The efficient transmission of signals is achieved by superimposing electrical audio signals on a high frequency carrier wave (the process is known as modulation). When the amplitude of high frequency carrier wave is changed in accordance with the intensity of modulating signal, it is called amplitude modulation. The extent to which the amplitude of carrier wave is changed by the signal is described by modulation factor. It is given as
`m="Amplitude change of carrier wave"/"Amplitude of unmodulated carrier wave"`
Let a carrier wave is represented by
`V_c=V_c cos omega_ct`
Let the modulation factor be m, the maximum change in amplitude of carrier wave is `mV_c`
So, modulating signal can be represented as `v_m=mV_c cosomega_mt`
So, the amplitude of modulated wave is `=V_c+mV_c cosomega_m t`
Using this value, the instantaneous voltage of modulated wave is
`E=V_c cos omega_c t+ (mV_c)/2 cos (omega_c+omega_m)t + (mV_c)/2 cos (omega_c-omega_m ) t`
The above wave contains three frequencies namely, `f_c, f_c+f_m` and `f_c-f_m` . The frequencies `f_c+f_m` and `f_c-f_m` are called side band frequencies , USB and LSB respectively.
If modulation factor is 100% , the amplitude change of carrier wave is

Options

A. Equal to amplitude of modulating signal
B. Equal to amplitude of unmodulated carrier wave
C. Equal to amplitude of modulated wave
D. Equal to zero

Answer

To solve the problem, we need to understand the relationship between the modulation factor and the amplitude change of the carrier wave when the modulation factor is given as 100%. Let's break down the solution step by step.

### Step 1: Understand the modulation factor
The modulation factor (m) is defined as the ratio of the amplitude change of the carrier wave to the amplitude of the unmodulated carrier wave. Mathematically, it can be expressed as:
\[ m = \frac{\text{Amplitude change of carrier wave}}{\text{Amplitude of unmodulated carrier wave}} \]

### Step 2: Set the modulation factor to 100%
Given that the modulation factor is 100%, we can express this in decimal form:
\[ m = 100\% = 1 \]

### Step 3: Express the relationship using the modulation factor
From the definition of the modulation factor, we can rearrange the equation to find the amplitude change of the carrier wave:
\[ \text{Amplitude change of carrier wave} = m \times \text{Amplitude of unmodulated carrier wave} \]

### Step 4: Substitute the value of m
Now, substituting the value of m (which is 1) into the equation:
\[ \text{Amplitude change of carrier wave} = 1 \times \text{Amplitude of unmodulated carrier wave} \]
This simplifies to:
\[ \text{Amplitude change of carrier wave} = \text{Amplitude of unmodulated carrier wave} \]

### Step 5: Conclusion
Thus, if the modulation factor is 100%, the amplitude change of the carrier wave is equal to the amplitude of the unmodulated carrier wave.

### Final Answer
The amplitude change of the carrier wave is equal to the amplitude of the unmodulated carrier wave.

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