A carrier wave of peak voltage `12 V` is used to transmit a message signal. The peak voltage of the modulating signal in order to have a modulation index of `75%` is

Options

A. 6V
B. 7V
C. 8V
D. 9V

Explanation

To solve the problem step by step, we need to find the peak voltage of the modulating signal (Am) given the peak voltage of the carrier wave (Ac) and the modulation index (μ).

### Step 1: Identify the given values
- Peak voltage of the carrier wave (Ac) = 12 V
- Modulation index (μ) = 75% = 0.75 (as a decimal)

### Step 2: Recall the formula for modulation index
The modulation index (μ) is defined as the ratio of the peak voltage of the modulating signal (Am) to the peak voltage of the carrier wave (Ac):
\[ \mu = \frac{A_m}{A_c} \]

### Step 3: Rearrange the formula to find Am
From the formula, we can rearrange it to solve for the peak voltage of the modulating signal (Am):
\[ A_m = \mu \times A_c \]

### Step 4: Substitute the known values into the equation
Now, substituting the known values into the equation:
\[ A_m = 0.75 \times 12 \, V \]

### Step 5: Calculate Am
Now, perform the multiplication:
\[ A_m = 9 \, V \]

### Conclusion
Thus, the peak voltage of the modulating signal is **9 V**.

### Final Answer
The peak voltage of the modulating signal is **9 V**.

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