Question

Suppose the amplitude of a modulated wave is equal to the signal amplitude. Then modulation is

• A. $10\%$
• B. $25\%$
• C. $50\%$
• D. $100\%$

Answer 1

The correct option is D

$100\%$

The explanation for the correct option:

In the case of option D,

1. The modulation occurs due to the superposition of two signals.
2. Modulation percentage relates the amplitude of the modulated signal to the amplitude of the carrier signal.
3. According to the problem, the amplitude of the modulated signal is equal to the amplitude of the carrier signal.
4. So, $A_m=A_c$ where $A_m$ is the amplitude of modulated signal, $A_c$ is the amplitude of the carrier signal.
5. Modulation factor will be $\raisebox{1ex}{$A_m$}\!\left/ \!\raisebox{-1ex}{$A_c$}\right.$.
6. Modulation percentage is defined as-

$$\begin{gathered} =\frac{A_m}{A_c}\times 100 \\ =\frac{A_m}{A_m}\times 100 \\ =100\% \end{gathered}$$

Thus, Then modulation percentage is $100\%$.

The explanation for the incorrect options:

In the case of option A,

1. The modulation percent will be $10\%$,
2. Modulation factor, in this case, will be-$10\%=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$10$}\right.$
3. Thus, in this case, the amplitude of the carrier signal will be equal to ten times of amplitude of the modulation signal i.e $A_c=10A_m$.

In the case of option B,

1. The modulation percent will be $25\%$
2. Modulation factor, in this case, will be $25\%=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$
3. Thus, in this case, the amplitude of the carrier signal $A_c$ equals four times of amplitude of the modulation signal $A_m$ i.e $A_c=4A_m$

In the case of option C,

1. The modulation percent will be $50\%$.
2. Modulation factor, in this will be $50\%=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$.
3. Thus, in this case, the amplitude of the carrier signal will be equal to two times the amplitude of the modulation of signal i.e $A_c=2A_m$

Hence, option D is the correct answer.