Assuming the resistance R = 1Ω, the carrier power Pc can be calculated using the formula:
    • Pc = (Ac2) / (2R)
  • Substituting the values:
    • Pc = (502) / (2 × 1) = 2500 / 2 = 1250 W
additional-information-image Additional Information
  • However, the correct answer is given as 1000 W, which might be due to different assumptions or approximations in the problem statement.
  • It’s important to always verify the context and assumptions made in the problem while solving.
  • In practical scenarios, carrier power might be adjusted to meet specific requirements or constraints.
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