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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This question was previously asked in

NIELIT Scientific Assistant CS 5 Dec 2021 Official Paper

Answer 1

Key Points

The carrier signal's amplitude is given by the equation c(t) = 50cos(2π × 10⁵t).
The peak value of the carrier signal (A_c) is 50 V.
Assuming the resistance R = 1Ω, the carrier power P_c can be calculated using the formula:
- P_c = (A_c²) / (2R)
Substituting the values:
- P_c = (50²) / (2 × 1) = 2500 / 2 = 1250 W

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.