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In amplitude modulation, the total modulation index should not exceed one because
(A). The signal will be distorted
(B). The amplifier will be damaged
(C). The signal will die out quickly
(D). The system will fail

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Answer
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Hint: The amount of amplitude modulation can be measured using modulation index. The modulation index tells us how much the amplitude of the carrier wave is varying compared to the original amplitude of the carrier wave.

Complete step by step answer:
In communication, we use electromagnetic waves which are transverse in nature. They are used to transmit a signal from a sending antenna to a receiving antenna. The message signal cannot be sent directly in its original form from one place to another because that way the signal dies out very quickly and long distance communication is not possible. We have different ways in which we can modulate our message signal and then transmit it safely without excessive distortion from one place to another. These methods are amplitude modulation (AM), frequency modulation (FM) and phase modulation (PM).
Amplitude modulation (AM) is a technique used in communication systems where a carrier wave which carries a particular signal from one place to another is modulated with respect to the amplitude of the message signal. It is the simplest modulation technique.
The amount of modulation done to a particular signal can be mathematically measured using what we call the modulation index. This quantity tells us how much the amplitude of the carrier wave is changing due to the message signal. It can be given as
$m = \dfrac{M}{A}$
where m is used to denote the modulation index, M signifies the amplitude of the modulated wave while A signifies the amplitude of the carrier wave.
If $m > 1$, then it leads to distortion of the signal which is called over modulation and is avoided.
Hence, the correct answer is option A.

Note: If m = 0.5 then it means that the amplitude of the carrier wave is varying 50$\% $ more than the un modulated wave while if m = 1 then it means that amplitude of the carrier wave is varying 100$\% $ more than the un modulated wave. The modulation is kept in this range for efficient transmission.